Boundary Element Formulations for Thick Plates
Published in September 1999
Book
Hardback
176 pages
978-1-85312-628-4 (ISBN)
Description
Plate bending problems have many applications in civil and mechanical engineering. The analysis of plates using the Boundary Element Method (BEM), however, has received little attention in existing research and literature. This book presents new Boundary Element formulations for plate bending problems in which the Reissner plate bending theory is used to model the bending behaviour of the plate. The author applies several integral equations to solve engineering problems relating to a building slab, beam, footing, and simple raft and the results are compared against analytical solutions such as a finite difference method, a finite element method and a three-dimensional boundary element method. These confirm that the Boundary Element formulations presented are a competitive alternative to existing numerical methods.
More details
Series
Language
English
Place of publication
Southampton
United Kingdom
Target group
College/higher education
Professional and scholarly
Illustrations
illustrations
Dimensions
Height: 242 mm
Width: 165 mm
ISBN-13
978-1-85312-628-4 (9781853126284)
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Schweitzer Classification
Content
Section 1 - Introduction: General; Numerical models in plate bending; Overview of the present work. Section 2 - Theory of Plates: Introduction; Basic definitions; Equilibrium equations; Stress resultant-strain relationships; Boundary conditions; Evaluation of the constants; Significance of the generalised displacements; Notes on Mindlin's theory; Foundation plates; Summary. Section 3 - The Boundary Element Method: Introduction; Integral representation; Boundary integral equation; Discretisation; Treatment of the singularities; System of equations; Internal point functions; Examples; Summary and conclusions. Section 4 - Hypersingular Integral Equation Formulation: Introduction; Hypersingular integral equations; The traction integral equations; Numerical implementation; Singularities; Boundary stress resultants; Numerical examples; Summary and conclusions. Section 5 - Integral Equation Formulation and Fundamental Solution for Foundation Plates: Introduction; Integral representation; Fundamental solutions; Summary. Section 6 - Transformation of Domain Integrals to the Boundary for Foundation Plates: Introduction; Relevant domain integrals; Cell integration; Equivalent boundary integrals; Evaluation of the particular solutions; Singular terms; Boundary collocation; Internal collocation; Numerical discussions; Summary and conclusions. Section 7 - The Boundary Element Method for Foundation Plates: Introduction; Boundary integral equation; Matrix equation; Internal point functions; Examples; Summary and conclusions. Section 8 - Applications in Structural Analysis: Introduction; Applications; Summary and conclusions.