Boundary Element Method for Plate Analysis offers one of the first systematic and detailed treatments of the application of BEM to plate analysis and design.
Aiming to fill in the knowledge gaps left by contributed volumes on the topic and increase the accessibility of the extensive journal literature covering BEM applied to plates, author John T. Katsikadelis draws heavily on his pioneering work in the field to provide a complete introduction to theory and application.
Beginning with a chapter of preliminary mathematical background to make the book a self-contained resource, Katsikadelis moves on to cover the application of BEM to basic thin plate problems and more advanced problems. Each chapter contains several examples described in detail and closes with problems to solve. Presenting the BEM as an efficient computational method for practical plate analysis and design, Boundary Element Method for Plate Analysis is a valuable reference for researchers, students and engineers working with BEM and plate challenges within mechanical, civil, aerospace and marine engineering.

This book presents the Boundary Element Method, BEM, for the static and dynamic analysis of plates and membranes. It is actually a continuation of the book Boundary Elements: Theory and Applications by the same author and published by Elsevier in 2002. The latter was well received as a textbook by the relevant international scientific community, which is ascertained by the fact that it was translated into three languages, Japanese by the late Prof. Masa Tanaka of the Shinshu University, Nagano (Asakura, Tokyo 2004), in Russian by the late Prof. Sergey Aleynikov of the Voronezh State Architecture and Civil Engineering University (Publishing House of Russian Civil Engineering Universities, Moscow 2007), and in Serbian by Prof. Dragan Spasic of the University of Novi Sad (Gradjevinska Κnjiga, Belgrade 2011).

Foreword viii

Preface xi

1 Preliminary Mathematical Knowledge 1

1.1 Introduction 1

1.2 Gauss-Green Theorem 2

1.3 Divergence Theorem of Gauss 3

1.4 Green's Second Identity 4

1.5 Adjoint Operator 5

1.6 Dirac Delta Function 6

1.7 Calculus of Variations; Euler-Lagrange Equation 11

1.8 References 18

Problems 19

2 BEM for Plate Bending Analysis 21

2.1 Introduction 22

2.2 Thin Plate Theory 23

2.3 Direct BEM for the Plate Equation 40

2.4 Numerical Solution of the Boundary Integral Equations 61

2.5 PLBECON Program for Solving the Plate Equation with Constant Boundary Elements 72

2.6 Examples 79

2.7 References 109

Problems 110

3 BEM for Other Plate Problems 113

3.1 Introduction 114

3.2 Principle of the Analog Equation 115

3.3 Plate Bending Under Combined Transverse and Membrane Loads; Buckling 118

3.4 Plates on Elastic Foundation 141

3.5 Large Deflections of Thin Plates 152

3.6 Plates with Variable Thickness 166

3.7 Thick Plates 177

3.8 Anisotropic Plates 187

3.9 Thick Anisotropic Plates 196

3.10 References 203

Problems 207

4 BEM for Dynamic Analysis of Plates 211

4.1 Direct BEM for the Dynamic Plate Problem 212

4.2 AEM for the Dynamic Plate Problem 217

4.3 Vibrations of Thin Anisotropic Plates 237

4.4 Yiscoelastic Plates 241

4.5 References 251

Problem s 253

5 BEM for Large Deflection Analysis of Membranes 257

5.1 lntroduction 257

5.2 Static Analysis of Elastic Membranes 259

5.3 Dynamic Analysis of Elastic Membranes 270

5.4 Yiscoelastic Membranes 275

5.7 References 283

Problems 285

Appendix A: Derivatives of r and Kernels, Particular Solutions and Tangential Derivatives 287

A ppendix B: Gauss Integration 297

A ppendix C: Numerical Integration of the Equations of Motion 313

Index 325

中科院文献情报中心