Kuczma / Wilmanski Computer Methods in Mechanics

Lectures of the CMM 2009
1. Auflage 2010
ISBN: 978-3-642-05241-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 1, 528 Seiten

Reihe: Advanced Structured Materials

Prominent scientists present the latest achievements in computational methods and mechanics in this book. These lectures were held at the CMM 2009 conference.

Autoren/Hrsg.

Kuczma, Mieczyslaw

Wilmanski, Krzysztof

Inhaltsverzeichnis

1;Foreword;6
2;Preface;13
3;Contents;16
4;Part I Mathematical Methods;27
4.1;Explicit Discrete Dispersion Relations for the AcousticWave Equation in d-Dimensions Using Finite Element, Spectral Element and Optimally Blended Schemes;28
4.1.1;Introduction;28
4.1.2;AcousticWave Equation;30
4.1.2.1;Continuous Dispersion Relation;30
4.1.2.2;Framework for Discrete Dispersion Relation;31
4.1.3;Higher Order Discrete Dispersion Relations for Finite Element, Spectral Element and Optimally Blended Schemes in d-Dimensions;33
4.1.3.1;Standard Finite Element Scheme;33
4.1.3.2;Spectral Element Scheme;35
4.1.3.3;Optimally Blended Scheme;36
4.1.4;Numerical Examples;38
4.1.5;References;42
4.2;hp-Adaptive Finite Elements for Coupled Multiphysics Wave Propagation Problems;43
4.2.1;Introduction;43
4.2.2;Examples of Coupled Multiphysics Problems;44
4.2.2.1;Dual Mixed Formulation for Elasticity with Weakly Imposed Symmetry;44
4.2.2.2;Acoustics Coupled with (visco-)Elasticity;50
4.2.2.3;Coupled Acoustics and Poroelasticity;53
4.2.2.4;Exact Sequence and the de Rham Diagram;56
4.2.3;hp Technology;56
4.2.3.1;Handling Multiphysics;57
4.2.3.2;Constrained Approximation;58
4.2.3.3;Automatic hp Adaptivity;59
4.2.4;Numerical Examples;60
4.2.4.1;Mixed-Dual Elasticity;60
4.2.4.2;The Streamer Problem;62
4.2.4.3;Modeling of Sonic Tools;64
4.2.5;Conclusions;65
4.2.6;References;66
4.3;Nonconvex Inequality Models for Contact Problems of Nonsmooth Mechanics;67
4.3.1;Introduction;67
4.3.2;Physical Setting of Dynamic Viscoelastic Problem;69
4.3.3;Integrodifferential Hemivariational Inequalities and Viscoelastic Frictional Contact;74
4.3.4;Thermoviscoelastic Frictional Contact Problem;74
4.3.5;Bilateral Frictional Contact Problem in Viscoelasticity;76
4.3.6;Bilateral Contact Problem for Viscoelastic Piezoelectric Materials with Adhesion;77
4.3.7;Comments on Other Nonconvex Inequality Models;79
4.3.8;References;80
4.4;Quadrature for Meshless Methods;83
4.4.1;Introduction;83
4.4.2;First Analysis;85
4.4.2.1;Preliminaries;85
4.4.2.2;An Example / Numerical Results;86
4.4.2.3;Theoretical Results;88
4.4.2.4;Numerical Results;90
4.4.3;Second Analysis;91
4.4.3.1;Preliminaries;91
4.4.3.2;Theoretical Results;94
4.4.3.3;Numerical Results;94
4.4.4;Comparison of the Results of the Two Analyzes;97
4.4.5;References;97
4.5;Shape and Topology Sensitivity Analysis for Elastic Bodies with Rigid Inclusions and Cracks;98
4.5.1;Introduction;99
4.5.1.1;Cracks and Rigid Inclusions;99
4.5.2;Problem Formulation;100
4.5.2.1;Dual Problem Formulation;103
4.5.2.2;Passage from Elastic Inclusion to Rigid Inclusion;104
4.5.3;Topological Asymptotic Analysis;106
4.5.3.1;Domain Decomposition;108
4.5.3.2;Shape Sensitivity Analysis of the Energy Functional;109
4.5.3.3;Topological Derivatives Calculation;110
4.5.3.4;Approximation of Solutions for Variational Inequalities;117
4.5.4;References;120
4.6;A Boundary Integral Equation on the Sphere for High-Precision Geodesy;122
4.6.1;Boundary Integral Equation;122
4.6.2;Meshless Galerkin Method with Boundary Integral Equations;126
4.6.3;Numerical Example;128
4.6.4;Conclusion;133
4.6.5;References;133
4.7;Unresolved Problems of Adaptive Hierarchical Modelling and hp-Adaptive Analysis within Computational Solid Mechanics;134
4.7.1;Introduction;134
4.7.1.1;Considered Problems of Solid Mechanics;135
4.7.1.2;Considered Types of Complexity within the Elastic Bodies;138
4.7.2;Assessed Methodology;140
4.7.2.1;3D-Based Hierarchy of Numerical Models;141
4.7.2.2;Error Estimation;146
4.7.2.3;Adaptive Strategy;148
4.7.2.4;Possibility of Other Approaches;149
4.7.3;Chosen Problems to Be Resolved and Some Remedies;150
4.7.3.1;Hierarchical Modelling Issues;150
4.7.3.2;Problems within hp-Approximation;152
4.7.3.3;A Posteriori Error Estimation;155
4.7.3.4;A Posteriori Detection of the Undesired Phenomena;159
4.7.4;Conclusions;166
4.7.5;References;166
5;Part II Soft Computing and Optimization;169
5.1;Granular Computing in Evolutionary Identification;170
5.1.1;Introduction;171
5.1.2;Formulation of the Granular Identification Problem;171
5.1.2.1;Identification of Voids in Dynamical Systems;172
5.1.2.2;Identification of Boundary Conditions inThermo–Mechanical Systems;173
5.1.2.3;Identification of Elastic Constants in Laminates;174
5.1.3;Two–Stage Granular Strategy;175
5.1.3.1;The Global Optimization Stage;176
5.1.3.2;The Local Optimization Stage;176
5.1.4;Numerical Examples;178
5.1.4.1;Identification of Void;178
5.1.4.2;Identification of Boundary Conditions;179
5.1.4.3;Identification of Laminates’ Elastic Constants;181
5.1.5;Final Conclusions;183
5.1.6;References;184
5.2;Immune Computing: Intelligent Methodology and Its Applications in Bioengineering and Computational Mechanics;185
5.2.1;Introduction;185
5.2.2;Immunology as a Metaphor for Computational Information Processing;186
5.2.3;Applications of AIS in Computational Bioengineering;188
5.2.3.1;Negative Selection;188
5.2.3.2;Clonal Selection;190
5.2.3.3;Two Level Immune Classification of ECG Signals;191
5.2.3.4;Results of Feature Selection and Classification of ECG Signals;191
5.2.4;Applications in Computational Mechanics;194
5.2.4.1;Immune Optimization;194
5.2.4.2;Formulation of Immune Topology Optimization of Structures;195
5.2.4.3;Numerical Examples of Immune Topology Optimization;198
5.2.5;Conclusions;201
5.2.6;References;201
5.3;Bioinspired Algorithms in Multiscale Optimization;202
5.3.1;Introduction;202
5.3.2;The Multiscale Model;203
5.3.3;The Optimization Problem Formulation;204
5.3.4;The Bioinspired Optimization Algorithms;204
5.3.5;Numerical Example;207
5.3.6;Conclusions;210
5.3.7;References;210
5.4;Sensor Network Design for Spatio–Temporal Prediction of Distributed Parameter Systems;212
5.4.1;Introduction;212
5.4.2;Optimal Sensor Location Problem;214
5.4.2.1;Quantification of Prediction Accuracy;214
5.4.2.2;Problem of Finding Optimal Sensor Densities;216
5.4.3;Reduction to a Weight Optimization Problem;218
5.4.4;Simplicial Decomposition for Problem 2;219
5.4.4.1;Algorithm Model;219
5.4.4.2;Termination Criterion for Algorithm;220
5.4.4.3;Solution of the Column Generation Subproblem;221
5.4.4.4;Solution of the Restricted Master Subproblem;221
5.4.5;Computer Example;223
5.4.6;Concluding Remarks;225
5.4.7;References;226
6;Part III Multiscale Methods;227
6.1;A Multiscale Molecular Dynamics / Extended Finite Element Method for Dynamic Fracture;228
6.1.1;Introduction;228
6.1.2;Molecular Dynamics;230
6.1.2.1;Governing Equations in the Atomistic Domain;230
6.1.2.2;Equilibrium of the Atomistic Domain;231
6.1.3;Continuum Model;232
6.1.4;Coupling Scheme;234
6.1.4.1;Coupling Functions;234
6.1.4.2;Discretized Problem;235
6.1.4.3;Time Integration Scheme;237
6.1.4.4;Energy Transfer between the Atomistics and ContinuumDomains;239
6.1.5;Dynamic Fracture;241
6.1.5.1;Mechanical Quantities in the Atomistic Domain;241
6.1.5.2;Examples: Crack Propagation under Velocity Loading;242
6.1.6;Concluding Remarks;249
6.1.7;References;251
6.2;Nonlinear Finite Element and Atomistic Modelling of Dislocations in Heterostructures;255
6.2.1;Introduction;255
6.2.2;Continuum Theory of Discrete Dislocations;256
6.2.2.1;Burgers Vector;257
6.2.2.2;Analytical Equations for Mixed Straight Dislocation;258
6.2.3;Atomistic Reconstruction of Dislocations;259
6.2.3.1;HRTEM Investigations of Partial Dislocations in GaN;259
6.2.4;Misfit Dislocations in Heterostructure GaN/Al2O3;261
6.2.4.1;Crystallographic Model;261
6.2.4.2;Finite Element Modelling of Misfit Dislocations;263
6.2.4.3;Reconstruction of 3D Structure into FEA;265
6.2.5;Conclusions;267
6.2.6;References;268
6.3;Accuracy and Robustness of a 3-D Brick Cosserat Point Element (CPE) for Finite Elasticity;270
6.3.1;Introduction;271
6.3.2;Basic Equations of the CPE Using the Bubnov-Galerkin Approach;272
6.3.3;Constitutive Equations of the CPE Using the Direct Approach;276
6.3.4;Restrictions Associated with a Nonlinear form of the Patch Test;278
6.3.5;Determination of the Constitutive Coefficients;279
6.3.6;Examples Demonstrating Accuracy of the CPE;280
6.3.7;Examples Demonstrating Robustness of the CPE;281
6.3.8;References;283
6.4;Possibilities of the Particle Finite Element Method in Computational Mechanics;285
6.4.1;Introduction;286
6.4.2;The Basis of the Particle Finite Element Method;287
6.4.2.1;Basic Steps of the PFEM;288
6.4.3;FIC/FEM Formulation for a Lagrangian Incompressible Thermal Fluid;290
6.4.3.1;Governing Equations;290
6.4.3.2;Discretization of the Equations;292
6.4.4;Overview of the Coupled FSI Algoritm;294
6.4.5;Generation of a New Mesh;297
6.4.6;Identification of Boundary Surfaces;298
6.4.7;Treatment of Contact Conditions in the PFEM;299
6.4.7.1;Contact between the Fluid and a Fixed Boundary;299
6.4.7.2;Contact between Solid-Solid Interfaces;301
6.4.8;Modeling of Bed Erosion;302
6.4.9;Examples;306
6.4.9.1;Rigid Objects Falling into Water;306
6.4.9.2;Impact of Water Streams on Rigid Structures;308
6.4.9.3;Dragging of Objects by Water Streams;308
6.4.9.4;Impact of Sea Waves on Piers and Breakwaters;309
6.4.9.5;Erosion of a 3D Earth Dam Due to an Overspill Stream;311
6.4.9.6;Melting and Spread of Polymer Objects in Fire;311
6.4.10;Conclusions;317
6.4.11;References;320
6.5;A Framework for the Two-Scale Homogenization of Electro-Mechanically Coupled Boundary Value Problems;325
6.5.1;Introduction;325
6.5.2;Boundary Value Problems on the Macro- and the Mesosca;327
6.5.2.1;Macroscopic Electro-Mechanically Coupled BVP;327
6.5.2.2;Mesoscopic Electro-Mechanically Coupled BVP;328
6.5.3;Effective Properties of Piezoelectric Materials;330
6.5.4;Numerical Examples;335
6.5.4.1;Material Parameters and Invariant Formulation;335
6.5.4.2;Numerical Investigation of Two-Dimensional Mesostructure;337
6.5.4.3;Determination of Effective Electro-Mechanical Moduli of a Three-Dimensional Voided Mesostructure;339
6.5.5;Conclusion;340
6.5.6;References;340
7;Part IV Geomechanics;344
7.1;Modeling Concrete at Early Age Using Percolation;345
7.1.1;Introduction;346
7.1.2;Hydration Models;347
7.1.2.1;Powers Model [5];347
7.1.2.2;Jennings and Tennis Model [6];347
7.1.2.3;Comparison of the Two Models;349
7.1.2.4;Generation of the Microstructure;349
7.1.3;Percolation;350
7.1.4;Evolution of Poro-Mechanical Properties;351
7.1.5;Autogenous Shrinkage;354
7.1.6;Conclusions;356
7.1.7;References;356
7.2;Simulation of Incompressible Problems in Geomechanics;359
7.2.1;Introduction;359
7.2.2;Weak Formulation for MPM and FEM;361
7.2.3;Explicit Solution Scheme;362
7.2.4;Dynamic Relaxation;363
7.2.5;Numerical Challenges with MPM;364
7.2.6;Implicit Mesh-Free Dynamic Analysis;365
7.2.7;Overcoming Limitations of Low Order;366
7.2.8;Example - Slope Stability;367
7.2.9;Treatment of Pore Pressure Generation;369
7.2.9.1;Scheme A;369
7.2.9.2;Scheme B;370
7.2.10;Example - Pore Pressure Generation under a Footing;371
7.2.11;Concluding Remarks;372
7.2.12;References;373
7.3;Effect of Boundary, Shear Rate and Grain Crushing on Shear Localization in Granular Materials within Micro-polar Hypoplasticity;374
7.3.1;Introduction;374
7.3.2;Micro-polar Hypoplastic Model;375
7.3.3;Boundary Effects on Behaviour of Granular Material;375
7.3.4;Effect of Shear Rate;380
7.3.5;Effect of Grain Crushing;383
7.3.6;Conclusions;386
7.3.7;References;386
8;Part V Biomechanics;388
8.1;Biomechanical Basis of Tissue–Implant Interactions;389
8.1.1;Introduction;389
8.1.2;Material and Method;390
8.1.3;Results;394
8.1.4;Conclusion;398
8.1.5;References;399
8.2;Tooth-Implant Life Cycle Design;401
8.2.1;Introduction;402
8.2.2;Motivation;403
8.2.3;Numerical Simulation of Dental Implantsn;405
8.2.3.1;Model;405
8.2.3.2;FE Analyses - Strength Analyses;413
8.2.3.3;Fatigue Calculations - Strain-Life Approach;414
8.2.3.4;Screw Loosing Simulation;419
8.2.4;Optimization Using Genetic Based Algorithms;420
8.2.4.1;Optimization Algorithm - Genetic Algorithm;421
8.2.4.2;Goal;422
8.2.4.3;Design Parameters;422
8.2.4.4;Constraints;423
8.2.4.5;Genetic Algorithm Settings;424
8.2.4.6;Incorporation of the Genetic Algorithm into Abaqus/CAE;425
8.2.4.7;Results;427
8.2.5;Conclusions;430
8.2.6;References;430
8.3;Predictive Modelling in Mechanobiology: Combining Algorithms for Cell Activities in Response to Physical Stimuli Using a Lattice-Modelling Approach;433
8.3.1;Introduction;433
8.3.2;A Lattice-Based Mechanobiological Model;435
8.3.2.1;Simulation of Cellular Activity;435
8.3.2.2;Computational Implementation;438
8.3.3;Applications;439
8.3.3.1;Bone Fracture Healing;439
8.3.3.2;Tissue Regeneration Inside a Scaffold;440
8.3.4;Discussion and Perspective;442
8.3.5;References;443
9;Part VI Structural Mechanics;446
9.1;The Beam-to-Beam Contact Smoothing with Bezier’s Curves and Hermite’s Polynomials;447
9.1.1;Introduction;447
9.1.2;Frictional Beam-to-Beam Contact;448
9.1.3;3D Curve Smoothing Procedures;452
9.1.4;Finite Element Discretization;454
9.1.5;Numerical Examples;456
9.1.6;Conclusion;459
9.1.7;References;460
9.2;Synergic Combinations of Computational Methods and Experiments for Structural Diagnoses;461
9.2.1;Introduction;462
9.2.2;Local Diagnostic Analyses of Concrete Dams;463
9.2.2.1;Preliminary Remarks;463
9.2.2.2;Tests on Dam Surfaces by Flat-Jacks;464
9.2.2.3;Dilatometric Tests in Depth;470
9.2.3;Diagnostic Analysis of Metallic Industrial Components;473
9.2.3.1;Assessments of Material Parameters by Indentation;473
9.2.3.2;Assessment of Residual Stresses by Indentations;479
9.2.4;Closing Remarks;481
9.2.5;References;482
9.3;Optimization of Marine Propulsion System’s Alignment for Aged Ships;485
9.3.1;Introduction;485
9.3.2;Methodology of Shaft Line Alignment;487
9.3.3;Assumption Influence on Analysis Results;490
9.3.4;Identification Method;491
9.3.5;Software Description;493
9.3.6;Analysis Example for the Container Ship;494
9.3.7;Identification of the Middle-Speed Propulsion System;496
9.3.8;Summary;497
9.3.9;References;498
9.4;Experimental-Numerical Assessment of Impact-Induced Damage in Cross-Ply Laminates;500
9.4.1;Introduction;500
9.4.2;Experimental Campaign;501
9.4.3;Numerical Model;504
9.4.4;Results;507
9.4.5;Closing Remarks;509
9.4.6;References;510
9.5;Finite Element Modeling of Stringer-Stiffened Fiber Reinforced Polymer Structures;512
9.5.1;Introduction;512
9.5.2;Intralaminar Damage;513
9.5.2.1;Transverse Isotropy;514
9.5.2.2;Damage Initiation;514
9.5.2.3;Damage Propagation;516
9.5.2.4;Validation Example;518
9.5.3;Interlaminar Damage;520
9.5.3.1;Interface Element;521
9.5.3.2;Cohesive Zone Model;523
9.5.3.3;Validation Example;524
9.5.4;Conclusions;527
9.5.5;References;528
10;Index;531