Computational Methods in Engineering & Science: Proceedings of Enhancement and Promotion of Computational Methods in Engineering and Science X -- Aug. 21-23, 2006 Sanya, China

Z. H. Yao M. W. Yuan

Computational Methods in Engineering & Science Proceedings of "Enhancement and Promotion of Computational Methods in Engineering and Science X" Aug. 21-23,2006, Sanya, China

With 241 figures

fglTSINGHUA \Sg? UNIVERSITY PRESS

£} Springer

EDITORS: Prof. Z. H. Yao Dept. of Engineering Mechanics Tsinghua University 100084, China E-mail: [email protected]

ISBN 10 ISBN 13 ISBN 10 ISBN 13

Prof. M. W. Yuan Academician, Chinese Academy of Sciences Dept. of Mechanics and Engineering Sciences Peking University 100080, China E-mail: [email protected]

7-302-13530-4 Tsinghua University Press, Beijing 978-7-302-13530-2 Tsinghua University Press, Beijing 3-540-48259-8 Springer Berlin Heidelberg New York 978-3-540-48259-8 Springer Berlin Heidelberg New York

Library of Congress Control Number: 2006937887 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable to prosecution under the German Copyright Law. © 2007 Tsinghua University Press, Beijing and Springer-Verlag GmbH Berlin Heidelberg Co-published by Tsinghua University Press, Beijing and Springer-Verlag GmbH Berlin Heidelberg Springer is a part of Springer Science+Business Media springer.com The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: Frido Steinen-Broo, EStudio Calamar, Spain Printed on acid-free paper

PREFACE The 9th EPMESC was successfully held in Macao in November of 2003. At the end of the conference the Board of the EPMESC series decided that the next conference would be held in a city of the mainland of China. Also I was assigned to be the Chair person of the Conference. No doubt this is a great honor to me and also a challenge because there are so many professional international conferences in computational mechanics happening frequently in the world. After the successful organizing of WCCM6 in Beijing, September of 2004,1 engaged to organize the 10th EPMESC. First of all, I had to choose the venue of the Conference. After some investigation and a lot of negotiation we went to see the site of the venue in Sanya, Hainan Island, the south-most city in China. Finally we made the decision. The most important reason for the choice was the ecological environment of this city. It is beneficial to our health after hard work. We scientists and engineers need a good relaxing place after working hard- a place to enjoy life with friends and family. Sanya is an ideal place and a real green city. Blue sky and white clouds, the peaceful sea and the long beach with white sand, shells and pearls, no pollution and no industry. Everything is so beautiful. After the first call for papers, the response was unexpectedly strong. We got more than 190 abstracts from 23 countries and regions. About half of the participants come from the mainland of China. The rest were from Macao of China, Japan, Portugal, Australia, USA, Germany, Russia, Poland, Singapore, Malaysia, Brazil, UK, Israel, Indonesia, France, Spain, India, Korea, Czech, Chile, Hong Kong, and Taiwan of China etc. We are glad to have so many friends from so many countries and regions getting together to exchange their research results and take part in social activities. We have the honor of inviting many famous experts in computational mechanics to give plenary and semi-plenary lectures in the conference. Serge Cescotto, Genki Yagawa, Zhenhan Yao are the plenary speakers. Win Kam Liu, Fred W. Williams, Roman Lackner, Ioannis Doltsinis, Helder Rodrigues, Nasser Khalili, Nori Miyazaki, Yao Zheng, Yeong-Bin Yang, Ka Veng Yuen, Gui Rong Liu, Chung-Bang Yun and Dajian Han are the semi-plenary speakers. All of them have achieved great success in their own fields of computational mechanics. I appreciate their outstanding contributions to the conference. This is the mark of the scientific level of this conference. One of the highlights, the student paper competition, is a traditional program that has been retained throughout the history of the EPMESC series. This will keep the young students following the latest advances in research in computational mechanics. Also it will encourage them to reach the peaks of science and technology. I'd like to thank my friend, Prof. Kai Meng Mok of the University of Macau, for his assistance in organizing the student paper competition. I'd like to thank my friend, Prof. Zhenhan Yao of Tsinghua University, for his outstanding work on the proceedings. He patiently worked long and hard on the abstracts and full length papers. He carefully read all the papers and abstracts and corrected a lot of mistakes. He made this proceedings a consistent, valuable reference and beautiful looking. I'd also like to thank my colleagues, Dr. Yongqian Chen and Yang Kuei, for their assistance in my work. I'd like to show my appreciation to the China National Science Foundation for their generous support. 21-25 August 2006. Mingwu Yuan Chairman, EPMESC X Professor, Peking University

CONFERENCE BOARD J. Bento

(Instituto Superior Tecnico, Portugal)

S. Cescotto

(University of Liege, Belgium)

Y. K. Cheung

(University of Hong Kong, Hong Kong, China)

C. K. Choi

(Korea Advanced Institute of Sc. & Tech., Korea)

I. Doltsinis

(Stuttgart University, Germany)

D. J. Han

(South China University of Technology, China)

V. P. Iu

(University of Macau, Macao, China)

T. Kawai

(Nippon Marc Co., Japan)

S. P. Lin

(Shanghai Jiao Tong University, China)

W. K. Liu

(Northwestern University, USA)

H. Mang

(Vienna University of Technology, Austria)

E. Arantes e Oliveira

(Instituto Superior Tecnico, Portugal)

B. A. Schrefler

(University of Padova, Italy)

A. I. Tolstykh

(Russian Academy of Sciences, Russia)

S. Valliapan

(University of New South Wales, Australia)

F. W. Williams

(University of Wales, Cardiff University, UK)

G. Yagawa

(University of Tokyo, Japan)

Y. B. Yang

(Taiwan University, Taiwan, China)

M. W. Yuan

(Peking University, China)

W. X. Zhong

(Dalian University of Technology, China)

ORGANIZING COMMITTEE Mingwu Yuan

Chairman

(China)

Dajian Han

Vice-Chairman

(China)

Zhenhan Yao

Secretary -General

(China)

Members: S. Cescotto C. K. Choi I. Doltsinis L. N. Lamas S. Sloan G. R. Liu S. P. Lin W. K. Liu H. Mang E. Pereira B. A. Schrefler A. I. Tolstykh S. Valliappan F. W. Williams G. Yagawa Y. B. Yang

(Universityof Liege, Belgium) (Korea Advanced Institute of Sc. & Tech., Korea) (Stuttgart University, Germany) (National Laboratory of Civil Engineering, Portugal) (University of Newcastle, Australia) (National University of Singapore, Singapore) (Shanghai Jiao Tong University, China) (Northwestern University, USA) (Vienna University of Technology, Austria) (Instituto Superior Tecnico, Portugal) (University of Padova, Italy) (Russian Academy of Sciences, Russia) (University of New South Wales, Australia) (University of Wales, Cardiff University, UK) (University of Tokyo, Japan) (Taiwan University, Taiwan, China)

LOCAL ORGANIZING COMMITTEE Mingwu Yuan

Chairman

(Peking University, Beijing, China)

Zhenhan Yao

Secretary -General

(Tsinghua University, Beijing, China)

Members: Dajian Han,

(South China University of Technology, Guangzhou, China)

Shaopei Lin

(Shanghai Jiaotong University, Shanghai, China)

Kai Meng Mok

(University of Macau, Macao, China)

Yao Zheng

(Zhejian University, Hangzhou, China)

Jiashou Zhuo

(Hohai University, Nanjing, China)

CONFERENCE SECRETARIAT Yongqiang Chen

Scientific Secretary

(Peking University, Beijing, China)

Kai Meng Mok

Scientific Secretary

(University of Macau, Macao, China)

Yazheng Yang

Administration Secretary

(Chinese Society of Theoretical and Applied Mechanics, Beijing, China)

Yanan Tang

Administration Secretary

(Chinese Society of Theoretical and Applied Mechanics, Beijing, China)

Yang Kuei

Administration Secretary

(Peking University, Beijing, China)

CONTENTS Preface

i

Conference Board and Committees

ii * denotes the presenter

in alphabet order of the regular session and first-author's name Plenary Lectures 1

Management of water pollutants based on multi-criteria analysis and fuzzy logics,

1

Cescotto S*, Roubens M, Rigo N, Gao SX et al 2

Enriched element method and its applications to solid mechanics,

15

Yagawa G*, Matsubara H 3

Large-scale boundary element analysis in solid mechanics using fast multipole method,

19

Yao ZH*, Wang PB, Lei T, Wang HT Semi-plenary Lectures 4

Optimization and robustness of deformable systems with randomness,

35

Doltsinis /*, Kang Z 5

Simulation of Stochastic Fluctuating Wind Field Using the Wave Superposition Method with Random Frequencies, Han DJ*, Luo J J

51

6

Monotonic and Cyclic Analysis of Granular Soils,

59 Khalili N*

7

Adaptive meshfree methods using local nodes and radial basis functions,

8

Multiresolution mechanics for material design and manufacturing,

71

Liu GR*, Kee BBT, Zhong ZH, Li GY, Han X 87 Liu WK* 9

Application of computational mechanics to reliability studies of electronic packaging,

88

Miyazaki N*, Ikeda T 10

Topology optimization of structures: applications in the simulation and design of cellular materials, Rodrigues HC*

101

11

Rigid body considerations for geometric nonlinear analysis of structures based on the updated Lagrangian formulation, Yang YB*, Lin SP, Chen CS

113

12

Nano-modeling structure and micromechanical properties of mesoscopic composite systems, Yanovsky YuG*

129

13

An extremely efficient finite-element model updating methodology with applications to damage detection, Yuen KV*

139

14

Dynamic infinite elements for soil-structure interaction analysis in a layered soil medium,

153

Yun CB*, Kim JM List of other semi-plenary lectures

168

ABSTRACTS OF REGULAR SESSIONS Computational Fluid Mechanics 15

Numerical simulation of cavitation generation in tandem cascades,

169

Kang C* Liu D, Yang MG 16

Numerical simulation of atrium fire using two CFD tools,

170

Sin VK, Tarn LM, Lao SK, Choi HF* 17

Investigation of the particulate matters with the aid of CFD, .

18

CFD analysis of fire in a forced ventilated enclosure,

171

Tarn LM, Sin VK, Sun HI*, Wong KI 172

Tarn LM, Sin VK, Lao SK*, Choi HF 19

Development of the diffusion control system using air shutter,

173

20

Asami T*, Nakabayashi Y A high order compact difference scheme for solving the unsteady convection-diffusion equation, Xie ZH* Lin JG, Zhou JT

174

21

Computation of one-dimensional dam-break flow using ENO scheme,

175

Liu YL*, Guo YT, Fan WB 22

Numerical simulation of 2D dam-break flood waves using TVD scheme,

176

Wei WL*, He WY 23

Motion analysis of the elevating ball by the effect of buoyant force,

177

Matsuo Y*, Nakabayashi Y 24

Development of an educational flow simulation system,

178

Nakanishi T*, Shibata H, Sato M 25

Using finite element program generator to solve N-S equation,

179

26

Wan S*, Nielsen MP, Chai G. Experimental and CFD study of the effects of design parameters on Reynolds number in a short duration hypersonic test facility, Al-Ralahi A * YusafT, YusoffMZ

180

27 28 29 30

Investigation of multiphase flows near walls with textures by the lattice Boltzmann method* Chew YT*, Huang JJ, Shu C, Zheng HW Numerical Simulation of the microstructure of magnetorheological fluids in magnetic fields > PengXH*,LiHT Implementation of a 3D multilaminated hydromechanical model for analysis of an unlined high pressure tunnel, Leitao NS, Lamas LN*

181

Prediction of mixing and reacting flow inside a combustor,

184

182 183

De Bortoli AL* 31 32 33

Large Eddy Simulation of Turbulent Reactive Flow, Liu Y*, Chen YQ, Chen JG, Yang R Computational modeling of coal water slurry combustion processes in industrial heating boiler > Zhu U, Gu BQ* Large eddy simulation of unsteady turbulent flow and pressure fluctuation in an axial-flow pump with various SGS models, Cong GH*, Wang FJ, Zhang L

185 186 187

34

Computation of turbulent flows in natural gas pipes with different rectifiers,

188

Li ZL*, Zhang YX 35

Computation of unsteady incompressible turbulent flow by using an implicit SMAC method, Zhang YX*, Li ZL, Zhu BS

189

36

Simulation on vortex effect for superconducting devices,

190 Lei SL, Lao M*, Chan IN

Computational Solid Mechanics 37

Simulation of corrosion rate of carbon steel subjected to elastic/plastic strain,

191

Ridha M*, Aoki S 38

Effect of surface traction on the shakedown limit under moving surface loads,

39

Elasto-plastic finite element analysis of tapered steel silo,

192 Shiau J* 193

Xu CL*, Luo YF, Song HJ 40

Numerical simulation of failure process in heterogeneous elastoplastic materials,

194

Li YZ, Chen YQ* 41

Fatigue damage analysis of reactor vessel model under repeated thermal loading,

195

42

Takagaki M*, Toi Y, Asayama T Interaction of moving interfacial cracks between bonded dissimilar elastic strips under antiplane shear, Qas £*

196

43

Stress intensity factor of a wide range of semi-elliptical partly through-wall crack in a finite-thickness plate, KOU £/>*

197

44

Numerical simulation of the fracture spacing in two-layered material subjected to thermal and mechanical loading, Li LC*f Tang CA, Liang ZZ

198

45

VCCM rule-based meshing algorithm for an automatic 3D analysis of crack propagation of mixed mode, Murotani K*, Yasuyoki K, Fujisawa T, Yagawa G

199

46

The state-of-the-art methodology to compute 3-D stress intensity factors for arbitrary shaped cracks in complex shaped structures,

200

Okada H*, Yagawa G, Kawai H, Shijo K et al 47

3D crack propagation analysis using free mesh method,

201

Osaki H*, Matsubara H, Yagawa G 48

Finite element method for analyzing stress intensity factor of a surface crack in tubular joints, Shao YB*, Du ZF, Hu WD

202

49

The solutions of stress and displacement fields of orthogonal anisotropic plate with edge-crack, Tian ZR*, Sun Z, Li ZY

203

Computational Structural Mechanics 50 51

Nonlinear FE model for RC shear walls based on multi-layer shell element and micro-plane constitutive model, Miao ZW, Lu XZ*, Jiang JJ, Ye LP Numerical modelling and simulation of an internal combustion engine piston with a surface coating, Niezgoda T, Kurowski Z, Malachowski J*

204 205

52

Reliability analysis using saddlepoint approximation,

206 Wang J*, Yuen KV, Au SK

53

Advanced computational method for reliability analysis of concrete-faced rockfill dam,

207

Wu QX*, Zhao KZ, Yang MZ 54

Structural dynamic reliability of solid rocket motor grains,

208 Zhang SJ*, Ren JG

55

Wave propagation in orthotropic elastic shells: theoretical and numerical modeling,

209

Tie B*, Aubry D 56

Study on the criterion of in-plane instability of non-reinforced U-shaped bellows,

210

Chen Y* Gu BQ 57

Coupled thermal-dynamic stability analysis of large-scale space structures by FEM,

211

Li W*, Xiang ZH, Xue MD 58

Numerical modelling of the lateral-torsional buckling of stainless steel I-beams: comparison with Eurocode 3,

212

Lopes N*, Vila Real PMM, Simoes da Silva L, Mirambell E 59

Research on simulation analysis for stability problem of pressure-penstock with imperfection, Meng WY*, Li XQ, Zhuo JS

213

60

Nonlinear finite element buckling analysis of square reinforced concrete long columns confined with carbon fiber reinforced plastic sheets under axial compression,

214

61

Ren QX*, Chen TG, Huang CK, Liu YH A kind of channel-section beam element for transient coupled thermal-structural dynamic analysis, Duan J*, Xue MD, Xiang ZH

215

62

Semi-analytical analysis of super tall building bundled-tube structures,

216 Gong YQ*, Li K

63

Computational design of beam sections under impact loading,

217

Hou SJ*, Li Q, Long SY, Yang XJ 64

Pretension control of the long-span roof structure of South Shanghai Railway Station,

218

Huang Y*, Luo YF, Yu R 65

Damage detection and sensor placement design for two highway bridges,

219

Li YQ, Xiang ZH*, Zhou MS, Swoboda G, Cen ZZ 66

A new iterative method for solution of rectangular elastic structure,

220 Lin FY*

67

Overall stability of the long span steel roof structure of Hangzhou International Conference Center, Luo YF*, Liu X, Wang ZB

221

68

Regionwise modeling approach for the analysis of layered structures,

222

69

Mohite PM, Upadhyay CS* Computational and experimental study of energy absorption metter by composite structures, Niezgoda T*, Barnat W

223

70

The dynamic analysis of main building of Hangzhou International Conference Center,

224

Song HJ*, Luo YF, Xu CL, Yang MW

71

Second-order analysis for steel frame structures with a distributed plasticity numerical model, Wang K*t Tong L w, Li T

225

72

Pretension simulation of the long span truss string supported by the temporary structures,

226

Yu R* Luo YF, Huang Y 73

Accurate form-finding method for cable-dome structures based on catenary element,

227

Zhao XZ*, Tang RW, Shen ZY 74

Higher order modes in thin-walled beam analysis,

228

75

Vieira R*, Virtuoso F, Pereira E Research on rigidity limits of bridge with conventional spans for Chinese high-speed railway, Gao MM*, Pan JY, Yang YQ

229

76

Numerical implementation and calibration of a hysteretic model for cyclic response of end-plate beam-to-column steel joints under arbitrary cyclic loading,

230

Nogueiro P*, Simoes da Silva L, Bento R Finite Element Analysis 77

Finite element analysis of singular inplane stress field around an inclusion's corner tip,

231

Chen MC*, Ping XC 78

Finite element analysis for the metallic gasket effective width,

232

79

Feng X*, Gu BQ, Liu R Finite element analysis of electrochemical-poroelastic behaviors of conducting polymer (PPy) films, Jung WS* Toi Y

233

80

Finite element analyses of multi-material wedges and junctions with singular antiplane stress field, Ping XC*, Chen MC, Xie JL

234

81

Plane strain finite element analysis of a piled bridge abutment on soft ground,

235

Wang HT*, Chen ZP, Xiao U 82

Finite element analysis of a coal liquefaction reactor during lifting,

83

Finite element analysis of welded cruciform joint,

236

Wang ZB* Luo YF, Liu X 237 Wu AH*, Syngellakis S, Mellor BG 84

Static and dynamic testing of the SATUOeiras viaducts,

238

Xu M*, Santos LO, Rodrigues J 85

Finite element approach to resin flow during the resin film infusion process,

86

Numerical simulation of a new complex FRP pipe culvert by FEA,

239

Yang M, Yan SL* 240 Yang MW* Heat Transfer and Temperature Related Problems 87 88

Numerical study of two-dimensional transient heat conduction using finite element method, Choi LY* Keong WS, Woon OH, Kiong SC Chemical reaction, heat and mass transfer on nonlinear MHD boundary layer flow through a vertical porous surface with thermal stratification in the presence of suction, Kandasamy R*, Periasamy K, Sivagnana Prabhu KK

241 242

89 90 91 92

Development of a mathematical model for heat and mass transfer inside a granular medium, Petty VJ*, De Bortoli AL, Khatchatourian O Factor Analysis for convective heat transfer problem by using the ANN method, Tarn HK*, Tarn SC, Ghajar AJ, Tarn LM Thermally induced mechanical changes around a potential nuclear waste repository in china > Liu YM*, Wang J, Cai MF, Wang SR Research on thermo quality transmission problems for large-scale slab with creep,

243 244 245 246

93

Wang JX*, Wang XC Current developments on the coupled thermomechanical computational modeling of metal casting processes, Agelet de Saracibar C* Chiumenti M, Cervera M

247

94

Application of the mushy cell tracking method for Gallium melting,

248

Liang SJ*, Jan YJ, Chung MS High Performance FEM and SBFEM 95 96

New FDM for plane elasticity in polar coordinate, Zhu BQ*, Zhuo JS, Zhou JF Computational strategies for curved-side elements formulated by quadrilateral area coordinates (QAC), Cen S* Song DP, Chen XM, Long YQ

249 250

97

Studies of 4-node membrane element with analytical stiffness-matrix based on the quadrilateral area coordinates (QAC), Du Y*, Cen S Special hybrid multilayer finite elements for 3-D stress analyses around quasi-elliptic hole in laminated composites, Tian ZS*, Yang QP, Zhang XQ

251

98 99

A 3-dimensional assumed stress hybrid element with drilling degrees of freedom,

252 253

Wang AP*, Tian ZS, Zhang XQ 100 Suppression of zero-energy modes in hybrid finite elements via assumed stress fields,

254

Zhang CH*, Wang DD, Zhang JL 101 Analysis of concentrated boundary loads in the scaled boundary finite element method,

255

Vu TH*, Deeks AJ 102 A frequency-domain approach for transient dynamic analysis using scaled boundary finite element method (I): approach and validation, Yang ZJ*, Deeks AJ, Hong H

256

103 A frequency-domain approach for transient dynamic analysis using scaled boundary finite element method (II): application to fracture problems, Yang ZJ, Deeks AJ*, Hong H

257

Inverse Problems 104 A novel fuzzyexpert diagnosis system of inner-faults for three-phase squirrel cage induction motors, Cheang TS*, Chan SL, Sekar BD, Dong MC

258

105 Updating noise parameters of Kalman filter using Bayesian approach,

259

Hoi KI*, Yuen KV, Mok KM 106 Damage detection of vibrating structure from limited natural frequencies,

260

Li XL*, Okuda H, Yagawa G Meshless Methods 107 Error estimations in LBIEM and other meshless methods, Chen HB*, Fu DJ, Guo XF, Zhang PQ

261

108 Parallel computing for enriched free mesh method (EFMM),

262 Kobayashi Y*, Yagawa G

109 3D animation for free mesh method,

263

Nagaoka S*, Inaba M, Yagawa G 110 A stabilized conforming integration procedure for Galerkin meshfree analysis of thin beam and plate, Wang DD *

264

111 Element-free Galerkin method with wavelet basis,

265 Liu YH*, Liu YN, Cen ZZ

Micromechanics and Intelligent Materials 112 The numerical prediction of effective properties of non-continuous carbon nano-reinforced composites by the macro-microscopic homogenization method,

266

Luo DM*, Wang WX, Takao Y, Kamimoto K 113 Molecular dynamics simulation of length size effect on mechanical properties of nano-metal, Huang D * Zhuo JS

267

114 Molecular dynamic simulations of CNT-water nanostructures,

268

Zou J*, Feng XQ, Ji B, Gao H 115 Computer simulation of quantum dot surface under stress,

269 Liu XM, Zhuang Z*, Zhang T

116 3D BEM for piezoelectric solids of general anisotropy,

270

Denda M*, Wang CY 117 Analysis of quantum dots induced strain and electric-field in piezoelectric semiconductor substrate of general anisotropy, Wang CY*, Denda M, Pan E

271

Numerical Algorithms 118 Adaptive under-frequency load shedding scheme by genetic algorithm,

272

Lou CW*, Dong MC, Wong CK 119 An effective computer generation method for the domain with random distribution of large numbers of heterogeneous grains, Yu Y* CuiJZ Han F

273

120 Three-dimensional mesh generation using the crossed circle method,

274

Suzuki H*, Ezawa Y 121 Study on displacement prediction of landslide based on grey system and evolutionary neural network, Qao jy*

275

122 Prediction of ambient PM10 concentration with artificial neural network,

276

Lam LH*, Mok KM 123 A note on the complexity of the PCG algorithm for solving Toeplitz systems with a Fisher-Hartwig singularity, Vong SW*, Wang W, Jin XQ

277

124 One-point integration that handles shear-locking in cubic splines,

278 Wang SM*, Zhang YS

125 An improved ICCG method of large-scale sparse linear equation group, Zhang YJ*, Sun Q

279

126 A parallel computing method of object-oriented FEM based on substructure,

280

Zhao HM*, Zhang K, Dong ZZ 127 Promotion of frontier science research by aid of automatic program generation technology, Wu BX*, Qian HS, Wan S

281

128 Uniformed NURBS surface deformation subject to boundary conditions,

282

Lo KM*, Yang ZX 129 The pseudo-spectral method and Matlab implement,

283 Wang SL, Wu ZR*, Cheng YL

Rock, Soil and Concrete 130 Composite construction in reinforced concrete taking into consideration the non-rigid bond of interfaces in joints, Lindig V* 131 Optimization of observation condition on inverse analysis for identifying corrosion of steel in concrete, Suga K*, Ridha M, Aoki S 132 A study on temperature distribution in a cross section of concrete box girder bridges,

284 285 286

Tan YP*, Han DJ L33 Stress-based effective space anisotropic damage model for concrete,

287

Wu JY* Li J [ 34 Identification of electric conductivity and impedance of reinforced concrete by boundary element inverse analysis, Yoshida M*, Suga K, Ridha M, Aoki S, Amaya K

288

L35 Stresses and cracking caused by hydration heat in massive concrete structures,

289

Zhang ZM*, Song ZT, Zhang Y [ 36 Numerical modeling of consolidation of marine clay under vacuum preloading incorporating prefabricated vertical drains, / / 0 ^M Lok TMH*

290

[37 Drag forces applied on rock matrix by fluid flow through fracture network in rock mass,

291

Chai JR* [38 A 2-D natural element model for jointed rock masses,

292

Yu TT*, Ren QW [39 Numerical implementation of a bounding surface bubble model for structured soils, 293 MaranhaJR*, VieiraA [40 Numerical simulation of nonlinear interaction of soil, superstructure and thick raft with 294 irregular plan, Du YF* Di SK, Li H, Song Y, Dang XH [41 Soil additionally affected by non force loading and its influence on upper structure,

295

Kuklik P*, Broucek M [42 Advances in unsaturated soil mechanics,

296 Mi ZK*, Shen ZJ

[43 Numerical simulations of the behavior of foundations on reinforced soil,

297

Tou CM, Lok TMH* 144 Stress-strain modeling of tire chip-sand mixture,

298 Yu HJ* Lok TMH

Structural Optimization 145 Multi-objective optimization for shape design of arch dams,

299

Sun LS*, Zhang WH, Xie NG 146 Optimal shape control of multilayered piezoelectric smart plate structure,

300

Wang JG*, Ding GF, Qin Y 147 Engineering structural optimization with an improved ant colony algorithm,

301

Gong YB*, Li QY 148 Optimization studies for crashworthiness design using response surface method,

302

Liao XT*, Li Q, Zhang WG 149 Path optimization of large-scale automated three-dimensional garage based on ant colony algorithm, jj*f Yang ZQ, Peng ZR Meng

303

150 A continuous approach to discrete structural optimization,

304

Tan T* Li XS 151 Parametrical analysis and optimization of partial double-layer reticulated shells using uniform design method and second order rotation method, Xiao JC*, Liang T, Liu Y

305

152 Optimum design of spiral grooved mechanical seal based on thermo-hydrodynamics,

306

Zhou JF*, Gu BQ 153 Evolutionary topological design of frame for impact loads,

307

Chen XY*, Li Q, Long SY, Yang XI 154 Topology optimization of space vehicle structures considering attitude control effort,

308

Kang Z*, Zhang C 155 Application and research of structure topology optimization of scraper conveyer with MSC.Nastran.optishape, Sang JB*, Liu B, Xing SF, Yang LC, Qie YH

309

156 Structural topology optimization using level set method,

310

Wang MY* 157 Topological optimization analysis of 3-D continuum structure with stress and displacement constraints, ye HL*, Sui YK

311

Topics of Computer Software Technology 15 8 Cross-level sentence alignment,

312

Ho A*, Oliveira F, Wong F 159 CSAT: a Chinese segmentation and tagging module based on the interpolated probabilistic model > Leong KS*, Wong F, Tang CW, Dong MC 160 Overcoming data sparseness problem in statistical corpus based sense disambiguation,

313 314

Oliveira F * Wong F, Ho AN, Li YP, Dong MC 161 Application of translation corresponding tree (TCT) annotation schema for Chinese to Portuguese machine translations, Tang CW*, Wong F, Leong KS, Dong MC, Li YP

315

162 Development of a knowledge based system for the Portuguese code for building acoustics,

316

Graga JM*, Patricio J, Lopes LS 163 Interfacing vision system with robot for pick and place operation,

317 Lalitha R*

164 A web-based data management and decision support system for slope safety inspection and evaluation, Wang j * Hung

318 MC

Vibration, Impact and Control 165 Simplified doubly asymptotic approximation boundary for foundations dynamic analysis,

319

Lei WJ, Wei DM* 166 Limit state analysis of seismically excited 3d r/c beam bearing structures,

320 Kaufinann N*

167 Earthquake response analysis and energy calculation based on wavelet transform,

321

Wu C* Zhou RZ 168 Elastoplastic impact of the sphere upon the Uflyand-Mindlin plate,

322

Lokteva IA*, Loktev AA 169 Numerical analysis of impact between cue and ball in billiard (effect of tip structure),

323

Shimamura S*, Aoki S 170 A new multi-harmonic method for predicting the forced response of mistuned bladed disks with dry friction damping, He EM> Wang HJ*

324

171 Coupled vibration analysis of multiple launch rocket system by finite element method,

325

Li BS, Xu XQ* 172 Three-dimensional vibration analysis of functionally graded material rectangular plates by Chebyshev polynomials, Li g* Iu VP> Kou KP

326

173 A hybrid elasticity method for bending and free vibration of composite laminates,

327

Lu CF, Chen WQ* 174 Vibration assessment of railway viaducts under real traffic using bridge-track models,

328

Rigueiro C, Rebelo C* Simoes da Silva L 175 In-plane vibration of rectangular plates with rectangular cutouts,

329

Shufrin I, Eisenberger M* 176 Optimal control of temperature gradient in a large size crystal growth by response surface methodology,

magnetic Czochralski silicon

330

Yu HP*, Sui YK, Wang J, Dai XL, An GP 177 Active vibration control analysis of piezoelectric intelligent beam,

331

Wang T, Qin R*, Li GR 178 Interval dynamic analysis using interval factor method,

332 Gao W*

179 Sensibility analysis of violin plates,

333 Razeto M*, Staforelli C, Barrientos G

180 Effect of pier and abutment non-uniform settlement on train running behavior,

334

Xiong JZ*, Yu HB, Gao MM Author Index

335

COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer

Management of Water Pollutants Based on Multi-Criteria Analysis and Fuzzy Logics Serge Cescotto l*, Marc Roubens 2, Nicolas Rigo 3, Shixiang Gao 4, Xiaodong Wang 4, Aiquan Zhang 4, Nelson Lourenco5, Jiti Zhou 4, Xuemin Xiang4, Joao Paulo Lobo Ferreira6 1

Department M&SANAST, University of Liege, Belgium Department of Mathematics, University of Liege, Belgium 3 Department ANAST, University of Liege, Belgium 4 School of the Environment, Nanjing University, Nanjing, China 5 Faculdade de Ciencias Sociais e Humanas da Universidade Nova de Lisboa, Lisboa, Portugal 6 Laboratorio Nacional de Engenharia Civil, Lisboa, Portugal 2

Email: [email protected] Abstract This work has been developed in the frame of the MANPORIVERS research project funded by the European Commission. The goal is to identify effective and sustainable policies for the management of surface and ground water pollutants, taking account of their relationships with food production and human health. A methodology based on the combination of fuzzy logics and multicriteria analysis is proposed as a decision aid tool for the development of such policies. An example of application in the Huai river basin is given. Key words: Rivers, pollutant, methodology, management, policy OBJECTIVES AND ACTIVITIES The goal of the MANPORIVERS project is to identify effective and sustainable policies for the management of surface and ground water pollutants, taking account of their relationships with food production and human health. The aim is the definition of policies with a very broad range of applicability that could be used for many river basins. They can be used interactively for different basins exchanging water. They can also be used at different scales in a recursive manner, from small tributary basins to large basins. Table 1 Description of the tasks 1 Task 1 number WPl.a IWPl.b

IwPl.c WP2.a |WP2.b WPS.a WP3.b WP4.a WP4.b WP4.c WP4.d WP4.e WP4.f WP5 WP6

Description of the tasks The different tasks develop methodologies for : Evaluation of non accidental pollutant input Evaluation of accidental pollutant input Evaluation of input evolution in the future Analysis and selection of surface water pollutant transport models Analysis and selection of groundwater pollutant transport models Identification and analysis of techniques for water cleaning Identification and analysis of accident remediation techniques Assessment of the use of drink water Assessment of the use of irrigation water Assessment of water used in food industries Assessment of water used for fish breeding Assessment of other uses of water Evaluation of water use in the future Analysis of the relationships of pollutants with health Pollution management priority policies by fuzzy logics and multicriteria analysis

| | ] | | | | | j | j j | | | | I |

The activities presented in this paper are summarized in Fig. 1 and Table 1. Although we mainly concentrate here on task WP6, it is worth giving some information on the work achieved in tasks WPl to WP5 as they constitute a support for WP6. METHODOLOGIES FOR THE ANALYSIS OF FACTS WPL WP2, WP3, YVP4, WP5

1

~

METHODOLOGIES FOR THE CHOICE OF PRIORITIES IN THE MANAGEMENT OF POLLUTION IN RIVER BASINS VVP6

Figure 1: General Organization of the activities

METHODOLOGIES FOR THE ANALYSIS OF FACTS 1. Methodologies for the evaluation of accidental and non accidental pollutant input (WPl) [1] Pollutant sources are classified into two categories: non accidental pollutant input and accidental pollutant input. The research work completed consists of two parts: (1) Development of evaluation methodologies for the two categories; (2) Application to the Xuyi County (Huai river basin) and to the Xizhijiang River basin (Pearl River delta). 2. Methodologies for the choice of models for the transport of pollutant by surface water and groundwater (WP2) [2-5] The objective is to evaluate existing models for pollutant transport, both for surface waters and groundwater, as tools contributing to the management policies of water pollutants. 1) Transport of pollutant by surface waters The analysis of different softwares has been performed. The following ones were considered and a methodology for their selection and use developed: (a) Mike 11 DHI Danish Hydraulic Institute from Denmark; (b) U.S. Geological Survey (USGS) from USA: a set of 42 sofwares for different purposes; (c) SOBEK Delft Hydraulics from Netherlands; (d) InfoWorks RS; Wallingford from Great Britain; (e) HEC-RAS (Army Corps of Engineer's Hydraulic Engineering Center (HEC)); (f) River Analysis System (RAS) from USA; (f) WOLF software from Belgium. The required parameters, the basic characteristics and use limitations are examined. 2) Transport of pollutant by groundwater The application capabilities of several flow and pollutant transport models available on the Internet are studied, aiming at creating a methodology for their selection and use: (a) FEFLOW (Diersch, 1998); (b) MT3D (McDonald e Harbaugh, 1988); (c) ASMWIN (Chiang et al., 1998); (d) RBCA Tiers Analyser (Roy et al., 2000); (e) AQUA3D (Vatnaskil Consulting Engineers, 1988); (f) FLOWPATHII (Eviksov et al., 1998); (g) WINTRAN (Rumbaugh e Rumbaugh, 1995). Conclusions on the possibilities, data requirements and accuracy corresponding to these softwares are summarized in tables that help decision makers to chose the appropriate model according to the site to be studied. 3. Methodologies for the choice of sanitation and remediation techniques (WP3) [6] The objective is to identify and evaluate existing techniques to decrease pollution levels in waters, due to accidental and non accidental input in order to support management policy decisions by appropriate selection charts and methodology. 1) Non accidental pollutant input Various sanitation techniques are examined according to the specific pollutants. Their working mechanisms and characteristics, the advantages and disadvantages, the suitable application domains, the equipments and technologies used as well as the costs are considered. The emerging innovative techniques are also identified and their potentials are evaluated. The technical specifications and the financial aspects are also taken into consideration so that they could be applied in real industrial cases. 2) Accidental pollutant input This part recapitulates and analyses some of the major accidents in drinking water as well as surface and groundwater pollution in order to gain a better understanding of the causes of accidental pollutant input. It is found that traffic accidents and vehicle overloads are the two main factors causing the release of some toxic chemicals into water body. A variety of remediation technologies are recommended for hazard minimization, among which chemical and biological methods provide successfully techniques. Biological degradation methods are also holding promising perspectives.

— 2 —

4. Methodologies for the evaluation of water use (WP4) [7] In order to develop and apply an effective and sustainable policy for the management of water use, it is necessary to have clear and quantitative responses to the following questions: (a) What is this water used for? (b) Where does this water come from? (c) What are the quantities used for different purposes? (d) How do these quantities evolve in a year time? (e) What is the foreseen evolution in the future? The objective of this work package is to develop methodologies to answer these questions and demonstrate their applicability in the chosen case areas. The following methodologies have been developed: (a) Methodology for evaluating the present water use; (b) Methodology for evaluating water demand in future; (c) Methodology for evaluation of the rationality of water use structure. 5. Methodologies for the evaluation of relationships of pollutants with human health (WP5) [8] The objective is to build a quantitative and qualitative database on the influence of various pollutants in river basins on human health. To reach this goal different complementary approaches have been used. (1) Various human health risk assessment methodologies have been evaluated. The data and information on human exposure to pollutants and their potential health effects have been catalogued. The realistic health risks that environmental pollutants impose on human have been evaluated by comparing their exposure concentration and their toxic potency, leading to a priority list of main pollutants in river basins. (2) Considering that almost all data on health effect and toxicological information are based on animal studies and that there is great difference between animal and human beings, a short-term in vitro Micronuclei Assay based on human peripheral blood lymphocytes micronuclei has been developed and applied to directly evaluate the human health effect of pollutants. Toxic potencies of some aromatic compounds have been tested by this assay. (3) Important efforts have been devoted to develop the Quantitative Structure Activity Relationships (QSAR) models. These are mathematical models that relate the biological activity (e.g. toxicity) of molecules to their chemical structures and to the corresponding chemical and physicochemical properties. This development aims at filling in the data gap for some pollutants. They can be used as indicators of the human health effect of pollutants and also for the development of to predict health effect of other pollutants. METHODOLOGIES FOR THE CHOICE OF PRIORITIES IN THE MANAGEMENT OF POLLUTION IN RIVER BASINS BASED ON MULTICRITERIA ANALYSIS AND FUZZY LOGICS (WP6) 1. The MANPORIVERS methodology [9-11] Based on the combined use of multicriteria analysis and of fuzzy logics, a general methodology has been developed to help decision makers establish sustainable management policies for priority water pollutants and their effects on foods and human health. It is called the MANPORIVERS methodology (Fig. 2). Strategic socio-economic development in a given river basin Action i (i= 1 ,n) Sink j (j=l ,m)

Impacts

I

I

Action data

Methodologies for the analysis of facts

Interface

Basin data

Evaluation tools

Ranking

Figure 2: General Scheme of the MANPORIVERS Methodology This methodology is a major original contribution of this research project and constitutes an efficient tool to help decision makers to undertake environmentally, socially and economically sustainable actions in a river basin. It is applicable to any river basin and takes account not only of the environmental impacts (typically the concentrations of pollutants in water) but also of the social and economical aspects of the problem. The MANPORIVERS methodology is a tool that is able to rank different Actions or Scenarii (i.e. combinations of Actions) in order to maximize their positive effects and minimize their negative effects. — 3 —

The terminology used in Fig. 2 is detailed below. Actions: any type of industrial, economical, political... action or event. Sinks: different entities possibly affected by the impacts of the considered strategic socio-economic development in the region. Action data: specific to a given action (economic, social, pollution data). Regional data: specific to a region, we consider variable regional data (population, migration...) and permanent regional data (geology, rainfall, topography...). Impacts: the different effects of actions, e.g. investment, annual cost, modification of pollutant levels, migration of population, aspect of landscape, ...; each impact must be expressed by a quantifier which can be quantitative (e.g. amount of money invested, pollutant concentration or mass, ...) or qualitative (e.g. good, neutral or bad effect on landscape). Methodologies: all the means (software, data bases, selection charts, recommendations ...) by which the impacts quantifiers of different actions can be obtained. Interface: integration of different impacts in three stages: a geographic integration, an integration within the set of all major pollutants and the integration within the set of sinks. Scenarii: different combinations of Actions and different weights for the social, economical and pollution impacts. Evaluation tools: softwares based on multicriteria analysis and fuzzy logics taking account of the impacts and their respective weights to give a classification of different actions. Ranking: ordering from the best to the worst action. Of course, this global methodology makes use of the specific methodologies for the analysis of facts presented in section 3 above. In must be noted that the MANPORIVERS methodology is capable to take account of: (a) the different uses of water; (b) the effects of pollutants on human health; (c) the direct and indirect costs of Actions (investments, maintenance, functioning,..); (d) the effects of Actions on population (creation or loss of jobs, change of water price, change of water consumption,...; (e) the effects of Actions on landscape, on the quality of life, ...; (f) the coherence and feasibility of Actions. It is able to consider not only deterministic quantitative criteria but also fuzzy criteria as well as qualitative criteria (such as linguistic statements). The MANPORIVERS methodology is also characterized by the fact that it allows decision makers to estimate the robustness of their decision: by modify the weights given to the different criteria, they can see if their decision is modified by slight weight changes (no robust decision) or if, on the contrary, the decision is not affected by reasonable weight changes (robust decision). To use this methodology, it is necessary to be able to evaluate the different scenarii on the basis of different criteria. In others words, it is necessary to quantify or qualify the impacts of the actions on a set of comparison indicators that must be defined by the decision makers. After having quantified/qualified these different impacts (using the specific methodologies presented in the last section), it is possible to use a decision aiding software based on multicriteria and fuzzy logics to select the best scenario according to the weight given to the different comparison criteria. For complex management projects, it is necessary to have a global view, i.e. it is important to consider social, economic and environmental aspects but also, the concept of the coherence and the feasibility of the measures. The selection of the best scenario must be made according to these different aspects. We have to evaluate the different impacts of the measures on the criteria. However, the evaluation of some impacts is quite difficult because of the lack of data or the complexity of the reality. Then, the use of quantitative model is impossible and we have to use qualitative models. This is where fuzzy logics enter into the picture: in classical multicriteria analysis, impacts are normally expressed by figures, usually some amount of money. In the methodology, fuzzy logics has been introduced: it is possible to consider criteria expressed by fuzzy expressions and even to use linguistic scales (see Fig. 3). Furthermore, the importance of the different comparison criteria is also essential in the selection. The decision makers will choose according to their convictions, their points of view. So, the methodology allows them to weigh the different criteria according to their convictions. Then, it is clear that the final choice will be different according to the specific weights given to each comparison criterion. In fact, we can say that the weighting is the mathematical translation of the convictions of the decision makers. — 4 —

I 1

Types of measurement scales or « quantifiers » Quantitative

«■+>

An integer or a decimal number e.g.: 1250 persons, 10,25 kWh Ordinal e.g.: good/neutraMad Nominal e.g.: yes/no; green/red A statement involving uncertainties e.g.: probably between 15 and 20 but certainly not below 12 and not above 24

1

Fuzzy

■#

1 1 1

1 r^ 1 /

1 c1

!

1—1 12 15

1

1 20

\

1

* + 24

Figure 3: Examples of Measurement Scales or Quantifiers Among the comparison criteria, the different pollutants of water constitute very important indicators for the final selection of a management strategy for the basin. However, there are many pollutants that are important in the analysis. The large number of pollutants could be an obstacle to the clarity of the reasoning. That is why the MANPORIVERS methodology contains a functionality allowing to "integrate" the effects of the different pollutants. This functionality involves 3 levels of integration: (1) Integration of the impact of a pollutant over the entire basin: this takes account of their potential danger of the pollutant over the considered period of time and of the population potentially affected. (2) Integration on the pollutants : this takes account of the relative toxicities of the different pollutants present in the basin. (3) Integration on the sinks: the sinks correspond to the different fields of water use: consumption, irrigation, fishing, food and domestic use. The methodology proposes a linguistic scale to give a weight to each of them. Thanks to this functionality, it is possible to characterize the pollution of the considered basin by a simple result integrating not only the concentrations of the different pollutants but also their toxicity and the populations potentially affected. For the economic criteria (direct cost, investments, maintenance costs, interest rates,...) classical methods of economy can be used to integrate them in order to get the global cost of an Action. So, this point is considered as classical and well known. For the social criteria and for the criteria of coherence and feasibility, no attempt is made to try to "integrate" them. They are considered one by one. Indeed, the "aggregation" of criteria like number of jobs created or lost, modification of water consumption, change of water price, change of land use,... .does not seem reasonable and is not easily feasible in practice since linguistic scales are often used for some of these criteria. Once all the criteria defined, evaluated on the basis of the methodologies for the analysis of facts and integrated if necessary, a multicriteria table is obtained (see an example in Table 8). Then, a multicriteria decision aiding software can be used. In this research, we use the software Decision Lab using the PROMETHEE methodology. It is a multicriteria decision aiding software including fuzzy logic aspects. It allows the ranking of different Actions or Scenarii taking account of the different criteria and of their respective weights. 2. Integration of pollutants: the global Environment Pollution Risk Criterion (EPRC) Among the comparison criteria, the different pollutants of water constitute very important indicators for the final selection of a management strategy for the considered river basin. However, there are many pollutants that are important in the analysis. The large number of pollutants could be an obstacle to the clarity of the reasoning. That is why the MANPORIVERS methodology contains a functionality allowing to "integrate" the effects of the different pollutants. This functionality is the global Environment Pollution Risk Criterion (EPRC). — 5 —

It involves 3 levels of integration: (1) Integration of the impact of a pollutant over the entire basin: this takes account of their potential danger of the pollutant over the considered period of time and of the population potentially affected. (2) Integration on the pollutants: this takes account of the relative toxicities of the different pollutants present in the basin. (3) Integration on the sinks: the sinks correspond to the different fields of water use: drinking water, irrigation, fish breeding, water for food industries and water for non food industries. The methodology proposes a linguistic scale to give a weight to each of them. Thanks to this EPRC, it is possible to characterize the pollution of the considered basin by a simple result integrating not only the concentrations of the different pollutants but also their toxicity and the populations potentially affected. 1) Geographic integration The goal of this first step is to evaluate the effect of each pollutant on the considered basin. It is suggested to divide the basin in different zones in order to determine the impact of a pollutant on the basin with precision. Actually, it would be dangerous to consider the basin as a whole because, in that case, the calculated impact would show an unrealistic homogeneity. We have to take the diversification of the area into account, particularly for the density of population and for the pollutants concentration. The proposed methodology is based on these basic considerations. The ideal would be to have a division highlighting zones with various pollutants concentrations and densities of population in order to have an optimal representation of reality. Concerning the pollutants concentration distribution and the evolution of these concentrations with time, they can be obtained by the complementary use of pollutant transport models and in field data analysis. Given the pollutant input data, they enable to predict the concentration c(x, y, t) of a given pollutant at point (x,y) of the considered basin at time t. These models can be calibrated with the help of in situ measurements. Geographic integration formula In order to aggregate the impact of a pollutant over the entire basin, we propose the following expression in which the notation « year » indicates the considered year (we cannot forget the evolution with time; the "sustainable development" concept is very important). Iijk (year) = J Dijk (x, y, year) x F™ (x, y, year)dA A

Let us clarify the content of this expression: (1) The subscripts i,j and k represent the action or scenario /, the sinky, and the considered pollutant k. (2) A is the area of the considered basin entire basin. (3) Dijk(x, y, year) defines the « potential danger » of pollutant k for one year. It is based on the concentration of the considered pollutant c,y* (x, y, t) and is expressed in jug 11; it is defined below; (4) Ffnp(xy ,year) is a function of the distribution of population density in the considered year expressed in pers./km2; it is also defined below; (5) The integrated impact is expressed in: pers x fig jl Definition of function Dyk(x, y, year) The definition of the potential danger of a pollutant must be considered with care. A first idea is be to integrate the concentration over 1 year: this gives an idea of the average amount of pollutant to which the population is exposed during the year under consideration. However, this approach erases potential concentration peaks presenting severe danger for human health. That is why we propose to consider another element: the maximum of the pollutant concentration. Then, the questions to answer are: "When should we use the maximum?" "When should we use the average?" Usually, each pollutant is characterized by a critical threshold that cannot be exceeded: over this critical threshold, the consequences for human health could be very serious. This threshold is used as discriminant. Let us consider the two following cases for a given pollutant. First, we consider the case where the yearly trend of the pollutant concentration is quite stable (Fig. 4). In this case, there is no reason to include the maximum of the concentration because it is lower than the critical concentration, and therefore, the average represents fairly enough the reality. — 6 —

Then, we consider the following case (Fig. 5). The maximum concentration of pollutant k is higher than the critical level. By itself, the average does not represent correctly the reality because it doesn't reflect this peak. Then, the use of the maximum of the concentration would be favourable. That is why; we propose the following expression to calculate the potential danger of pollutant k: c(t) ^critical

average

Figure 4: Stable evolution of pollutant concentration

c(t)

average

Figure 5: Evolution of pollutant concentration with peak DiJtk (x, y, year) = a — f cijk (x, yy t)dt 4- 0 max cijk (x, y, t) A^ = lyear \(0,l)if3f.c.M(x,y,t)>ccrilical

{ -0.101

|5_J ►—WM ' 1 k

1 mull -0.131

if

5 0.17

Figure 6: The final ranking of the scenario for the horizon 2005 with all criteria in same weight We can continue the analysis and compare the ranking of the scenarii if we change the weights of the criteria. For example, if we put emphasis on the social point of view, we give more importance to the social criteria. It is just an example to illustrate the possible different final results according to the different points of view of the decision makers. In fact, we keep the weight 1 for all the criteria except for the three social criteria: we give the weight 3 to the employment and the increased demand of water, and 5 to the public health risks. The result for the horizon 2005 is shown in Fig. 7. — 12 —

|

fj

PROMETHEE 2 Complete Ranking PROMETHEE 1 Partial Ranking j

i 1_•Scenario 3

■ r L

*+ *-

0.49 "— 0.25

■

2 1

"P~"

Scenario 4 4>+ 0.42 *0.33

3 1

2 m ♦Scenario + 0 38 *-

0.35

"■■'

'W

5

m• 1

Scenario 1 *+ 0.35 +0.46

w

m

I

Scenario 0 *+ 0.32 +0.58

om

S 0.2

Figure 7: The final ranking of the scenario for the horizon 2005 with all criteria in different weight In the present case, the best scenario is the scenario 3 while scenario 4 is placed at the second rank. The result is different compared to a homogeneous distribution of weights. This demonstrates that the MANPORIVERS methodology makes it possible to analyze the robustness of the best scenario. To summarize, we can say that the MANPORIVERS methodology makes possible to construct pollution management scenarii, to compare them according to criteria defined previously and to propose a final ranking indicating which scenario is the best. CONCLUSION The MANPORIVERS methodology is based on the combined use of multicriteria analysis and of fuzzy logics. It constitutes a decision aid tool to help decision makers establish environmentally, socially and economically sustainable management policies for priority water pollutants taking account of their effects on foods and human health. It is applicable to any river basin and takes account not only of the environmental impacts (typically the concentrations of pollutants in water) but also of the social and economical aspects of the problem. This methodology can be used interactively for different basins exchanging water. It can also be used at different scales in a recursive manner, from small tributary basins to large basins. These properties constitute a strong incentive to harmonize and coordinate the policies of different basins but these policies can be applied progressively according to the circumstances and available budgets, starting from small basins, since the results of small basins can be directly utilized for larger ones. Acknowledgements This reseach was performed under the contract number: ICA4-CT-2001-10039 MANPORIVERS: 01/01/2002 to 31/12/2005 of the European Community. The authors acknowledge the support of the European Community. REFERENCES 1. Gao Shixiang, Zhang Aiqian, Wang Xiaodong, Han Shuokui, Wang Liansheng, Wang Xiangde, Zhu Bin, Zhang Xiujuan, Ndiaye Alassane, MarchaL Jean. Methodology for Pollutant Input Evaluation. Final Report on WP1: Deliverable D15, Annex 1 to the Second Annual Report of the MANPORIVERS research project, EC Contract ICA4-CT-2001 -10039. 2. Lejeune Andre, Pirotton Michel, Novo ME, Ikavalko VM, Diamantino C, Lobo-Ferreira JP, Brouyere S, Orban Ph, Dassargues A. Pollutant Transport Models. Final Report on WP2, part 1: Deliverable D16, Annex 2 to the Second Annual Report of the MANPORIVERS research project, EC Contract ICA4-CT-2001-10039. 3. Lejeune Andre, Pirotton Michel. Transport of Pollutants by Surface Waters. Final Report on WP2, part 1: Deliverable D16, Annex 2 to the Second Annual Report of the MANPORIVERS research project, EC Contract ICA4-CT-2001-10039. 4. Brouyere S, Orban Ph, Dassargues A. Applicability of Groundwater Pollutant Transport Models. Final Report on WP2, part 2: Deliverable D16, Annex 2 to the Second Annual Report of the MANPORIVERS research project, EC Contract ICA4-CT-2001-10039.

— 13 —

5. Novo ME, Ikavalko VM, Diamantino C, Lobo-Ferreira JP. Generic Characterization of Mathematical Models to Simulate the Pollutant Transport in Groundwater. Final Report on WP2, part 3: Deliverable D16, Annex 2 to the Second Annual Report of the MANPORIVERS research project, EC Contract ICA4-CT-2001-10039. 6. Zhang Ying, Zhou Jiti, Xiang Xuemin, Xu Yanli, Wang Xiangde, Liang Lianluan, Zhang Xiujuan. Selection Methodology for Sanitation and Remediation Techniques. Final Report on WP3: Deliverable D17, Annex 3 to the Second Annual Report of the MANPORIVERS research project, EC Contract ICA4-CT-2001 -10039. 7. Wang Xiangde, Li Chuanhong, Wang Min, Huang Xihua, Zhang Xiujuan, Xiang Xuemin, Zhou Jiti, Xu Yanli. Methodology for the evaluation of water use. Final Report on WP4: Deliverable D18, Annex 4 to the Second Annual Report of the MANPORIVERS research project, EC Contract ICA4-CT-2001-10039. 8. Wang Xiaodong, Gao Shixiang, Zhang Aiqian, Sun Cheng, Han Shuokui, Wang Liansheng. Relationships between Pollutants and Human Health. Final Report on WP5: Deliverable D19, Annex 5 to the Second Annual Report of the MANPORIVERS research project, EC Contract ICA4-CT-2001-10039. 9. Roubens Marc, N'Diaye Alassane, Rigo Nicolas, Cescotto Serge, Lourenco Nelson, Zhang Aiqian, Xiang Xuemin, Gao Shixiang. Development of the Manporivers Methodology. Final Report on WP6, part 1: Deliverable D23, Annex 1 to the Third Annual Report of the MANPORIVERS research project, EC Contract ICA4-CT-2001-10039. 10. Roubens Marc, N'Diaye Alassane, Rigo Nicolas, Cescotto Serge, Lourenco Nelson, Zhang Aiqian, Xiang Xuemin, Gao Shixiang. Application of the Manporivers Methodology in the Huai River Basin. Final Report on WP6, part 2: Deliverable D23, Annex 1 to the Third Annual Report of the MANPORIVERS research project, EC Contract ICA4-CT-2001-10039. 11. Erpicum Sebastien, Pirotton Michel, Lejeune Andre, Mao Yuanyuan, Wang Xiangde, Li Chuanhong, Wang Ming, Huang Xihua, Zhang Xiujuan. Application of the Manporivers Methodology in the Pearl River Delta. Final Report on WP6, part 3: Deliverable D23, Annex 1 to the Third Annual Report of the MANPORIVERS research project, EC Contract ICA4-CT-2001-10039.

— 14 —

COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer

Enriched Element Method and Its Applications to Solid Mechanics Genki Yagawa **, Hitoshi Matsubara2 1

Center for Computational Mechanics Research, Toyo University, 2-36-5, Hakusan, Bunkyo-ku, Tokyo, 112-8611 Japan 2 Center for Computational Science and Engineering, Japan Atomic Energy Agency, 6-9-3 Higashi-Ueno, Taito-ku, Tokyo, 110-0015 Japan Email: [email protected], [email protected] Abstract In the present paper, we discuss the accuracy improvement for the free mesh method (FMM): a node based finite element technique. We propose here a scheme where the strain field is defined over clustered local elements in addition to the standard finite element method displacement field. In order to determine the unknown parameter, the Hellinger-Reissner Principle is employed. The motivation of the study is to seek the better accuracy in the FMM. Key words: enriched element method, free mesh method, Hellinger-Reissner principle INTRODUCTION As is well known, mesh generation for the finite element analysis[l, 2] becomes very serious and time consuming if the degree of freedom of the analysis model is extremely large and the geometries of the model are complex. In order to overcome the above issue of the FEM, the so called mesh-free methods [3,4] have been studied. The Element-Free Galerkin Method (EFGM) [5,6] is one of them with the use of integration by background-cells instead of by elements, based on the moving least square and diffuses element methods. The Reproducing Kernel Particle Method (RKPM) [7,8] is another mesh-free scheme, which is based on a particle method and wavelets. The general feature of these mesh-free methods is that, contrary to the standard FEM, the connectivity information between nodes and elements is not required explicitly, since the evaluation of the total stiffness matrix is performed generally by the node-wise calculations instead of the element-wise calculations. On the other hand, a virtually mesh-free approach called the free mesh method (hereinafter referred to as "FMM") [9,10] is based on the usual FEM, and has a cluster of local meshes and equations constructed in a node-by-node manner. In other word, the FMM is a node-based FEM, which still keeps the well-known excellent features of the standard FEM. Through the node-wise manner of FMM, a seamless flow in simulation procedures from local mesh generation to visualization of the results without user's consciousness has been realized. The method has been applied to solid/fluid dynamics [11], crack problems [12], concrete problems [13], and so on. In addition, in order to achieve a highly accurate FMM, development of the FMM with vertex rotations was studied [14,15]. BASIC CONCEPT OF FREE MESH METHOD The basic concept of FMM starts with only the nodes distributed in the analysis domain ( Q ) , without the global mesh data, as following equation. />,(*,, v , , 0

V ; .e{l,2,-..,m}

(1)

where m is the number of node, /?,(*;,>>/) are the Cartesian coordinates, and rt is the nodal density information which is used to generate appropriate nodes as illustrated in Fig. 1(a). From above nodal information, a node is selected as a — 15 —

Other nodes Central node Local elements Satellite nodes (a) Domain of analysis y

(b) Clustered local elements

n - in -/* *

-'-

Stiffness matrix for ej

-P< &

V

Assembling

Stiffness matrix for t'j

p,

S/

S: S* Si Si

S6

Stiffness matrix for />,-

(c) Stiffness matrix for central node Figure 1: A 3D model with spherical particles Concept of Free Mesh Method central node and nodes within a certain distance from the central node are selected as candidate nodes. This distance is usually decided from the prescribed density of the distribution of nodes. Then satellite nodes are selected from the candidate nodes, which generate the local elements around the central node (show in Fig. 1(b)). For each local element, the element stiffness matrix is constructed in the same way as the FEM, however in FMM, only the row vector of stiffness matrix for each local element is necessary. The local stiffness matrix of each temporary element is given by kej=[kPi

ks

ksJ

(2)

where k^ is the row vector of the stiffness matrix for element e, and k^ , k 5 and k 5 are components for node of pi, Sj and Sk (j and k are number of current satellite nodes). Through the above procedures are carried out for all local elements, the stiffness matrix for central node is given by

*„=2X where kp

(3) is the stiffness matrix for central node /?,, and ne the number of local elements. Through the above

procedures for all nodes is carried out, the global stiffness matrix is given by assembling k

which are computed by

node-wise manner. ~km K=

PI

(4)

Brief of the nodal stiffness matrix is shown in Fig. 1(c). After the construction of the global stiffness matrix, a derivation of the solution is processed. The great advantage of FMM is that the global stiffness matrix can be evaluated in parallel with respect to each node through the node-wise manner, and only satellite node information is required with each nodal calculation. Finally, a derivation of the solution is performed as the usual FEM. Thus, the FMM is a node-wise FEM, which still keeps the well-known excellent features of the usual FEM. The features of FMM are summarized as follows, (1) Easy to generate a large-scale mesh automatically (2) Processed without being conscious of mesh generation (3) The result being equivalent to that of the FEM

DERIVATION OF ENRICHED FREE MESH METHOD On the other hand, "Assumed strain on the clustered local elements" is the concept of the EFMM: a revised version of the FMM, as shown in Fig. 2. In the EFMM, the strain field on the clustered local elements and the displacement field — 16 —

^

Mixed

Element-wise displacement

fields

Node-wise strain field

Figure 2: Concept of Enriched Free Mesh Method of each local element are assumed independently. In order to combine these two independent fields, we discuss the approach based on the Hellinger-Reissner principle. In the EFMM based on the Hellinger-Reissner principle [1][17] (hereinafter referred to as "EFMM-HR"), the Hellinger-Reissner (hereinafter referred to as "HR") principle is employed to obtain better accuracy. Let the HR principle of a linear elastic body be defined on the clustered local elements by 1 n(«,«)= [i{€}T[D]{du}dQ--\n{e}T[D]{e}dn-

J[{i/}r{b}dCl-

[g{u}T{i}dS

(5)

where {du} = [B]{u} , {e} = [N']{e}

(6)

with {b} being the applied body force per unit mass, and {t} the applied traction on boundary Sa. {u} is the unknown nodal displacement and {c} the unknown nodal strain. The unknown values ( U , E ) of the HR principle satisfy the following equations in a weak manner, lS{e}T[D]([B]{u}-[N]{e})dil £S{u}T[B]T[D][N]{u}dQ-

=0

(7)

k>0 w < y-\y0x\ is valid. By expanding the fundamental functions into Taylor series, the first integral in Eq. (1) can be evaluated as (2) where Mt is the multipole moment centered at y0, and ft is a regular function related to the vector

y0x.

2. First page Multipole to multipole translation (M2M) The multipole moment can be shifted into a new one centered at y'0 defined as

^ U ) = Z^,(>'o>'o)M'(^)

(3)

i

where y.. is the coefficient of M2M translation. 3. Multipole to local translation (M2L) Assume the inequality \x'0x\ < My'0x\ is valid, the multipole moment can be translated into local moment centered at x'0 defined as

AW)=Z^(>'^)A/'(>'»)

(4)

where u is the coefficient of M2L translation. 4. Local to local translation (L2L) Similar to M2M, the local moment can be shifted from xf0 to x0 as follows:

AW)=Z4(>«)^U)

(5)

where £u is the coefficient of L2L translation. 5. Local expansion The first integral in Eq. (1) can be finally evaluated by

— 20 —

\T:,{x,y)ufi{y)dS{y)= £*,(*o*K(*J

(6)

where g{ is a regular function only related to x0x. The second integral in Eq. (1) can be evaluated in a similar formula. 6. Numerical implementation of fast multipole method The algorithm of fast multipole method consists of 6 steps which in all form the matrix-vector products. 1) Tree Construction: The fast multipole method utilizes the tree structure, which is constructed hierarchically. The root of the tree represents a box that contains all the elements and is at level 0 of the tree. The root is divided into 4 equal-sized child-boxes that are at level 1. Each of these boxes is divided into 4 more child-boxes until every box contains at most some fixed number of elements. The shape of the tree adapts to the distribution of elements because the tree will have more levels in regions having more elements. The resulted tree is called an adaptive quad-tree. An example is shown in Fig. 2, where the tree is constructed on the model of a square plate with 100 randomly distributed inclusions of different sizes. 2) Forming multipole moments of leaves: Leaves are the boxes at the finest levels. For each non-empty leaf, its multipole moments are formed by elements it contains.

oC?°oO 0 ° ° 0 Figure 2: Model of a square matrix with random inclusions (left) and its corresponding tree (right) 3) Upward Stage: For each non-leaf box, the multipole moment is formed by shifting the multipole moment of its children using Eq. (3) and adding up the four shifted multipole moments. This procedure is repeated up to level 2. 4) Downward Stage: For each box starting from level 2, the multipole moment of boxes in the interaction list, as depicted in Fig. 3, is transformed to this box's local moment using Eq. (4). Then the local moment is shifted to its children's one using Eq. (5), and the multipole moment in the interaction list of that children level is transformed using Eq. (4) and added on it. This procedure is repeated down to the finest level.

^

&

&

&

#

&

%

&

&

#

#

e- □

Interaction List of box X at level 3 Interaction List of box X' at level 2

Figure 3: Definition of interaction list (Boxes with dashed lines indicate empty boxes) 5) Evaluation of the integrals in Eq. (1): The integrals in Eq. (1) are evaluated in 2 parts. For each source point, the contributions from elements in the same leaf and neighbor leaves are evaluated directly in the way as conventional BEM. Contributions from others are evaluated using Eq. (6). 6) Update of the iterative vector: The iterative vector is updated and the next iteration is started from Step 2. — 21 —

7. New version of fast multipole method The new version of FMM with exponential expansion is developed in the late 1990s by Greengard and Rokhlin. In procedures of the new version, the dense translation operator from multipole moments to local moments in Eq. (4) is diagonalized by three new steps. 1) Multipole to exponential shift: In order to obtain a new series of exponential moments by multipole moments in the same cube. 2) Exponential to exponential shift: In order to transfer exponential moments from one cube containing field points to another cube containing source points. 3) Exponential to local shift: In order to obtain local moments by exponential moments in the same cube. Since operations needed in FMM to obtain local moments by multipole moments dominate most computer resources for 3D problems, successful simplification of these operations makes the new version FMM much effective than the original one. ACCURACY AND EFFICIENCY OF FMBEM To verify the accuracy and efficiency of the FMBEM, a series of test examples have been computed. 1. Accuracy of FMBEM related to the orders of multipole and local expansion A square sheet with a circular hole in the center under uniform normal displacement along 4 edges as shown in Fig. 4 (plane stress problem) is tested. The side length / = 10cm, the radius of the hole r= 2 cm, prescribed normal displacement un = 0.001 cm. All boundaries are discretized into 4,720 DOF.

■mttmiittmmr \f

4

(3 ; !

zn

^3

fc'sinoo.WAi v-o.t

' ♦ T » » f f * » T » » ' f » » * » l ' t

Figure 4: A square sheet with a circular hole in the center under uniform normal displacement along 4 edges The numerical results of normal displacement at three location of hole boundary, using FMBEM with different orders of multipole and local expansions, are listed in Table 1, in comparison with conventional BEM. The comparison has shown that the FMBEM can obtain as accurate results as the conventional BEM provided enough orders of multipole and local expansions are taken. Table 1 Numerical results of FMBEM in comparison with conventional BEM un mm (0=0°)

relative error

« n mm (0=45°)

relative error

un m m (0= 90°)

relative error

Gauss elimination

-0.009191605

—

-0.009374642

—

-0.009191605

—

FMM (p=20)

-0.009191627

2xl0-6

-0.009374664

2x10~ 6

-0.009191607

2xl0-7

¥MM(p=\5)

-0.009191628

2xl0-6

-0.009374664

2xl0-6

-0.009191620

lxlO-6

¥MM(p=\0)

-0.009187775

4xl0-4

-0.009374608

3xl0"6

-0.009187732

4xl0-4

¥MM(p=5)

-0.009218128

3xl0-3

-0.009401706

2xl0-3

-0.009220656

3xl0-3

2. Accuracy of large-scale computation using FMBEM The plane strain model of a square with a circular inclusion in the center (the left of Fig. 5) is periodically repeated to form larger computational models: 2x2 model with 10,880 DOF (the right of Fig. 5) and 30x30 model with 696,000 DOF. The length / = 10cm, the radius of the hole r= 2 cm. The — 22 —

material properties are: Em= 1000MPa, v m = 0.3 for the matrix, and E\= 5000MPa, vi= 0.3 for the inclusions. The prescribed normal displacements are proportional to the side length of the square: un = 0.002 cm for 2x2 model and wn = 0.03 cm for 30x30 model respectively. In this way the traction and the normal displacement relative to each inclusion center along the inclusion boundary should be the same for different models. The numerical results (Table 2) have shown high accuracy of the large-scale computation using FMBEM.

inclusion

!

/■

( ■9 matrix

Figure 5: A square with a circular inclusion in the center (left) and the corresponding 2x2 model Table 2 Numerical results of 2x2 model and 30x30 model FMM (p=20) 2X2

un (mm)

error

0=0° -0.0112337

30X30

-0.0112334

2X2

0. 552577

error

-0.0152802

-0.0112337 3xl0-5

0. 547221

2xl0-5

-0.0112334

0. 547241

0.552595

error

0=90°

-0.0152808 2xl0-5

2xl0-5

/n (MPa) 30X30

0=45°

0. 552578 3x10~ 5

2x10~ 5

0. 552595

3. Efficiency and convergency of FMBEM The computation time and memory requirement using FMBEM for different problem scale, are shown in Fig. 6 in comparison with those using conventional BEM. For the FMBEM computation the order of multipole and local expansions is taken as p = 20, and the tolerance for the iteration e- lxlO 5 , and for the conventional BEM computation the package LAPACK is applied for the Gauss elimination. Computation Time (sec)

Memory Requirement (MB)

, 800

Conventional BEM

60O

.,,

,

r.

,

" » Conventional BEM

"

-

400 a 20O

FMBEM

FMBEM 5000

1O000

R - A « f , i A ( ,«£»„„ 5000

15000

Degree of Freedom

■ £

--

At-A

,

A

100O0

,

*

■*

15000

Degree of Freedom

Figure 6: The comparison of computation time and memory requirement between FMBEM and BEM The convergency of the FMBEM is shown in Fig. 7, the order of multipole and local expansion is taken as p=20. The results have shown good efficiency and convergency of FMBEM. — 23 —

Residual _j

r

j i

01 a

0 01

C A

, , , DOF=2400 | J)OK=280TW)i

A a

_ ^ A A A

1E-3 °

A A

Ifc-b

a

C

1E-6

A D

D A

IE-7 1E-8

•

1

>

1, , , ,

i

1

.n ,

20

,

'A

30

Iteration Number Figure 7: The convergency of the computation using FMBEM APPLICATION OF FMBEM ON SIMULATION OF COMPOSITE MATERIALS The FMBEM has been applied in the 2D and 3D simulation of composite material and the obtained equivalent material properties have shown good agreement with the available results in micromechanics. But the computation using FMBEM can obtain not only the equivalent properties, but also the whole fields of displacements and stresses, which is useful for the further investigation of the failure process of the composite materials. 1. 2D simulation of long-fiber reinforced composite material Long-fiber reinforced composite material can be simulated using 2D model of plane strain. Fig. 8 shows two models of square containing 1600 randomly distributed circular inclusions discretized into 544,000 DOF. Fig. 9 shows the results of equivalent volume modulus obtained using FMBEM in comparison with that obtained using Mori-Tanaka method.

W

M

msmm %s^M*Mk%

Figure 8: Models of square containing 1600 circular inclusions, volume fraction = 0.2 (left), 0.4 (right) 1

1

1

1

1

1

1 -—

i—i

-1—

-T

J

-i

-

|

1

—l

' — l —

—O— Mon-Taiiaka 30

"

A

FMBEM ■O

25

.XI'"'" -"'..A--"'

::2V*

1.6

1

1

r

"

-

lf>

-

-

f

1

1

1

"

— a — Mori-Tanaka —A— FMBEM CJV

"

/A

,^'

1.4

/A 20

1

r-

1.5

J ja' . „&' A?"

"

i

-

_

J?

1.3

"

..> KJ Request

-4

>

^ ^

%

r >! r >i r >j L) LJ K ) !

tc ^j M

»

Return

ww w ; j Interaction List of X' box

Figure 17: Remote checks in parallel tree traversing (Empty boxes are not returned) 2. Parallelization of the tree traversing The most time-consuming step in fast multipole method is the downward stage. It is also the most complicated step in parallel formulations since interactions from interaction list and neighbor boxes are needed. And these boxes may be in the same or other tasks, and may be empty anywhere. So a remote-check procedure is used as a simple example shown in Fig. 17 for the case of interaction list only, where box marked with X in task / need the — 27 —

remote boxes in task/ In that case task / sends a checking request toy and a checking result of non-empty boxes are returned. The overhead of this procedure can be neglected since it costs only a few seconds in a model with tens of thousands unknowns and also the checking result does not change from iteration to iteration for elastostatics. 3. Accuracy verification To verify the accuracy of FMBEM, two models with 1 inclusion centered at the origin of the matrix and 343 (7x7x7) inclusions that are periodically distributed are used, as shown in Fig. 18. The edge length of matrix is 20x20x20(cm) and the inclusion volume fraction is 0.1. Each inclusion is discretized into 392 triangle piecewise constant elements and 120,000 elements for the outer boundary of matrix. The multipole/local expansion order is 12 and the residual of GMRES is l.OxlO"7.

it f *

. ''°'s -

* *d

Figure 18: Model with periodically distributed inclusions and local coordinate of an inclusion (right) The relative displacement u.0) - u\ ' and the traction ry are given in Fig. 19. The slight difference of the last 49 inclusions, which are near the front surface (in +JC direction) of the matrix, comes from matrix discretization error. The results have shown satisfactory accuracy of the parallel FMBEM computation.

Figure 19: The results of relative displacement uy —u^' and the traction rx' for point 1 and 0 of each inclusion 4. Performance and Efficiency of Parallel FMBEM The following computations are carried out on a 16-node SMP PC cluster. The nodes are connected via 1,000Mb Ethernet switch hub. Each node owns 2 Pentium IV Xeon processors and 1 GB memory. C++ is used as the programming language and a message passing interface, LAM/MPI, is used for communications. To show the scalability of parallel FMBEM, 6 models with different number of inclusions are used. The edge length of matrix is 20x20x20 (cm) and the radius of inclusion is 0.45 71 (cm). The matrix is applied with an axial traction of lOOMPa. The inclusions are distributed randomly by using Sobol sequence, as shown in Fig. 20. Total 32 processors are used for those calculations. The multipole/local expansion order is 12 and the residual of GMRES is l.OxlO-5. Table 3 demonstrates the performance and memory requirements of the computation. Both time and storage complexity are approximately proportional to the scale of the problem. For the largest model, the running CPU time is about 43 hours and approximately 9GB memory is required. Fig. 21 shows the computing time versus numbers of processors and the speedup for the parallel FMBEM. — 28 —

, "^"-ij 1".' „ ^ > 3 ? ' .'-■".. ■

/ = lOOMPa

/ =100MPa

r = 100MPa 1000 inclusions DOF=l.536,000

500 inclusions DOF=948,000

100 inclusions DOF=477,600

/ =100MPa

r = 100MPa

2000 inclusions DOF=2.71 2.000

4000 inclusions DOF=5,064.000

3000 inclusions DOF=3,888,000

Figure 20: Models with different number of inclusions Table 3 Performance of parallel FMBEM computation Inclusion number

100

500

1000

2000

3000

4000

Volume fraction

0.005

0.025

0.05

0.1

0.15

0.2

Number of DOF

477,600

948,000

1,536,000

2,712,000

3,888,000

5,064,000

Memory requirement (MB)

1,976

3,070

4,067

5,989

7,543

9,182

Computing time (s)

4,660

15,179

32,136

71,636

103,635

161,190

90000

ideal adlkJ speedUfJ ---

\>

X . . - - ■ '

,

70000

1_

60000 1

50000

i

r,x'

../"

,.y

f g.

/-'""

,>

, , ■ ■ • " - "

40000

,

-

-

■

'

30000 20000

\

10000

-.... 4._.._.

-.._ 10

12 14 16 18 20 Number of processors

22

24

26

29

M

32

y

/•"' 18 20 Number of processors

22

24

26

28

30

32

Figure 2 1 : The computing time versus number of processors (left), and the speedup for parallel F M B E M 5. Application on the simulation of fiber reinforced composites Two fiber shapes, bone-shaped short fiber (as shown in Fig. 22) and conventional straight short fiber, are simulated and compared. Fig. 23 shows a typical configuration of RVE model of well-aligned bone-shaped short-fiber reinforced composites. There are 200 fibers in the RVE, the volume fraction is 0.05. It is discretized into 2,596,800 DOF, and the computing time is approximately 38 hours. Fig. 24 shows the comparison of effective tensile modulus for two types of fiber shapes, and a normalized histogram with fitted Weibull probability density functions. — 29 —

Figure 22: Well-aligned bone-shaped Ni-fiber reinforced polyester matrix fiber composites and a fiber model

Figure 23: The BEM model of a RVE of matrix containing 200 randomly dispersed bone-shaped short fibers ;j Two ryp»s of TiBftr tnapes J ! Bone-shaped short fibers I i Conventional straight short fiber*

£

! T A o t> pes of fiber sr»ape% jBorte-*bep*v

;_

"'

■ : ; •; .;

:,';''';

■-; ;>

;

1 v^

„' ' „:. , -j

Figure 33: A sheet containing 4000 microcracks

Dilute SCM DM Feng-Yu GSCM • Numerical

crack density

Figure 34: Effective in-plane bulk modulus versus crack density

Furthermore, the effect of crack non-uniform distribution on effective in-plane bulk modulus is also investigated using the FMDBEM. This work assumes that the microcracked solid contains some local regions having a crack density coL higher or lower than the average crack density co0 and analyze the variation of the effective in-plane modulus with coL when co0 is fixed. Fig. 35 shows a square sheet containing 4 higher crack density region, and Fig. 36 shows the results of Ke /K0 versus coL /co0 for the case of co0 = 0.3 . The results show that the non-uniform distribution of microcracks increases the effective in-plane bulk modulus of the whole microcracked solid. * Numerical restsJte — A « r a g e iame

*

0*

*.s

Figure 35: A square sheet containing 4 local regions

G.O

as

ia

20

26

Figure 36: Ke/K0 versus a>L/CD0 (co0= 0.3)

CONCLUDING REMARKS Based on the progress of FMBEM, the authors' group carried out a series of investigation on the applications of FMBEM in solid mechanics. The investigations on large-scale FMBEM analysis in solid mechanics, including 2D and — 33 —

3D elasticity and 2D fracture problems, have shown its attractive advantages, high accuracy and efficiency. Combining with FMM the boundary element method become suitable to deal with large-scale practical engineering and scientific problems. The first author has been involved in the research on boundary element methods since 1979. The BEM is regarded as an important complement of the widely-applied FEM, but if the BEM is only capable to obtain the same results as obtained by FEM, such complement was not necessary. For the complement it is important to do something, which FEM could not do, or do something significantly better than FEM. The development of FMBEM have shown good prospects at this aspect. FMBEM have been successfully applied in the field of MEMS design and electro-magnetic field analysis. In the field of solid mechanics, the most important thing is to develop practical applications of FMBEM. The further investigation in authors' group is concentrated on several topics, including FMBEM of elasto-plasticity problems, thin structure problems, dynamic and coupling problems. Acknowledgements Financial support for the projects from the National Natural Science Foundation of China, under grant No. 10172053, 10472051 is gratefully acknowledged. REFERENCES 1. Rokhlin V. Rapid solution of integral equations of classical potential theory. J. Comput. Phys., 1985; 60: 187-207. 2. Greengard L, Rokhlin V. A fast algorithm for particle simulations. J. Comput. Phys., 1987; 73: 325-348. 3. Greengard L, Rokhlin V. A new version of the fast multipole method for the Laplace equation in three dimensions. Acta Numerica, 1997; 6: 229-269. 4. Nishimura N. Fast multipole accelerated boundary integral equation methods. Applied Mechanics Review, 2002; 55: 299-324. 5. Peirce AP, Napier JAL. A spectral multipole method for efficient solutions of large scale boundary element models in elastostatics. Int. J. Numer. Meth. Engng., 1995; 38: 4009-4034. 6. Yoshida K, Nishimura N, Kobayashi S. Application of new fast multipole boundary integral equation method to crack problems in 3D. Engrg. Anal. Boundary Elements, 2001; 25: 239-247. 7. Wang HT, Yao ZH. Application of a new fast multipole BEM for simulation of 2D elastic solid with large number of inclusions. Acta Mechanica Sinica, 2004; 20: 613-622. 8. Wang PB, Yao ZH, Wang HT. Fast multipole BEM for simulation of 2-D solids containing large numbers of cracks. Tsinghua Science and Technology, 2005; 10: 76-81. 9. Wang HT, Yao ZH. A new fast multipole boundary element method for large scale analysis of mechanical properties in 3D particle-reinforced composites. Comput. Model, in Engrg & Sciences, 2005; 7: 85-96. 10. Wang HT, Yao ZH, Wang PB. On the preconditioners for fast multipole boundary element methods for 2D multi-domain elastostatics. Engrg. Anal. Boundary Elements, 2005; 29: 673-688. 11. Wang PB, Yao ZH. Fast multipole DBEM analysis of fatigue crack growth. Comput. Mech., in press. 12. Lei T, Yao ZH, Wang HT, Wang PB. A parallel fast multipole BEM and its applications to large-scale analysis of 3-D fiber-reinforced composites. Acta Mechanica Sinica, in press. 13. Warren MS, Salmon JK. A parallel hashed oct-trees N-body algorithm, in Proc. Supercomputing' 93, Portland, Oregon, US, 1993, pp. 12-21. 14. Liu YJ, Nishimura N, Otani Y. Large-scale modeling of carbon-nanotube composites by a fast multipole boundary element method. Comput. Materials Science, 2005; 34: 173-187. 15. Isida M. Effects of width and length on stress intensity factor for the tension of internal cracked plates under various boundary conditions. Int. J. Fract. Mech., 1971; 7: 301-306. 16. Portela A, Aliabadi MH, Rooke DP. Dual boundary element incremental analysis of crack propagation. Comput. Struct., 1993; 46: 237-247. 17. Feng XQ, Yu SW. Estimate of effective elastic moduli with microcrack interaction effects. Theor. Appl. Fract. Mech., 2000; 34: 225-233. — 34 —

COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer

Optimization and Robustness of Deformable Systems with Randomness I. Doltsinis1*, Z.Kang 2 1 2

Faculty of Aerospace Engineering and Geodesy, University of Stuttgart, 70569 Stuttgart, Germany State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, 116024 Dalian, China

Email: [email protected] Abstract Synthetic Monte Carlo sampling and analytic Taylor series expansion offer two different techniques for the treatment of random input scatter. The paper expounds on the Taylor series approximation as applied to the stochastic analysis and design optimization of structures and deforming solids, including robustness against uncertainties. A unified approach is presented starting with linear elastic structures, extending to nonlinear and path dependent response, and progressing to deformation processes of inelastic solids. The methodology refers to finite element systems, and assumes that the response is a continuous function of the input; representation of the probability distribution is restricted to mean and variance. The approach is applicable to input scatter of practical relevance and is computationally efficient; its analytic nature allows utilization of optimization algorithms. Key words: Stochastic optimization, robust design, structures, deformation processes, Taylor series approach INTRODUCTION The present account addresses the design of deformable mechanical systems, from linear elastic structures to inelastic solids. The randomness inherent to input parameters induces fluctuations of the performance. Characterization by mean and variance demands the determination of these two quantities for the output. An expansion by Taylor series about the mean input is used for the approximation of the mean response to the second order, and of the variance to the first order. The method requires continuity between input and output variables, and allows only restricted representation of the probability distribution as by the two first moments. The procedure covers input scatter of practical relevance and is computationally efficient. The random variability of the performance entails considerations on design optimization different from deterministic. If only the mean is targeted, the statement of the optimization problem and its algorithmic treatment are as in the deterministic counterpart, but the participating quantities result from the analysis of the stochastic case. Apart from best performance in the mean, least variability is frequently requested as well. Then the design variables are to be specified such that the system is not sensitive to the scatter of the input. This is the issue of robust optimum design which demands observation of both the mean value and the variance of the objective function. The analysis formalism is developed for the finite element representation of deformation problems. The case of linear elastic structures [1] exemplifies the determination of mean response and variance. In addition, the computation of sensitivity expressions with respect to the design variables is pursued, which allows employment of gradient based optimization algorithms. Advancing the theory, nonlinear structures with path dependent response as in elastoplasticity are treated by incrementation [2]. The stochastic analysis is executed consistently, equally the formulation of the design sensitivity expressions. At the end, deformation processes of inelastic solids are considered [3], which require attention to propagating fluctuations. The stochastic problem is stated for nonlinear viscous solids and is considered under station­ ary conditions as well as for unsteady deformation. The proposed computational technique complies with an iterative solution basing on the secant matrix of the system in which case a tangent operator is not available. The theoretical exposition is complemented by numerical examples elucidating robust design. A software package available in the internet [4] is used to solve the optimization problem in conjunction with the input supplied by the stochastic analysis. The optimization software is based on sequential quadratic programming. — 35 —

DESIGN OPTIMIZATION, ROBUSTNESS The purpose of engineering design is the achievement of a certain performance of the product. If design variations are possible, optimization can be envisaged with respect to specified objectives. The following deals with solids and structures as deformable systems represented by finite elements. The response to applied actions is defined by the TV displacements of the mesh nodal points of the discretized object, in the TV x 1 vector u(z). It is considered in dependence of a set of/? design parameters in the p x 1 vector z = {z\ • • -zp} which are disposable in optimization. Optimum design will be attempted by minimizing a scalar objective function which defines the posed requirements: /0(z)=/[u(z),z]. The minimum off0(z)

(1) specifies the values of the design parameters z. Formally,

find z minimizing f0(z) subject to gclr (z) < 0, and

/ = 1, • • •, k

ZL