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Author Xiao, Hongtian, author

Title Fracture mechanics in layered and graded solids : analysis using boundary element methods / Hongtian Xiao, Zhongqi Yue
Published Berlin ; Boston : De Gruyter, [2014]
Online access available from:
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Description 1 online resource (xii, 305 pages .)
Contents 880-01 Chapter 1 Introduction; 1.1 Functionally graded materials; 1.2 Methods for fracture mechanics; 1.2.1 General; 1.2.2 Analytical methods; 1.2.3 Finite element method; 1.2.4 Boundary element method; 1.2.5 Meshless methods; 1.3 Overview of the book; References; Chapter 2 Fundamentals of Elasticity and Fracture Mechanics; 2.1 Introduction; 2.2 Basic equations of elasticity; 2.3 Fracture mechanics; 2.3.1 General; 2.3.2 Deformation modes of cracked bodies; 2.3.3 Three-dimensional stress and displacement fields
880-01/(S 3.3.3 Asymptotic representation of the solution matricesΦ(ρ, z) and Ψ(ρ, z)3.4 Solution in the physical domain; 3.4.1 Solutions in the Cartesian coordinate system; 3.4.2 Closed-form results for singular terms of the solution; 3.5 Computational methods and numerical evaluation; 3.5.1 General; 3.5.2 Singularities of the fundamental solution; 3.5.3 Numerical integration; 3.5.4 Numerical evaluation and results; 3.6 Summary; Appendix 1 The matrices of elastic coefficients; Appendix 2 The matrices in the asymptotic expressions of Φ(ρ, z) and Ψ(ρ, z)
2.3.4 Stress fields of cracks in graded materials and on the interface of bi-materials2.4 Analysis of crack growth; 2.4.1 General; 2.4.2 Energy release rate; 2.4.3 Maximum principal stress criterion; 2.4.4 Minimum strain energy density criterion; 2.4.5 The fracture toughness of graded materials; 2.5 Summary; References; Chapter 3 Yue's Solution of a 3D Multilayered Elastic Medium; 3.1 Introduction; 3.2 Basic equations; 3.3 Solution in the transform domain; 3.3.1 Solution formulation; 3.3.2 Solution expressed in terms of g
880-02 4.8.3 Strongly singular integrals4.9 Evaluation of displacements and stresses at an internal point; 4.10 Evaluation of boundary stresses; 4.11 Multi-region method; 4.12 Symmetry; 4.13 Numerical evaluation and results; 4.13.1 A homogeneous rectangular plate; 4.13.2 A layered rectangular plate; 4.14 Summary; References; Chapter 5 Application of the Yue's Solution-based BEM toCrack Problems; 5.1 Introduction; 5.2 Traction-singular element and its numerical method; 5.2.1 General; 5.2.2 Traction-singular element; 5.2.3 The numerical method of traction-singular elements
880-02/(S Appendix 3 The matrices Gs[m, z, Φ] and Gt [m, z, Φ]References; Chapter 4 Yue's Solution-based Boundary Element Method; 4.1 Introduction; 4.2 Betti's reciprocal work theorem; 4.3 Yue's solution-based integral equations; 4.4 Yue's solution-based boundary integral equations; 4.5 Discretized boundary integral equations; 4.6 Assembly of the equation system; 4.7 Numerical integration of non-singular integrals; 4.7.1 Gaussian quadrature formulas; 4.7.2 Adaptive integration; 4.7.3 Nearly singular integrals; 4.8 Numerical integration of singular integrals; 4.8.1 General; 4.8.2 Weakly singular integrals
Summary Mechanical responses of solid materials are governed by their material properties. The solutions for estimating and predicting the mechanical responses are extremely difficult, in particular for non-homogeneous materials. Among these, there is a special type of materials whose properties are variable only along one direction, defined as graded materials or functionally graded materials (FGMs). Examples are plant stems and bones. Artificial graded materials are widely used in mechanical engineering, chemical engineering, biological engineering, and electronic engineering. This work covers and d
Bibliography Includes bibliographical references
Notes In English
Print version record
Subject Functionally gradient materials -- Fracture
Boundary element methods.
Fracture mechanics.
Boundary element methods.
Fracture mechanics.
Genre/Form Electronic books
Form Electronic book
Author Yue, Zhongqi, author
ISBN 3110369559