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 Numericalexperiments
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-conditioningtreatments
1．5．4 Inhomogeneousproblems
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 Displacementcomponents
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 Equilibriumequations
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 Governingequations
2．4．3 Boundary conditions
2．5 Equations for Euler-Bernoulli beams
2．5．1 Deformation mode
2．5．2 Governingequations
2．5．3 Boundary conditions
2．5．4 Continuity requirements
2．6 Equations for thin plates
2．6．1 Deformation mode
2．6．2 Governingequations
2．6．3 Boundary conditions
2．7 Equations for piezoelectricity
2．7．1 Governingequations
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 Solutionprocedures
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
……
Appendix A Derivatives of functions in terms of radial
variable r
Appendix B Transformations
Appendix C Derivatives of approximated particular solutions
in inhomogeneous plane elasticity
