Murín / Kutiš / Kompis Computational Modelling and Advanced Simulations

1. Auflage 2010
ISBN: 978-94-007-0317-9
Verlag: Springer Netherlands
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 24, 366 Seiten

Reihe: Computational Methods in Applied Sciences

This book contains selected, extended papers presented at the thematic ECCOMAS conference on Computational Modelling and Advanced Simulations (CMAS2009) held in Bratislava, Slovakia, June 30 - July 3, 2009. Modelling and simulation of engineering problems play a very important role in the classic and new composite material sciences, and in design and computational prototyping of modern and advanced technologic parts and systems. According to this, the existing numerical methods have been improved and new numerical methods have been established for modelling and simulation of more and more complex and complicated engineering problems. The present book should contribute to the effort to make modelling and simulation more effective and accurate.

Autoren/Hrsg.

Kutiš, Vladimír

Kompiš, Vladimír

Murín, Justín

Kompis, Vladimír

Kutis, Vladimír

Inhaltsverzeichnis

1;Introduction;6
2;Contents;9
3;Contributors;11
4;1 Nonlinear Dynamic Analysis of Partially Supported Beam-Columns on Nonlinear Elastic Foundation Including Shear Deformation Effect;14
4.1;1.1 Introduction;15
4.2;1.2 Statement of the Problem;17
4.3;1.3 Integral Representation – Numerical Solution;24
4.3.1;1.3.1 For the Transverse Displacements v, w;24
4.3.2;1.3.2 For the Axial Displacement u;27
4.4;1.4 For the Stress Functions (y,z) and (y,z);28
4.5;1.5 Numerical Examples;29
4.5.1;1.5.1 Example 1;29
4.5.2;1.5.2 Example 2;30
4.5.3;1.5.3 Example 3;35
4.5.4;1.5.4 Example 4;37
4.5.5;1.5.5 Example 5;41
4.6;1.6 Concluding Remarks;42
4.7;References;44
5;2 Mechanics of Viscoelastic Plates Made of FGMs;46
5.1;2.1 Introduction;46
5.2;2.2 Governing Equations of a 5-Parametric Plate Theory;48
5.3;2.3 Effective Properties;50
5.4;2.4 Example of Effective Properties;52
5.4.1;2.4.1 Homogeneous Plate;52
5.4.2;2.4.2 FGM Plate;54
5.4.3;2.4.3 Sandwich Plate;57
5.5;2.5 Bending of a Symmetric Isotropic Plate;58
5.6;2.6 Conclusions;59
5.7;References;60
6;3 Indirect Trefftz Method for Solving Cauchy Problem of Linear Piezoelectricity;62
6.1;3.1 Introduction;62
6.2;3.2 Governing Equations of Linear Piezoelectricity;63
6.3;3.3 Indirect Trefftz Collocation Method;65
6.4;3.4 The Stroh Formalism and the T-Complete Functions;66
6.5;3.5 The Cauchy Inverse Problem Formulation;68
6.6;3.6 Numerical Examples;72
6.7;3.7 Conclusions;77
6.8;References;78
7;4 New Phenomenological Model for Solid Foams;79
7.1;4.1 Introduction;79
7.2;4.2 Modeling of Cellular Solids;81
7.2.1;4.2.1 Micromechanical Models;81
7.2.2;4.2.2 Phenomenological Models;84
7.3;4.3 New Phenomenological Model for Solid Foams;86
7.3.1;4.3.1 Foam Model;86
7.3.2;4.3.2 Model Solving;88
7.4;4.4 Compression Test of Polyurethane Foam;90
7.5;4.5 Model Application;90
7.6;4.6 Estimation of Stress-Strain Curve;91
7.7;4.7 Conclusion;93
7.8;References;94
8;5 The Effect of an Interphase on Micro-Crack Behaviour in Polymer Composites;95
8.1;5.1 Introduction;95
8.2;5.2 Estimation of the Composite Stiffness;97
8.2.1;5.2.1 Influence of Space Distribution;98
8.2.2;5.2.2 Influence of Aspect Ratio;98
8.3;5.3 Micro-Crack Behaviour in Particulate Composite;100
8.3.1;5.3.1 Influence of Particles Morphology;104
8.4;5.4 Discussion and Conclusions;106
8.5;References;108
9;6 Temperature Fields in Short Fibre Composites;110
9.1;6.1 Introduction;110
9.2;6.2 Method of Continuous Source Functions – MCSF;112
9.2.1;6.2.1 Source Functions;113
9.2.2;6.2.2 MCSF Model;114
9.2.3;6.2.3 Shape Functions;114
9.3;6.3 Examples;117
9.3.1;6.3.1 Single Fibre;118
9.3.2;6.3.2 Patch of Fibres;120
9.3.3;6.3.3 Two Fibres in a Matrix;123
9.4;6.4 Conclusions;126
9.5;References;127
10;7 Simulation of Distributed Detection of Ammonia Gas;128
10.1;7.1 Introduction;128
10.2;7.2 Proposed Model of the Sensing System;130
10.2.1;7.2.1 General Features;130
10.2.2;7.2.2 Chemo-Optical Transducer;132
10.2.3;7.2.3 Light Intensity Propagating Along the Fiber;134
10.3;7.3 Results and Discussion;136
10.4;7.4 Conclusions;143
10.5;References;144
11;8 Exact Solution of Bending Free Vibration Problem of the FGM Beams with Effect of Axial Force;145
11.1;8.1 Introduction;145
11.2;8.2 Second Order Beam Theory Differential Equation for the FGM-Beam Deflection;146
11.3;8.3 Calculation of the Eigenfrequencies and Eigenmodes;151
11.4;8.4 Numerical Experiments;151
11.4.1;8.4.1 Free Vibration Analysis of the Multilayered FGM Sandwich Beams with Effect of Large Axial Force;151
11.4.1.1;8.4.1.1 Example 1 -- Clamped Beam at the Left Side;154
11.4.1.2;8.4.1.2 Example 2 -- Clamped Beam at the Both Sides;155
11.4.1.3;8.4.1.3 Example 3 -- Beam Simply Supported at Both Sides;157
11.4.2;8.4.2 Free Vibration Analysis of One-Layer FGM Beams with Effect of the Axial Force;159
11.5;8.5 Conclusions;163
11.6;References;163
12;9 Wavelet Analysis of the Shear Stress in Soil Layer Caused by Dynamic Excitation;165
12.1;9.1 Introduction;165
12.2;9.2 Governing Set of Equations in Soil Dynamic Consolidation Theory – FEM Implementation;166
12.3;9.3 Constitutive Relation;168
12.4;9.4 Numerical Calculation;169
12.5;9.5 Wavelet Analysis;170
12.6;9.6 Wavelet Analysis of the Shear Stresses;174
12.7;9.7 Conclusions;175
12.8;References;176
13;10 Strength of Composites with Fibres;177
13.1;10.1 Introduction;177
13.2;10.2 Micromechanics of Composite Materials with Short Fibres;178
13.3;10.3 Classical Lamination Theory;182
13.4;10.4 Failure Criteria for Fibre-Reinforced Orthotropic Layers;183
13.4.1;10.4.1 Maximum Stress and Maximum Strain Criteria;183
13.4.2;10.4.2 Tsai-Wu Criterion;184
13.5;10.5 Finite Element Formulation;186
13.6;10.6 Numerical Examples;186
13.6.1;10.6.1 Example 1;186
13.6.2;10.6.2 Example 2;188
13.6.3;10.6.3 Example 3;190
13.7;10.7 Conclusion;191
13.8;Appendix;192
13.9;References;193
14;11 A Direct Boundary Element Formulation for the First Plane Problem in the Dual System of Micropolar Elasticity;194
14.1;11.1 Introduction;194
14.2;11.2 Preliminaries;196
14.3;11.3 Supplementary Compatibility Conditions;200
14.4;11.4 Basic Equations and Fundamental Solutions of Order One;203
14.5;11.5 Fundamental Solutions of Order Two;208
14.5.1;11.5.1 Calculating Dual Stresses from the Fundamental Solution of Order One;208
14.6;11.6 Dual Somigliana Formulae for Inner Regions;210
14.6.1;11.6.1 The Dual Somigliana Identity;210
14.6.2;11.6.2 The Dual Somigliana Formulae for Inner Region;212
14.6.3;11.6.3 Formulae for Stresses;216
14.7;11.7 Dual Somiglian Formulae for Outer Regions;217
14.7.1;11.7.1 Stresses at Infinity;217
14.7.2;11.7.2 Derivation of the Dual Somigliana Formulae for Outer Regions;219
14.8;11.8 Calculations of the Stresses on the Boundary;222
14.9;11.9 Solution Algorithm and Numerical Examples;223
14.9.1;11.9.1 The Algorithm;223
14.9.2;11.9.2 The Equation System to be Solved;224
14.9.3;11.9.3 Examples;228
14.10;11.10 Concluding Remarks;231
14.11;References;232
15;12 Implementation of Meshless Method for a Problem of a Plate Large Deflection;234
15.1;12.1 Introduction;234
15.2;12.2 Governing Equations;235
15.2.1;12.2.1 System of Equations;235
15.2.2;12.2.2 Boundary Conditions;235
15.3;12.3 Numerical Approach;236
15.3.1;12.3.1 Picard Iterations;237
15.3.2;12.3.2 Homotopy Analysis Method (HAM);238
15.3.3;12.3.3 Method of Fundamental Solutions;240
15.4;12.4 Numerical Approach;243
15.4.1;12.4.1 Numerical Solution of Bihamonic Problem;243
15.4.2;12.4.2 Numerical Solution of Large Deflection of Simply Supported Plate;245
15.5;12.5 Conclusions;247
15.6;References;247
16;13 Modelling and Spatial Discretization in Depletion Calculations of the Fast Reactor Cell with HELIOS 1.10;249
16.1;13.1 Introduction;250
16.2;13.2 Fundamentals of Computational Code HELIOS 1.10;251
16.3;13.3 Transmutation Fuel Cycle;252
16.3.1;13.3.1 Inventories from NPP V1 Bohunice;253
16.3.2;13.3.2 VVER-440 and SUPERPHENIX;253
16.3.3;13.3.3 Transmutation Fuel Cycle Indicators;255
16.4;13.4 Spatial Model Discretization;255
16.4.1;13.4.1 Strategies for Optimal Discretization;257
16.4.2;13.4.2 Spatial Discretization in the Fuel;258
16.4.3;13.4.3 Spatial Discretization in the Coolant;259
16.4.4;13.4.4 Optimized Strategy;259
16.5;13.5 Results and Discussion;259
16.6;13.6 Conclusions;260
16.7;References;261
17;14 Linear Algebra Issues in a Family of Advanced Hybrid Finite Elements;263
17.1;14.1 Introduction;263
17.2;14.2 Generalized Variational Formulation for Time-Dependent Problems;266
17.3;14.3 Non-singular Fundamental Solutions in the Frequency Domain;269
17.4;14.4 Advanced Modal Analysis of the Time-Dependent Problem;273
17.5;14.5 Accuracy and Linear Algebra Issues;275
17.6;14.6 Numerical Example;277
17.7;14.7 Conclusions;279
17.8;References;281
18;15 On Drilling Degrees of Freedom;284
18.1;15.1 Introduction;284
18.2;15.2 The Cosserat Continuum as a Basis for Membrane Elements with Drilling Degrees of Freedom;288
18.2.1;15.2.1 Derivation of the Field Problem;289
18.2.2;15.2.2 Reduction of the Field Problem and Its Weak Form;291
18.2.3;15.2.3 Hu-Washizu Enhancements and the B-Bar Form;293
18.3;15.3 Numerical Procedure – Development of Membrane Elements;295
18.3.1;15.3.1 Elements that Fulfill the Kinematic Relations in a Strong Form;296
18.3.2;15.3.2 Modifications for Improved Accuracy and Efficiency;300
18.4;15.4 Results;305
18.5;References;308
19;16 Hybrid System for Optimal Design of Mechanical Properties of Composites;310
19.1;16.1 Introduction;310
19.2;16.2 Object of Analysis;311
19.3;16.3 Optimization Problem;315
19.4;16.4 Series Hybrid Optimization System;316
19.4.1;16.4.1 Analysis of Structural Behavior;316
19.4.2;16.4.2 Initial Optimization;319
19.4.3;16.4.3 Final Optimization;322
19.4.4;16.4.4 Sensitivity Analysis of Structural Behavior;323
19.5;16.5 Numerical Examples;325
19.5.1;16.5.1 Example 1;325
19.5.2;16.5.2 Example 2;331
19.5.3;16.5.3 Example 3;334
19.6;16.6 Conclusions;336
19.7;References;337
20;17 Analysis of Representative Volume Elements with Random Microcracks;339
20.1;17.1 Introduction;339
20.2;17.2 Effective Properties of Solids with Microcracks;341
20.3;17.3 The Boundary Element Method for Crack Problems;341
20.4;17.4 Numerical Results;342
20.4.1;17.4.1 Representative Volume Elements Subjected to Static Loading;342
20.4.2;17.4.2 Representative Volume Elements Subjected to Dynamic Loading;345
20.5;17.5 Conclusions;346
20.6;References;347
21;18 Application of General Boundary Element Method for Numerical Solution of Bioheat Transfer Equation;348
21.1;18.1 Introduction;348
21.2;18.2 Bioheat Transfer Models;349
21.3;18.3 Boundary Element Method for Pennes Equation;351
21.4;18.4 General Boundary Element Method for DPL Equation;354
21.5;18.5 Results of Computations;360
21.6;18.6 Conclusions;364
21.7;References;365
22;Index;367