Format:
Online-Ressource (XII, 305 S.)
ISBN:
9783110297973
,
9783110297874
Series Statement:
De Gruyter eBook-Paket Mathematik und Physik
Content:
Biographical note: Zhongqi Yue, University of Hong Kong; Hongtian Xiao, Shandong University of Sciences and Technology, China.
Content:
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 develops boundary element methods (BEM) to investigate the properties of realistic graded materials. This book is a must have for practitioners and researchers in materials science, both academic and in industry.
Note:
Description based upon print version of record
,
Contents; 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
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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
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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)
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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
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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
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5.3 Computation of stress intensity factors
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In English
Additional Edition:
ISBN 9783110297874
Additional Edition:
Erscheint auch als Druck-Ausgabe Xiao, Hongtian Fracture mechanics in layered and graded solids Berlin : de Gruyter, 2014 ISBN 9783110297980
Additional Edition:
ISBN 3110297876
Additional Edition:
ISBN 9783110297874
Language:
English
Subjects:
Physics
Keywords:
Inhomogener Festkörper
;
Funktioneller Gradientenwerkstoff
;
Bruchmechanik
;
Randelemente-Methode
;
Electronic books
DOI:
10.1515/9783110297973
URL:
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