Computational Mechanics of Composite Materials

Cover -- Acknowledgements -- Preface -- Table of Contents -- 1 Mathematical Preliminaries -- 1.1 Probability Theory Elements -- 1.2 Monte Carlo Simulation Method -- 1.3 Stochastic Second moment Perturbation Approach -- 2 Elasticity Problems -- 2.1 Composite Model. Interface Defects Concept -- 2.2 Elastostatics of Some Composites -- 2.3 Homogenisation Approach -- 2.4 Conclusions -- 2.5 Appendix -- 3 Elastoplastic Problems -- 3.1 Introduction -- 3.2 Homogenisation Method -- 3.3 Finite Element Equations of Elastoplasticity -- 3.4 Numerical Analysis -- 3.5 Some Comments on Probabilistic Effective Properties -- 3.6 Conclusions -- 3.7 Appendix -- 4 Sensitivity Analysis for Some Composites -- 4.1 Deterministic Problems -- 4.2 Probabilistic Analysis -- 4.3 Conclusions -- 5 Fracture and Fatigue Models for Composites -- 5.1 Introduction -- 5.2 Existing Techniques Overview -- 5.3 Computational Issues -- 5.4 Perturbation-based Fracture Criteria -- 5.5 Concluding Remarks -- 5.6 Appendix -- 6 Reliability Analysis -- 6.1 Introductory Remarks -- 6.2 Perturbation-based Reliability Analysis for Contact Problem -- 6.3 Stochastic Model of Degradation Process -- 7 Multiresolutional Wavelet Analysis -- 7.1 Introduction -- 7.2 Multiscale Reduction and Homogenisation -- 7.3 Multiscale Homogenisation for the Wave Propagation Equation -- 7.4 Introduction to Multiresolutional FEM Implementation -- 7.5 Free Vibrations Analysis -- 7.6 Multiscale Heat Transfer Analysis -- 7.7 Stochastic Perturbation-based Approach to Wavelet Decomposition. -- 7.8 Concluding Remarks -- Appendix -- 8.1 Procedure of MCCEFF Input File Preparation -- 8.2 Input Data for ABAQUS Concrete Plate Analysis -- 8.3 MAPLE Script for Computations of the Homogenised Heat Conductivity Coefficients -- References.