Computational Methods for Solids and Fluids (eBook)

Multiscale Analysis, Probability Aspects and Model Reduction

Adnan Ibrahimbegovic (Herausgeber)

eBook Download: PDF

2016 | 1st ed. 2016
XII, 493 Seiten
Springer International Publishing (Verlag)
978-3-319-27996-1 (ISBN)

Infos

This volume contains the best papers presented at the 2nd ECCOMAS International Conference on Multiscale Computations for Solids and Fluids, held June 10-12, 2015. 

Topics dealt with include multiscale strategy for efficient development of scientific software for large-scale computations, coupled probability-nonlinear-mechanics problems and solution methods, and modern mathematical and computational setting for multi-phase flows and fluid-structure interaction. 

The papers consist of contributions by six experts who taught short courses prior to the conference, along with several selected articles from other participants dealing with complementary issues, covering both solid mechanics and applied mathematics.
  

Inhalt

Preface 6
Contents 12
Multiscale Analysis as a Central Component of Urban Physics Modeling 14
1 Introduction 14
2 Urban Physics: A State of the Art 15
2.1 From Environmental Physics 15
2.2 From Urban Planning 16
2.3 From Building Physics 16
2.4 From Smart City 17
3 Urban Physics: A New Framework 17
3.1 The City as an Interface 17
3.2 Multiband Aspects of the Radiation Interacting with the Cities 18
3.3 Shortwave 20
3.4 Long Waves 21
4 Computational Model 22
4.1 The Simplest Model 23
4.2 View Factors 26
4.3 Radiosity Equations 27
4.4 Neumann Series 31
5 Coupling Short and Long Waves in Transient Situations 33
5.1 Improving the Performances of the Finite Element Solution Using Super Elements 35
5.2 Other Aspects of the City Behavior Simulation 35
6 Conclusion 35
References 37
A Path-Following Method Based on Plastic Dissipation Control 41
1 Introduction 41
2 Path-Following Method Framework 43
3 Dissipation Constraint for Geometrically Nonlinear Small Strain Elasto-plasticity 44
3.1 Explicit Formulation---Version 1 45
3.2 Explicit Formulation---Version 2 47
3.3 Implicit Formulations 48
4 Dissipation Constraint for Embedded Discontinuity Finite Elements 49
5 Numerical Examples 53
5.1 Geometrically Nonlinear Elasto-plastic Shell Analysis 53
5.2 Failure of Steel Frame 54
6 Conclusions 57
References 58
Improved Implicit Immersed Boundary Method via Operator Splitting 60
1 Introduction 60
2 Methodology 62
2.1 Overview of the Immersed Boundary Methods 63
2.2 Moving Immersed Boundary Method 65
3 Numerical Results 67
3.1 Flow over a Stationary Circular Cylinder 67
3.2 Flow over an Oscillating Circular Cylinder 71
4 Conclusions 76
References 76
Modelling Wave Energy Conversion of a Semi-submerged Heaving Cylinder 78
1 Introduction 78
2 Problem Formulation 79
2.1 Fluid Equations 79
2.2 Rigid Body Equations of Motion 80
2.3 Boundary Conditions and Wave Generation 81
2.4 Pressure-Velocity Decoupling Algorithm 84
2.5 Fluid-Structure Interaction 86
3 Energy Extraction 88
4 Conclusions 89
References 89
Multiscale Modeling of Imperfect Interfaces and Applications 91
1 Introduction 92
2 Imperfect Interface Approach 95
2.1 Matched Asymptotic Expansion Method 95
2.2 Homogenization in Non-interacting Approximation (NIA) for Microcracked Media 107
3 A St. Venant-Kirchhoff Imperfect Interface Model 114
3.1 Matched Asymptotic Expansion Method in Finite Strains 114
3.2 Homogenization of the Microcracked Interphase 122
4 Numerical Applications 123
5 Conclusions 129
References 130
A Stochastic Multi-scale Approach for Numerical Modeling of Complex Materials---Application to Uniaxial Cyclic Response of Concrete 133
1 Introduction 133
2 Multi-scale Stochastic Approach for Modeling Concrete 136
2.1 Homogenized Material Behavior at Macroscale 137
2.2 Material Behavior Law at E-mesoscale 138
2.3 Stochastic Modeling of Heterogeneous E-mesoscale 143
3 Numerical Implementation 148
3.1 Random Vector Fields Generation Using FFT 148
3.2 Material Response at Mesoscale 149
3.3 Material Response at Macroscale 151
4 Numerical Applications 154
4.1 1D Homogenized Response at Macroscale 155
4.2 Heterogeneous Structure at E-mesoscale 156
4.3 Concrete Response in Uniaxial Compressive Cyclic Loading 160
5 Conclusion 164
Appendix 1 165
References 168
Relating Structure and Model 171
1 Introduction 171
2 Scaling 173
2.1 Scaling in Parameter Space 173
2.2 Scaling in Measurement Space 174
2.3 Scaling of Dynamically Loaded Structures 174
3 Loading Reconstruction 175
3.1 Treatment of Measurement Noise 176
3.2 Static Loading 176
3.3 Dynamic Loading 177
4 Examples 178
4.1 Scaling in Parameter Space 179
4.2 Scaling in Measurement Space 180
4.3 Scaling of Dynamic Properties 181
4.4 Force Reconstruction---Static Loading 181
4.5 Force Reconstruction---Dynamic Loading 183
5 Discussion and Conclusion 192
References 193
Fat Latin Hypercube Sampling and Efficient Sparse Polynomial Chaos Expansion for Uncertainty Propagation on Finite Precision Models: Application to 2D Deep Drawing Process 194
1 Introduction 195
2 FEM Error Assessment Using Finite Difference Scheme 197
3 Introduction to Polynomial Chaos Expansion 197
4 Sampling Scheme Taking into Account Model Resolution 200
4.1 Implementation of the Fat-LHS 201
5 Sparse PCE Models for Restricted Training Sets 203
5.1 Truncating Multi-variate Polynomials Expansion 203
5.2 Combining Q-norm and LARS 205
5.3 Error Evaluation of the Polynomial Expansion 206
6 Results and Discussions 207
6.1 Analytical Example 207
6.2 2D Deep Drawing Process 210
7 Conclusions and Prospects 219
References 220
Multiscale Atomistic-to-Continuum Reduced Models for Micromechanical Systems 223
1 Introduction 223
1.1 Models at Atomistic Scale 224
1.2 Concurrent Atomistic-to-Continuum Methods 225
2 Problem Definition with Multiple Scales 227
2.1 Atomistic Model Problem 227
2.2 QC and BD Formulations 229
3 Comparison and Unified Formulation with Reduced Model 239
3.1 Unified Coupling Formulation 240
4 Numerical Example 241
4.1 Error Convergence 245
5 Conclusion 247
References 247
Inverse Problems in a Bayesian Setting 252
1 Introduction 252
2 Bayesian Updating 256
2.1 Setting 256
2.2 Recollection of Bayes's Theorem 259
2.3 Conditional Expectation 260
3 Characterising the Posterior 267
3.1 The Posterior Distribution Measure 267
3.2 A Posterior Random Variable---Filtering 268
3.3 Approximations 273
4 Numerical Realisation 281
5 The Linear Bayesian Update 285
6 The Nonlinear Bayesian Update 288
7 Conclusion 291
References 292
Heterogeneous Materials Models, Coupled Mechanics-Probability Problems and Energetically Optimal Model Reduction 294
1 Introduction 295
2 Theoretical Formulation Heterogeneous Multiscale Method 297
2.1 State-of-the-art Developments 297
2.2 Meso-Scale Model of Material Heterogeneities With deterministic Material Parameters 298
2.3 Probability Aspects of Inelastic Localized Failure for Heterogenous Materials 302
3 Stochastic Fields Coupling 304
3.1 Heterogeneous Multiscale Model 305
3.2 Variational Low-Rank Approach with Successive Rank-1 Update (VLR-SR1U) 306
3.3 Basic VLR-SR1U 307
3.4 VLR-OPT: Optimisation of Given Low-Rank Approximation 309
3.5 RBSSE: Adaptive Construction of the Stochastic Solution Space 311
3.6 Numerical Experiments 313
References 320
Modelling of Internal Fluid Flow in Cracks with Embedded Strong Discontinuities 321
1 Introduction 321
2 Numerical Model Formulations 325
2.1 Enhanced Kinematics 327
2.2 The Enhanced Weak Form 330
2.3 Constitutive Model 331
2.4 The Finite Element Equations of a Coupled Poroplastic Problem 334
2.5 The Operator Split Algorithm 336
3 Numerical Simulations 337
3.1 Preparation of 2D Plain Strain Rock Specimens 337
3.2 Influence of Heterogeneity in Tension and Compression Tests 339
3.3 Drained Compression Test of the Poro-plastic Sample with the Localized Failure 341
4 Conclusions 345
References 346
Reliability Calculus on Crack Propagation Problem with a Markov Renewal Process 348
1 Introduction and Motivation 348
2 The Model Settings and Elements of Markov Renewal Theory 352
2.1 Basic Definitions 352
2.2 Markov Renewal Process and Semi-Markov Kernel 354
2.3 Markov Renewal Equation 357
2.4 Further Model Settings 359
2.5 The Transition Probability Function of the PDMP and Its Markov Renewal Equation 362
2.6 Practical Calculation of Semi-Markov Kernel 365
3 Reliability Calculus 365
3.1 Previous Method on Reliability Calculus 366
3.2 A New Method on Reliability Calculus 366
3.3 Practical Implementation 371
4 Estimation of Reliability 373
5 Simulation Results 376
5.1 Simulation Results on a Given Example 376
5.2 Simulation Results on Experimental Data 377
6 Conclusions 380
References 381
Multi-scale Simulation of Newtonian and Non-Newtonian Multi-phase Flows 384
1 Introduction 384
2 Mathematical Background 385
2.1 Macro-Scale Equations 386
2.2 Micro-Scale Equations 389
3 Numerical Methods 391
3.1 Macro-Scale Discretization 391
3.2 Micro-Scale Discretization 394
3.3 Efficient Solution to the Cubic Equation in the FENE Model 395
4 Results for Imposed and Complex Flows 397
4.1 Newtonian Fluids 398
4.2 Non-Newtonian Fluids 399
5 Conclusions 401
References 401
Numerical Modeling of Flow-Driven Piezoelectric Energy Harvesting Devices 404
1 Introduction 404
1.1 Harvesting Mechanical Vibrations 406
1.2 Models of Piezoelectric Energy Harvesting Devices 407
2 Flow Driven Piezoelectric Energy Harvesters 409
3 Model of a Flow-Driven Piezoelectric EHD 410
3.1 Fluid 411
3.2 Piezoelectric Structure 412
3.3 Circuit 414
3.4 Coupling Conditions 414
4 Weak Form of the Governing Equations 415
4.1 Fluid 416
4.2 Structure 417
4.3 Piezoelectric Material 418
4.4 Circuit 418
5 Discretization with Space-Time Finite Elements 419
5.1 Elements and Space-Time Interpolation 419
5.2 Monolithic Solution Strategy 425
6 Numerical Example 426
6.1 Problem Setup 426
References 430
Comparison of Numerical Approaches to Bayesian Updating 432
1 Introduction 433
2 Model Problem 434
3 Identification via Bayesian Regularisation 435
4 Computational Approaches 439
4.1 Markov Chain Monte Carlo 439
4.2 Proxy Modelling 441
4.3 Linear Bayesian Inference 442
5 Numerical Results 445
5.1 One Dimensional Heat Problem 445
5.2 Two Dimensional Heat Problem 456
5.3 Forward Problem 457
5.4 Identification 457
6 Conclusions 461
References 465
Two Models for Hydraulic Cylinders in Flexible Multibody Simulations 467
1 Introduction 467
2 Equations of Motion 469
3 Coupled Multibody System 469
4 Finite Element Formulations 472
4.1 Truss-Element Cylinder 472
4.2 Bending Flexible Hydraulic Cylinders 479
4.3 Bending Flexible Hydraulic Cylinder with Friction 484
5 Integration of the Coupled Two-Field Problem 486
5.1 The Rosenbrock Method 486
6 Numerical Examples 488
6.1 Influence of the Stribeck Effect 488
6.2 Discussion 489
6.3 Sudden Stop of a Boom 491
6.4 System Responses with Friction 493
7 Concluding Remarks 495
References 496

Produkt-Details

• Erscheint lt. Verlag: 12.2.2016
• Reihe/Serie: Computational Methods in Applied Sciences
• Reihe/Serie: Computational Methods in Applied Sciences
• Zusatzinfo: XII, 493 p. 224 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Coupled probability-mechanics problems • eccomas • large-scale computations • multi-physics problems • Multi-scale computations • Software development issues
• ISBN-10: 3-319-27996-3 / 3319279963
• ISBN-13: 978-3-319-27996-1 / 9783319279961