Boundary Methods: Elements, Contours, and Nodes, 1st Edition (Hardback) book cover

Boundary Methods

Elements, Contours, and Nodes, 1st Edition

By Subrata Mukherjee, Yu Xie Mukherjee

CRC Press

248 pages | 85 B/W Illus.

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pub: 2005-03-17
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Description

Boundary Methods: Elements, Contours, and Nodes presents the results of cutting-edge research in boundary-based mesh-free methods. These methods combine the dimensionality advantage of the boundary element method with the ease of discretization of mesh-free methods, both of which, for some problems, hold distinct advantages over the finite element method.

After introducing some novel topics related to the boundary element method (BEM), the authors focus on the boundary contour method (BCM)-a variant of the BEM that further reduces the dimensionality of a problem. The final section of the book explores the boundary node method, which combines the BEM with moving least-squares approximants to produce a mesh-free, boundary-only method.

The authors, who are also the primary developers of these methods, clearly introduce and develop each topic. In addition to numerical solutions of boundary value problems in potential theory and linear elasticity, they also discuss topics such as shape sensitivities, shape optimization, and adaptive meshing. Numerical results for selected problems appear throughout the book, as do extensive references.

Table of Contents

INTRODUCTION TO BOUNDARY METHODS

I SELECTED TOPICS IN BOUNDARY ELEMENT

METHODS

BOUNDARY INTEGRAL EQUATIONS

Potential Theory in Three Dimensions

Linear Elasticity in Three Dimensions

Nearly Singular Integrals in Linear Elasticity

Finite Parts of Hypersingular Equations

ERROR ESTIMATION

Linear Operators

Iterated HBIE and Error Estimation

Element-Based Error Indicators

Numerical Examples

THIN FEATURES

Exterior BIE for Potential Theory: MEMS

BIE for Elasticity: Cracks and Thin Shells

II THE BOUNDARY CONTOUR METHOD

LINEAR ELASTICITY

Surface and Boundary Contour Equations

Hypersingular Boundary Integral Equations

Internal Displacements and Stresses

Numerical Results

SHAPE SENSITIVITY ANALYSIS

Sensitivities of Boundary Variables

Sensitivities of Surface Stresses

Sensitivities of Variables at Internal Points

Numerical Results: Hollow Sphere

Numerical Results: Block with a Hole

SHAPE OPTIMIZATION

Shape Optimization Problems

Numerical Results

ERROR ESTIMATION AND ADAPTIVITY

Hypersingular Residuals as Local Error Estimators

Adaptive Meshing Strategy

Numerical Results

III THE BOUNDARY NODE METHOD

SURFACE APPROXIMANTS

Moving Least Squares (MLS) Approximants

Surface Derivatives

Weight Functions

Use of Cartesian Coordinates

POTENTIAL THEORY AND ELASTICITY

Potential Theory in Three Dimensions

Linear Elasticity in Three Dimensions

ADAPTIVITY FOR 3-D POTENTIAL THEORY

Hypersingular and Singular Residuals

Error Estimation and Adaptive Strategy

Progressively Adaptive Solutions: Cube Problem

One-Step Adaptive Cell Refinement

ADAPTIVITY FOR 3-D LINEAR ELASTICITY

Hypersingular and Singular Residuals

Error Estimation and Adaptive Strategy

Progressively Adaptive Solutions: Pulling a Rod

One-Step Adaptive Cell Refinement

Bibliography

Index

About the Series

Mechanical Engineering

A Series of Textbooks and Reference Books

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
TEC009020
TECHNOLOGY & ENGINEERING / Civil / General
TEC009070
TECHNOLOGY & ENGINEERING / Mechanical