固体力学中的基本解方法(英文版) 王辉,秦庆华 著 孙博华 编 专业科技 文轩网

About the authors
Preface
Acknowledgments
List of abbreviations
Part Ⅰ Fundamentals of meshless methods
1. Overview of meshless methods
1.1 Why we need meshless methods
1.2 Review of meshless methods
1.3 Basic ideas of the method of fundamental solutions
1.3.1 Weighted residual method
1.3.2 Method of fundamental solutions
1.4 Application to the two-dimensional Laplace problem
1.4.1 Problem description
1.4.2 MFS formulation
1.4.3 Program structure and source code
1.4.4 Numerical experiments
1.5 Some limitations for implementing the method of fundamental solutions
1.5.1 Dependence of fundamental solutions
1.5.2 Location of source points
1.5.3 Ill-conditioning treatments
1.5.4 Inhomogeneous problems
1.5.5 Multiple domain problems
1.6 Extended method of fundamental solutions
1.7 Outline of the book
References
2. Mechanics of solids and structures
2.1 Introduction
2.2 Basic physical quantities
2.2.1 Displacement components
2.2.2 Stress components
2.2.3 Strain components
2.3 Equations for three-dimensional solids
2.3.1 Strain-displacement relation
2.3.2 Equilibrium equations
2.3.3 Constitutive equations
2.3.4 Boundary conditions
2.4 Equations for plane solids
2.4.1 Plane stress and plane strain
2.4.2 Governing equations
2.4.3 Boundary conditions
2.5 Equations for Euler-Bernoulli beams
2.5.1 Deformation mode
2.5.2 Governing equations
2.5.3 Boundary conditions
2.5.4 Continuity requirements
2.6 Equations for thin plates
2.6.1 Deformation mode
2.6.2 Governing equations
2.6.3 Boundary conditions
2.7 Equations for piezoelectricity
2.7.1 Governing equations
2.7.2 Boundary conditions
2.8 Remarks
References
3. Basics of fundamental solutions and radial basis functions
3.1 Introduction
3.2 Basic concept of fundamental solutions
3.2.1 Partial differential operators
3.2.2 Fundamental solutions
3.3 Radial basis function interpolation
3.3.1 Radial basis functions
3.3.2 Radial basis function interpolation
3.4 Remarks
References
Part Ⅱ Applications of the meshless method
4. Meshless analysis for thin beam bending problems
4.1 Introduction
4.2 Solution procedures
4.2.1 Homogeneous solution
4.2.2 Particular solution
4.2.3 Approximated full solution
4.2.4 Construction of solving equations
4.2.5 Treatment of discontinuous loading
4.3 Results and discussion
4.3.1 Statically indeterminate beam under uniformly distributed loading
4.3.2 Statically indeterminate beam under middle-concentrated load
4.3.3 Cantilever beam with end-concentrated load
4.4 Remarks
References
5. Meshless analysis for thin plate bending problems
5.1 Introduction
5.2 Fundamental solutions for thin plate bending
5.3 Solutions procedure for thin plate bending
5.3.1 Particular solution
5.3.2 Homogeneous solution
5.3.3 Approximated full solution
5.3.4 Construction of solving equations
5.4 Results and discussion
5.4.1 Square plate with simple-supported edges
5.4.2 Square plate on a winkler elastic foundation
5.5 Remarks
References
6. Meshless analysis for two-dimensional elastic problems
6.1 Introduction
6.2 Fundamental solutions for two-dimensional elasticity
6.3 Solution procedure for homogeneous elasticity
6.3.1 Solution procedure
6.3.2 Program structure and source code
6.3.3 Results and discussion
6.4 Solution procedure for inhomogeneous elasticity
6.4.1 Particular solution
6.4.2 Homogeneous solution
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