1st Edition
Boundary Methods Elements, Contours, and Nodes
248 Pages
85 B/W Illustrations
by
CRC Press
248 Pages
by
CRC Press
Also available as eBook on:
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... Read more
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
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
Biography
Subrata Mukherjee, Yu Xie Mukherjee
