《層狀和梯度材料斷裂力學的邊界元法和應用(英文版)(精)》介紹了作者(肖洪天、嶽中琦)近十幾年來發展的新型邊界元法，以及采用建議方法分析層狀和梯度材料斷裂力學特性的研究成果。新型邊界元法基於層狀各向**材料基本解和雙層橫觀各向**材料基本解，采用子域和單一區域邊界元法分析斷裂力學問題，引入可描述裂紋**應力場和位移場變化特點的單元，采用沿材料梯度方向分層的方法逼近梯度材料力學參數的變化。采用建議方法計算了梯度材料中不同類型三維裂紋的應力強度因子，並分析了裂紋擴展。獲得梯度材料力學和幾何參數對裂紋應力強度因子和裂紋擴展的影響。本書內容可供土木、水利、交通、航空等部門從事力學、新材料的教學和科研的有關人員閱讀參考。

《層狀和梯度材料斷裂力學的邊界元法和應用( 英文版)(精)》介紹了作者(肖洪天、嶽中琦)近十幾 年來發展的新型邊界元法，以及采用建議方法分析層 狀和梯 度材料斷裂力學特性的研究成果。 新型邊界元法基於層狀各向同性材料基本解和雙 層橫觀各向同性材料基本解，采用 子域和單一區域邊界元法分析斷裂力學問題，引入可 描述裂紋尖端應力場和位移場變化 特點的單元，采用沿材料梯度方向分層的方法逼近梯 度材料力學參數的變化。采用建議 方法計算了梯度材料中不同類型三維裂紋的應力強度 因子，並分析了裂紋擴展。獲得梯 度材料力學和幾何參數對裂紋應力強度因子和裂紋擴 展的影響。 《層狀和梯度材料斷裂力學的邊界元法和應用( 英文版)(精)》首先介紹了彈性力學和斷裂力學的基 礎知識，簡單且完整地介紹了層狀材料的 基本解。在接下來的幾章裡，發展了基於層狀材料基 本解的邊界元方法，並分析了層狀 和梯度材料的斷裂力學問題。最後，發展了基於雙層 橫觀各向同性材料基本解的邊界元 方法，並分析了該類材料的斷裂力學問題。 《層狀和梯度材料斷裂力學的邊界元法和應用( 英文版)(精)》可供土木、水利、交通、航空等部門 從事力學、新材料的教學和科研的有關人 員閱讀參考。

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
2.3.4 Stress fields of cracks in graded materials and on the interface of bi-materials
2.4 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 ofg
3.3.3 Asymptotic representation of the solution matrices φ(p,z) and ψ(p,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(p,z) and ψ(p, z)
Appendix 3 The matrices Gx[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 m 70
4.8.3 Strongly singular integrals
4.9 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 to Crack 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
5.3 Computation of stress intensity factors
5.4 Numerical examples and results m 97
5.5 Summary
References
Chapter 6 Analysis of Penny-shaped Cracks in Functionally Graded
Materials
6.1 Introduction
6.2 Analysis methods for crack problems in a FGM system of infinite extent
6.2.1 The crack problem in a FGM
6.2.2 The multi-region method for crack problems of infinite extent
6.2.3 The layered discretization technique for FGMs
6.2.4 Numerical verifications
6.3 The SIFs for a crack parallel to the FGM interlayer
6.3.1 General
6.3.2 A crack subjected to uniform compressive stresses
6.3.3 A crack subjected to uniform shear stresses
6.4 The growth of the crack parallel to the FGM interlayer
6.4.1 The strain energy density factor of an elliptical crack
6.4.2 Crack growth under a remotely inclined tensile loading
6.5 The SIFs for a crack perpendicular to the FGM interlayer
6.5.1 General
6.5.2 Numerical verifications
6.5.3 The SIFs for a crack subjected to uniform compressive stresses
6.5.4 The SIFs for a crack subjected to uniform shear stresses
6.6 The growth of the crack perpendicular to the FGM interlayer
6.6.1 The crack growth under a remotely inclined tensile loading
6.6.2 The crack growth under a remotely inclined compressive loading
6.7 Summary
References
Chapter 7 Analysis of Elliptical Cracks in Functionally Graded Materials
7.1 Introduction
7.2 The SIFs for an elliptical crack parallel to the FGM interlayer
7.2.1 General
7.2.2 Elliptical crack under a uniform compressive stress
7.2.3 Elliptical crack under a uniform shear stress
7.3 The growth of an elliptical crack parallel to the FGM interlayer
7.4 The SIFs for an elliptical crack perpendicular to the FGM interlayer
7.4.1 General
7.4.2 Elliptical crack under a uniform compressive stress
7.4.3 Elliptical crack under a uniform shear loading
7.5 The growth of an elliptical crack perpendicular to the FGM interlayer
7.5.1 Crack growth under a remotely inclined tensile loading
7.5.2 Crack growth under a remotely inclined compressive loading
7.6 Summary
References
Chapter 8 Yue's Solution-based Dual Boundary Element Method
8.1 Introduction
8.2 Yue's solution-based dual boundary integral equations
8.2.1 The displacement boundary integral equation
8.2.2 The traction boundary integral equation
8.2.3 The dual boundary integral equations for crack problems
8.3 Numerical implementation
8.3.l Boundary discretization
8.3.2 The discretized boundary integral equation
8.4 Numerical integrations
8.4.1 Numerical integrations for the displacement BIE
8.4.2 Numerical integrations for the traction BIE
8.5 Linear equation systems for the discretized dual BIEs
8.6 Numerical verifications
8.6.1 Calculation of stress intensity factors
8.6.2 The effect of different meshes and the coefficient D on the SIF values
8.7 Summary
Appendix 4 Finite-part integrals and Kutt's numerical quadrature
A4.1 Introduction
A4.2 Kutt's numerical quadrature
References
Chapter 9 Analysis of Rectangular Cracks in the FGMs
9.1 Introduction
9.2 A square crack in FGMs of infinite extent
9.2.1 General
9.2.2 A square crack parallel to the FGM interlayer
9.2.3 A square crack having a 45° angle with the FGM interlaYer
9.2.4 A square crack perpendicular to the FGM interlayer
9.3 A square crack in the FGM interlayer
9.4 A rectangular crack in FGMs of infinite extent
9.4.1 General
9.4.2 A rectangular crack parallel to the FGM interlayer
9.4.3 A rectangular crack with long sides perpendicular to the FGM interlayer
9.4.4 A rectangular crack with short sides perpendicular to the FGM interlayer
9.5 A square crack in a FGM of finite extent
9.6 Square cracks in layered rocks
9.6.1 General
9.6.2 The crack dimensions and the parameters of layered rocks
9.6.3 A square crack subjected to a uniform compressive load
9.6.4 A square crack subjected to a non-uniform compressive load
9.7 Rectangular cracks in layered rocks
9.7.1 General
9.7.2 A rectangular crack subjected to a linear compressive load
9.7.3 A rectangular crack subjected to a nonlinear compressive load
9.8 Summary
References
Chapter 10 Boundary element analysis of fracture mechanics in transversely isotropic bi-materials
10.1 Introduction
10.2 Multi-region BEM analysis of cracks in transversely isotropic bi-materials
10.2.1 General
10.2.2 Calculation of the stress intensity factors
10.2.3 A penny-shaped crack perpendicular to the interface of transversely isotropic bi-materials
10.2.4 An elliptical crack perpendicular to the interface of transversely isotropic bi-materials
10.3 Dual boundary element analysis of a square crack in transversely isotropic bi-materials
10.3.1 General
10.3.2 Numerical verification
10.3.3 Numerical results and discussions
10.4 Summary
Appendix 5 The fundamental solution of transversely isotropic bi-materials
References