Computational Modelling and Advanced Simulations (eBook)

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