Ibrahimbegovic Computational Methods for Solids and Fluids

Multiscale Analysis, Probability Aspects and Model Reduction
1. Auflage 2016
ISBN: 978-3-319-27996-1
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 41, 497 Seiten

Reihe: Computational Methods in Applied Sciences

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.
  

Autoren/Hrsg.

Ibrahimbegovic, Adnan

Inhaltsverzeichnis

1;Preface;6
2;Contents;12
3;Multiscale Analysis as a Central Component of Urban Physics Modeling;14
3.1;1 Introduction;14
3.2;2 Urban Physics: A State of the Art;15
3.2.1;2.1 From Environmental Physics;15
3.2.2;2.2 From Urban Planning;16
3.2.3;2.3 From Building Physics;16
3.2.4;2.4 From Smart City;17
3.3;3 Urban Physics: A New Framework;17
3.3.1;3.1 The City as an Interface;17
3.3.2;3.2 Multiband Aspects of the Radiation Interacting with the Cities;18
3.3.3;3.3 Shortwave;20
3.3.4;3.4 Long Waves;21
3.4;4 Computational Model;22
3.4.1;4.1 The Simplest Model;23
3.4.2;4.2 View Factors;26
3.4.3;4.3 Radiosity Equations;27
3.4.4;4.4 Neumann Series;31
3.5;5 Coupling Short and Long Waves in Transient Situations;33
3.5.1;5.1 Improving the Performances of the Finite Element Solution Using Super Elements;35
3.5.2;5.2 Other Aspects of the City Behavior Simulation;35
3.6;6 Conclusion;35
3.7;References;37
4;A Path-Following Method Based on Plastic Dissipation Control;41
4.1;1 Introduction;41
4.2;2 Path-Following Method Framework;43
4.3;3 Dissipation Constraint for Geometrically Nonlinear Small Strain Elasto-plasticity;44
4.3.1;3.1 Explicit Formulation---Version 1;45
4.3.2;3.2 Explicit Formulation---Version 2;47
4.3.3;3.3 Implicit Formulations;48
4.4;4 Dissipation Constraint for Embedded Discontinuity Finite Elements;49
4.5;5 Numerical Examples;53
4.5.1;5.1 Geometrically Nonlinear Elasto-plastic Shell Analysis;53
4.5.2;5.2 Failure of Steel Frame;54
4.6;6 Conclusions;57
4.7;References;58
5;Improved Implicit Immersed Boundary Method via Operator Splitting;60
5.1;1 Introduction;60
5.2;2 Methodology;62
5.2.1;2.1 Overview of the Immersed Boundary Methods;63
5.2.2;2.2 Moving Immersed Boundary Method;65
5.3;3 Numerical Results;67
5.3.1;3.1 Flow over a Stationary Circular Cylinder;67
5.3.2;3.2 Flow over an Oscillating Circular Cylinder;71
5.4;4 Conclusions;76
5.5;References;76
6;Modelling Wave Energy Conversion of a Semi-submerged Heaving Cylinder;78
6.1;1 Introduction;78
6.2;2 Problem Formulation;79
6.2.1;2.1 Fluid Equations;79
6.2.2;2.2 Rigid Body Equations of Motion;80
6.2.3;2.3 Boundary Conditions and Wave Generation;81
6.2.4;2.4 Pressure-Velocity Decoupling Algorithm;84
6.2.5;2.5 Fluid-Structure Interaction;86
6.3;3 Energy Extraction;88
6.4;4 Conclusions;89
6.5;References;89
7;Multiscale Modeling of Imperfect Interfaces and Applications;91
7.1;1 Introduction;92
7.2;2 Imperfect Interface Approach;95
7.2.1;2.1 Matched Asymptotic Expansion Method;95
7.2.2;2.2 Homogenization in Non-interacting Approximation (NIA) for Microcracked Media;107
7.3;3 A St. Venant-Kirchhoff Imperfect Interface Model;114
7.3.1;3.1 Matched Asymptotic Expansion Method in Finite Strains;114
7.3.2;3.2 Homogenization of the Microcracked Interphase;122
7.4;4 Numerical Applications;123
7.5;5 Conclusions;129
7.6;References;130
8;A Stochastic Multi-scale Approach for Numerical Modeling of Complex Materials---Application to Uniaxial Cyclic Response of Concrete;133
8.1;1 Introduction;133
8.2;2 Multi-scale Stochastic Approach for Modeling Concrete;136
8.2.1;2.1 Homogenized Material Behavior at Macroscale;137
8.2.2;2.2 Material Behavior Law at E-mesoscale;138
8.2.3;2.3 Stochastic Modeling of Heterogeneous E-mesoscale;143
8.3;3 Numerical Implementation;148
8.3.1;3.1 Random Vector Fields Generation Using FFT;148
8.3.2;3.2 Material Response at Mesoscale;149
8.3.3;3.3 Material Response at Macroscale;151
8.4;4 Numerical Applications;154
8.4.1;4.1 1D Homogenized Response at Macroscale;155
8.4.2;4.2 Heterogeneous Structure at E-mesoscale;156
8.4.3;4.3 Concrete Response in Uniaxial Compressive Cyclic Loading;160
8.5;5 Conclusion;164
8.6;Appendix 1;165
8.7;References;168
9;Relating Structure and Model;171
9.1;1 Introduction;171
9.2;2 Scaling;173
9.2.1;2.1 Scaling in Parameter Space;173
9.2.2;2.2 Scaling in Measurement Space;174
9.2.3;2.3 Scaling of Dynamically Loaded Structures;174
9.3;3 Loading Reconstruction;175
9.3.1;3.1 Treatment of Measurement Noise;176
9.3.2;3.2 Static Loading;176
9.3.3;3.3 Dynamic Loading;177
9.4;4 Examples;178
9.4.1;4.1 Scaling in Parameter Space;179
9.4.2;4.2 Scaling in Measurement Space;180
9.4.3;4.3 Scaling of Dynamic Properties;181
9.4.4;4.4 Force Reconstruction---Static Loading;181
9.4.5;4.5 Force Reconstruction---Dynamic Loading;183
9.5;5 Discussion and Conclusion;192
9.6;References;193
10;Fat Latin Hypercube Sampling and Efficient Sparse Polynomial Chaos Expansion for Uncertainty Propagation on Finite Precision Models: Application to 2D Deep Drawing Process;194
10.1;1 Introduction;195
10.2;2 FEM Error Assessment Using Finite Difference Scheme;197
10.3;3 Introduction to Polynomial Chaos Expansion;197
10.4;4 Sampling Scheme Taking into Account Model Resolution;200
10.4.1;4.1 Implementation of the Fat-LHS;201
10.5;5 Sparse PCE Models for Restricted Training Sets;203
10.5.1;5.1 Truncating Multi-variate Polynomials Expansion;203
10.5.2;5.2 Combining Q-norm and LARS;205
10.5.3;5.3 Error Evaluation of the Polynomial Expansion;206
10.6;6 Results and Discussions;207
10.6.1;6.1 Analytical Example;207
10.6.2;6.2 2D Deep Drawing Process;210
10.7;7 Conclusions and Prospects;219
10.8;References;220
11;Multiscale Atomistic-to-Continuum Reduced Models for Micromechanical Systems;223
11.1;1 Introduction;223
11.1.1;1.1 Models at Atomistic Scale;224
11.1.2;1.2 Concurrent Atomistic-to-Continuum Methods;225
11.2;2 Problem Definition with Multiple Scales;227
11.2.1;2.1 Atomistic Model Problem;227
11.2.2;2.2 QC and BD Formulations;229
11.3;3 Comparison and Unified Formulation with Reduced Model;239
11.3.1;3.1 Unified Coupling Formulation;240
11.4;4 Numerical Example;241
11.4.1;4.1 Error Convergence;245
11.5;5 Conclusion;247
11.6;References;247
12;Inverse Problems in a Bayesian Setting;252
12.1;1 Introduction;252
12.2;2 Bayesian Updating;256
12.2.1;2.1 Setting;256
12.2.2;2.2 Recollection of Bayes's Theorem;259
12.2.3;2.3 Conditional Expectation;260
12.3;3 Characterising the Posterior;267
12.3.1;3.1 The Posterior Distribution Measure;267
12.3.2;3.2 A Posterior Random Variable---Filtering;268
12.3.3;3.3 Approximations;273
12.4;4 Numerical Realisation;281
12.5;5 The Linear Bayesian Update;285
12.6;6 The Nonlinear Bayesian Update;288
12.7;7 Conclusion;291
12.8;References;292
13;Heterogeneous Materials Models, Coupled Mechanics-Probability Problems and Energetically Optimal Model Reduction;294
13.1;1 Introduction;295
13.2;2 Theoretical Formulation Heterogeneous Multiscale Method;297
13.2.1;2.1 State-of-the-art Developments;297
13.2.2;2.2 Meso-Scale Model of Material Heterogeneities With deterministic Material Parameters;298
13.2.3;2.3 Probability Aspects of Inelastic Localized Failure for Heterogenous Materials;302
13.3;3 Stochastic Fields Coupling;304
13.3.1;3.1 Heterogeneous Multiscale Model;305
13.3.2;3.2 Variational Low-Rank Approach with Successive Rank-1 Update (VLR-SR1U);306
13.3.3;3.3 Basic VLR-SR1U;307
13.3.4;3.4 VLR-OPT: Optimisation of Given Low-Rank Approximation;309
13.3.5;3.5 RBSSE: Adaptive Construction of the Stochastic Solution Space;311
13.3.6;3.6 Numerical Experiments;313
13.4;References;320
14;Modelling of Internal Fluid Flow in Cracks with Embedded Strong Discontinuities;321
14.1;1 Introduction;321
14.2;2 Numerical Model Formulations;325
14.2.1;2.1 Enhanced Kinematics;327
14.2.2;2.2 The Enhanced Weak Form;330
14.2.3;2.3 Constitutive Model;331
14.2.4;2.4 The Finite Element Equations of a Coupled Poroplastic Problem;334
14.2.5;2.5 The Operator Split Algorithm;336
14.3;3 Numerical Simulations;337
14.3.1;3.1 Preparation of 2D Plain Strain Rock Specimens;337
14.3.2;3.2 Influence of Heterogeneity in Tension and Compression Tests;339
14.3.3;3.3 Drained Compression Test of the Poro-plastic Sample with the Localized Failure;341
14.4;4 Conclusions;345
14.5;References;346
15;Reliability Calculus on Crack Propagation Problem with a Markov Renewal Process;348
15.1;1 Introduction and Motivation;348
15.2;2 The Model Settings and Elements of Markov Renewal Theory;352
15.2.1;2.1 Basic Definitions;352
15.2.2;2.2 Markov Renewal Process and Semi-Markov Kernel;354
15.2.3;2.3 Markov Renewal Equation;357
15.2.4;2.4 Further Model Settings;359
15.2.5;2.5 The Transition Probability Function of the PDMP and Its Markov Renewal Equation;362
15.2.6;2.6 Practical Calculation of Semi-Markov Kernel;365
15.3;3 Reliability Calculus;365
15.3.1;3.1 Previous Method on Reliability Calculus;366
15.3.2;3.2 A New Method on Reliability Calculus;366
15.3.3;3.3 Practical Implementation;371
15.4;4 Estimation of Reliability;373
15.5;5 Simulation Results;376
15.5.1;5.1 Simulation Results on a Given Example;376
15.5.2;5.2 Simulation Results on Experimental Data;377
15.6;6 Conclusions;380
15.7;References;381
16;Multi-scale Simulation of Newtonian and Non-Newtonian Multi-phase Flows;384
16.1;1 Introduction;384
16.2;2 Mathematical Background;385
16.2.1;2.1 Macro-Scale Equations;386
16.2.2;2.2 Micro-Scale Equations;389
16.3;3 Numerical Methods;391
16.3.1;3.1 Macro-Scale Discretization;391
16.3.2;3.2 Micro-Scale Discretization;394
16.3.3;3.3 Efficient Solution to the Cubic Equation in the FENE Model;395
16.4;4 Results for Imposed and Complex Flows;397
16.4.1;4.1 Newtonian Fluids;398
16.4.2;4.2 Non-Newtonian Fluids;399
16.5;5 Conclusions;401
16.6;References;401
17;Numerical Modeling of Flow-Driven Piezoelectric Energy Harvesting Devices;404
17.1;1 Introduction;404
17.1.1;1.1 Harvesting Mechanical Vibrations;406
17.1.2;1.2 Models of Piezoelectric Energy Harvesting Devices;407
17.2;2 Flow Driven Piezoelectric Energy Harvesters;409
17.3;3 Model of a Flow-Driven Piezoelectric EHD;410
17.3.1;3.1 Fluid;411
17.3.2;3.2 Piezoelectric Structure;412
17.3.3;3.3 Circuit;414
17.3.4;3.4 Coupling Conditions;414
17.4;4 Weak Form of the Governing Equations;415
17.4.1;4.1 Fluid;416
17.4.2;4.2 Structure;417
17.4.3;4.3 Piezoelectric Material;418
17.4.4;4.4 Circuit;418
17.5;5 Discretization with Space-Time Finite Elements;419
17.5.1;5.1 Elements and Space-Time Interpolation;419
17.5.2;5.2 Monolithic Solution Strategy;425
17.6;6 Numerical Example;426
17.6.1;6.1 Problem Setup;426
17.7;References;430
18;Comparison of Numerical Approaches to Bayesian Updating;432
18.1;1 Introduction;433
18.2;2 Model Problem;434
18.3;3 Identification via Bayesian Regularisation;435
18.4;4 Computational Approaches;439
18.4.1;4.1 Markov Chain Monte Carlo;439
18.4.2;4.2 Proxy Modelling;441
18.4.3;4.3 Linear Bayesian Inference;442
18.5;5 Numerical Results;445
18.5.1;5.1 One Dimensional Heat Problem;445
18.5.2;5.2 Two Dimensional Heat Problem;456
18.5.3;5.3 Forward Problem;457
18.5.4;5.4 Identification;457
18.6;6 Conclusions;461
18.7;References;465
19;Two Models for Hydraulic Cylinders in Flexible Multibody Simulations;467
19.1;1 Introduction;467
19.2;2 Equations of Motion;469
19.3;3 Coupled Multibody System;469
19.4;4 Finite Element Formulations;472
19.4.1;4.1 Truss-Element Cylinder;472
19.4.2;4.2 Bending Flexible Hydraulic Cylinders;479
19.4.3;4.3 Bending Flexible Hydraulic Cylinder with Friction;484
19.5;5 Integration of the Coupled Two-Field Problem;486
19.5.1;5.1 The Rosenbrock Method;486
19.6;6 Numerical Examples;488
19.6.1;6.1 Influence of the Stribeck Effect;488
19.6.2;6.2 Discussion;489
19.6.3;6.3 Sudden Stop of a Boom;491
19.6.4;6.4 System Responses with Friction;493
19.7;7 Concluding Remarks;495
19.8;References;496