Computational Mechanics of Composite Materials: Sensitivity, Randomness and Multiscale Behaviour

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Springer Science & Business Media, 2005 - 418 Seiten

Composite materials play a vital role in modern engineering from aerospace to nuclear devices. Computational mechanics endeavours to provide precise numerical models of composites. More recently, it has been necessary to take account of the stochastic nature of their behaviour indicated by experiment. The approach of Computational Mechanics of Composite Materials lays stress on the advantages of combining theoretical advancements in applied mathematics and mechanics with the probabilistic approach to experimental data in meeting the practical needs of engineers.

Features:


Programs for the probabilistic homogenisation of composite structures with finite numbers of components allow composites to be treated as homogeneous materials with simpler behaviours.


Allows treatment of defects in the interfaces within heterogeneous materials and those arising in composite objects as a whole by stochastic modelling.


Provides new models for the reliability of composite structures.

Propounds novel numerical algorithms for more effective Monte-Carlo simulation.

Computational Mechanics of Composite Materials will be of interest to academic and practising civil, mechanical, electronic and aerospatial engineers, to materials scientists and to applied mathematicians requiring accurate and usable models of the behaviour of composite materials.

The Engineering Materials and Processes series focuses on all forms of materials and the processes used to synthesise and formulate them as they relate to the various engineering disciplines. The series deals with a diverse range of materials: ceramics; metals (ferrous and non-ferrous); semiconductors; composites, polymers biomimetics etc. Each monograph in the series will be written by a specialist and will demonstrate how enhancements in materials and the processes associated with them can improve performance in the field of engineering in which they are used.

 

Ausgewählte Seiten

Inhalt

Mathematical Preliminaries
1
112 Gaussian and QuasiGaussian Random Variables
7
12 Monte Carlo Simulation Method
14
13 Stochastic Second Moment Perturbation Approach
19
132 Elastodynamics with Random Parameters
23
Elasticity Problems
30
21 Composite Model Interface Defects Concept
31
22 Elastostatics of Some Composites
48
413 Sensitivity of Homogenised Young Modulus for Periodic Composite Bars
195
414 Material Sensitivity of Unidirectional Periodic Composites
200
415 Sensitivity of Homogenised Properties for FibreReinforced Periodic Composites
206
42 Probabilistic Analysis
218
43 Conclusions
220
Fracture and Fatigue Models for Composites
222
52 Existing Techniques Overview
224
53 Computational Issues
233

221 Deterministic Computational Analysis
49
222 Random Composite without Interface Defects
54
223 Fibrereinforced Composite with Stochastic interface Defects
60
224 Stochastic Interface Defects in Laminated Composite
63
225 Superconducting Coil Cable Probabilistic Analysis
66
23 Homogenisation Approach
70
232 2D and 3D Composites with Uniaxially Distributed Inclusions
84
233 FibreReinforced Composites
88
2332 Asymptotic Homogenisation Method
94
23322 Monte Carlo Simulation Analysis
115
23223 Stochastic Perturbation Approach to the Homogenisation
134
234 Upper and Lower Bounds for Effective Characteristics
146
235 Effective Constitutive Relations for the Steel Reinforced Concrete Plates
155
24 Conclusions
158
25 Appendix
159
Elastoplastic Problems
163
33 Finite Element Equations of Elastoplasticity
167
34 Numerical Analysis
170
35 Some Comments on Probabilistic Effective Properties
180
36 Conclusions
181
37 Appendix
182
Sensitivity Analysis for Some Composites
185
411 Sensitivity Analysis Methods
188
412 Sensitivity of Homogenised Heat Conductivity
191
531 Delamination of TwoComponent Curved Laminates
238
532 Fatigue Analysis of a Composite Pipe Joint
254
533 Thermomechanical Fatigue of Curved Composite Beams
265
54 Perturbationbased Fracture Criteria
279
55 Concluding Remarks
285
56 Appendix
286
Reliability Analysis
296
62 Perturbationbased Reliability for Contact Problem
299
63 Stochastic Model of Degradation Process
314
Multiresolutional Wavelet Analysis
317
72 Multiscale Reduction and Homogenisation
325
73 Multiscale Homogenisation for the Wave Propagation Equation
335
74 Introduction to Multiresolutional FEM Implementation
340
75 Free Vibrations Analysis
345
76 Multiscale Heat Transfer Analysis
353
77 Stochastic Perturbationbased Approach to the Wavelet Decomposition
368
78 Concluding Remarks
379
Appendix
382
82 Input Data for ABAQUS Reinforced Concrete Plate Analysis
385
83 MAPLE Script for Computations of the Homogenised Heat Conductivity Coefficients
390
References
393
Index
415
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Seite 395 - A. (1991) A homogenization approach to the yield strength of composite materials, Eur. J. Mech., A/ Solids, 10 (2), 129-154.
Seite 408 - Menstrual Cycle Variation in Mammographic Breast Density". Natl. J. Cancer Inst., 90, 875. [2] The Finite Element Method: Basic Concepts and .Applications (Series in Computational and Physical Processes in Mechanics and Thermal Sciences), Hemisphere Publishing Corporation.
Seite 395 - Data Analysis: Statistical and Computational Methods for Scientists and Engineers, Springer Verlag 1998 13 Optimization Toolbox User's Guide The Math Works, Inc.

Autoren-Profil (2005)

Marcin Kaminski teaches theoretical mechanics, strength of materials and computational and numerical methods in civil engineering as the Chair of Mechanics and Materials at the Technical University of Lodz. He has published over seventy articles in peer-reviewed academic journals and several books and has given many conference presentations. He spent a sabbatical leave at Rice University in Texas as the fellow of the Foundation for Polish Science in 1999/2000. He received the John Argyris Award in computational mechanics from ECCOMAS and Elsevier in 2001, the JT Oden Faculty Fellowship in the University of Texas at Austin in 2004 and is a member of IASS, SIAM, GAMM and IACM. Professor Kaminski's research interests include: probabilistic and stochastic methods in computational mechanics of solids, structures and fluids, numerical analysis of stochastic reliability in engineering structures, the implementations of probabilistic procedures into FEM, BEM and FDM-based computer programs, computational modeling of stochastic aging processes in engineering and applied science, homogenization methods for composite materials as well as the software development for stochastic symbolic computations using MAPLE.

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