层状和梯度材料断裂力学的边界元法和应用

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 ReferencesChapter 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 ReferencesChapter 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 and Gt ReferencesChapter 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 ReferencesChapter 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 ReferencesChapter 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 ReferencesChapter 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 ReferencesChapter 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 ReferencesChapter 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 ReferencesChapter 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 SummaryAppendix 5 The fundamental solution of transversely isotropic bi-materialsReferences

《层状和梯度材料断裂力学的边界元法和应用(英文版)(精)》介绍了作者(肖洪天、岳中琦)近十几年来发展的新型边界元法，以及采用建议方法分析层状和梯度材料断裂力学特性的研究成果。新型边界元法基于层状各向同性材料基本解和双层横观各向同性材料基本解，采用子域和单一区域边界元法分析断裂力学问题，引入可描述裂纹尖端应力场和位移场变化特点的单元，采用沿材料梯度方向分层的方法逼近梯度材料力学参数的变化。采用建议方法计算了梯度材料中不同类型三维裂纹的应力强度因子，并分析了裂纹扩展。获得梯度材料力学和几何参数对裂纹应力强度因子和裂纹扩展的影响。本书内容可供土木、水利、交通、航空等部门从事力学、新材料的教学和科研的有关人员阅读参考。 《层状和梯度材料断裂力学的边界元法和应用(英文版)(精)》介绍了作者(肖洪天、岳中琦)近十几年来发展的新型边界元法，以及采用建议方法分析层状和梯度材料断裂力学特性的研究成果。 新型边界元法基于层状各向同性材料基本解和双层横观各向同性材料基本解，采用子域和单一区域边界元法分析断裂力学问题，引入可描述裂纹尖端应力场和位移场变化特点的单元，采用沿材料梯度方向分层的方法逼近梯度材料力学参数的变化。采用建议方法计算了梯度材料中不同类型三维裂纹的应力强度因子，并分析了裂纹扩展。获得梯度材料力学和几何参数对裂纹应力强度因子和裂纹扩展的影响。 《层状和梯度材料断裂力学的边界元法和应用(英文版)(精)》首先介绍了弹性力学和断裂力学的基础知识，简单且完整地介绍了层状材料的基本解。在接下来的几章里，发展了基于层状材料基本解的边界元方法，并分析了层状和梯度材料的断裂力学问题。最后，发展了基于双层横观各向同性材料基本解的边界元方法，并分析了该类材料的断裂力学问题。 《层状和梯度材料断裂力学的边界元法和应用(英文版)(精)》可供土木、水利、交通、航空等部门从事力学、新材料的教学和科研的有关人员阅读参考。