Boundary element analysis in computational fracture mechanics
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Bibliographic Information
Boundary element analysis in computational fracture mechanics
（Mechanics : computational mechanics, 1）
Kluwer Academic Publishers, c1988
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Includes bibliographical references and index
Description and Table of Contents
Description
The Boundary Integral Equation (BIE) method has occupied me to various degrees for the past twenty-two years. The attraction of BIE analysis has been its unique combination of mathematics and practical application. The EIE method is unforgiving in its requirement for mathe matical care and its requirement for diligence in creating effective numerical algorithms. The EIE method has the ability to provide critical inSight into the mathematics that underlie one of the most powerful and useful modeling approximations ever devised--elasticity. The method has even revealed important new insights into the nature of crack tip plastic strain distributions. I believe that EIE modeling of physical problems is one of the remaining opportunities for challenging and fruitful research by those willing to apply sound mathematical discipline coupled with phys ical insight and a desire to relate the two in new ways. The monograph that follows is the summation of many of the successes of that twenty-two years, supported by the ideas and synergisms that come from working with individuals who share a common interest in engineering mathematics and their application. The focus of the monograph is on the application of EIE modeling to one of the most important of the solid mechanics disciplines--fracture mechanics. The monograph is not a trea tise on fracture mechanics, as there are many others who are far more qualified than I to expound on that topic.
Table of Contents
1.0 An Historical Perspective.- 1.1 Boundary Integral Equation Development.- 1.2 Boundary Formulations and Discretizations.- 1.3 Fracture Mechanics Problems.- References.- 2.0 Fracture Mechanics.- 2.1 Introduction.- 2.2 Some Definitions.- 2.3 Some Fundamental Results.- 2.4 Some Stress Intensity Factors.- References.- 3.0 Boundary-Integral Equation Formulation and Solution.- 3.1 Introduction.- 3.2 Governing Equations of Elasticity in Two and Three Dimensions.- 3.3 Fundamental Solutions.- 3.4 Two-Dimensional Anisotropic Fundamental Solution.- 3.5 Three-Dimensional Anisotropic Fundamental Solution.- 3.6 Somigliana Identities.- 3.7 Boundary-Integral Equations.- 3.8 Numerical Quadrature of the BIE.- References.- 4.0 BIE Modeling of Crack Surfaces.- 4.1 Introduction.- 4.2 Degeneration of the BIE for Co-Planar Surfaces.- 4.3 Multiregion BIE Applications.- 4.4 Strain Energy Based Crack Tip Modeling.- 4.5 Crack Surface Interpolations.- References.- 5.0 Green's Function Formulation in Two Dimensions.- 5.1 Introduction.- 5.2 Formulation of the Anisotropic Green's Function.- 5.3 Somigliana Identities for the Anisotropic Green's Function Formulation.- 5.4 Linear Variation Boundary Element Implementation.- 5.5 Applications.- References.- 6.0 Elastoplastic Fracture Mechanics Analysis.- 6.1 Introduction.- 6.2 Fundamental Elastoplastic Relations.- 6.3 The Somigliana Identities in Three-Dimensional Elastoplasticity.- 6.4 The Somigliana Identities in Two-Dimensional Elastoplasticity.- 6.5 The Somigliana Identities in Two-Dimensional Elastoplastic Fracture Mechanics.- 6.6 Numerical Implementation of the Elastoplastic BIE Formulation.- 6.7 Numerical Results in Two-Dimensional Elastoplasticity.- References.- 7.0 Displacement Discontinuity Modeling of Cracks.- 7.1 Introduction.- 7.2 Formulation of the Three-Dimensional Traction BIE for Flat Cracks.- 7.3 Formulation of the Two-Dimensional Traction BIE.- 7.4 Near Crack Tip Solution to BIE.- 7.5 Current Numerical Method.- 7.6 Numerical Results.- References.- 8.0 Two-Dimensional Weight Function Evaluation.- 8.1 Introduction.- 8.2 Formulation of the Weight Function BIE.- References.
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