醉染图书固体力学中的基本解方法(英文版)9787040558197

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 te eho 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 Numerica xermets

1.5 Some limitations for implementing te eho 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.. Strain components

. Equations for three-dimensional solids

..1 Strain-displacement relation

..2 Equilibrium equations

.. Constitutive equations

..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.. 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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