Book description
Boundary Element Techniques in Engineering deals with solutions of two and threedimensional problems in elasticity and the potential theory where finite elements are inefficient. The book discusses approximate methods, higherorder elements, elastostatics, timedependent problems, nonlinear problems, and combination of regions. Approximate methods include weighted residual techniques, weak formulations, the inverse formulation, and boundary methods. The text also explains Laplace's equation, indirect formulation, matrix formulation, Poisson's equation, and the Helmholtz equation. It describes how elements with linear variations of u and q (i.e. linear elements) can be developed for two dimensional problems, as well as for quadratic and higher order elements for twodimensional problems. The text investigates the Dirac delta function as a sum of Eigen functions, including some methods to determine the explicit form of fundamental solutions for recurrent problems. The book also tackles the application of boundary elements to problems with both material and certain types of geometric nonlinearities, and also the applications of boundary elements to plasticity problems. The text is ideal for mathematicians, students, and professor of calculus or advanced mathematics.
Table of contents
 Front Cover
 Boundary Element Techniques in Engineering
 Copyright Page
 Preface
 Table of Contents
 Chapter 1. Approximate Methods
 Chapter 2. Potential Problems

Chapter 3. HigherOrder Elements
 3.1 INTRODUCTION
 3.2 LINEAR ELEMENTS FOR TWODIMENSIONAL PROBLEMS (1/2)
 3.2 LINEAR ELEMENTS FOR TWODIMENSIONAL PROBLEMS (2/2)
 3.3 QUADRATIC AND HIGHERORDER ELEMENTS
 3.4 ELEMENTS FOR THREEDIMENSIONAL PROBLEMS (1/3)
 3.4 ELEMENTS FOR THREEDIMENSIONAL PROBLEMS (2/3)
 3.4 ELEMENTS FOR THREEDIMENSIONAL PROBLEMS (3/3)
 3.5 THREEDIMENSIONAL ELEMENTS
 3.6 ORDER OF INTERPOLATION FUNCTIONS
 REFERENCES
 BIBLIOGRAPHY

Chapter 4. Fundamental Solutions
 4.1 INTRODUCTION
 4.2 EIGENFUNCTIONS AND THE DIRAC DELTA FUNCTION
 4.3 FUNDAMENTAL SOLUTIONS ON A FINITE REGION
 4.4 INFINITE DOMAINS
 4.5 THE FUNDAMENTAL SOLUTION IN INFINITE SPACE
 4.6 NUMERICAL SOLUTIONS (ANISOTROPIC BODIES)
 4.7 THE METHOD OF IMAGES (1/2)
 4.7 THE METHOD OF IMAGES (2/2)
 4.8 THE FUNDAMENTAL SOLUTION AND BOUNDARY ELEMENTS
 4.9 EXPLICIT FORMS FOR THE FUNDAMENTAL SOLUTION
 REFERENCES
 Chapter 5. Elastostatics

Chapter 6. TimeDependent and NonLinear Problems
 6.1 INTRODUCTION
 6.2 TRANSFORM METHODS
 6.3 FOURIER TRANSFORMS
 6.4 LAPLACE TRANSFORMS10
 6.5 TRANSIENT ELASTODYNAMICS
 6.6 STEADY STATE ELASTODYNAMICS
 6.7 VISCOELASTIC PROBLEMS
 6.8 TIME INTEGRATION USING TIME STEPPING
 6.9 TIMEDEPENDENT FUNDAMENTAL SOLUTION
 6.10 NONLINEAR PROBLEMS
 6.11 PLASTICITY AND SOIL MECHANICS PROBLEMS
 REFERENCES

Chapter 7. Combination of Regions
 7.1 INTRODUCTION
 7.2 DIVISION INTO REGIONS (1/2)
 7.2 DIVISION INTO REGIONS (2/2)
 7.3 APPROXIMATE BOUNDARY SOLUTIONS (1/3)
 7.3 APPROXIMATE BOUNDARY SOLUTIONS (2/3)
 7.3 APPROXIMATE BOUNDARY SOLUTIONS (3/3)
 7.4 INFINITE ELEMENTS
 7.5 COMBINATION OF FINITE AND BOUNDARY ELEMENTS (1/2)
 7.5 COMBINATION OF FINITE AND BOUNDARY ELEMENTS (2/2)
 REFERENCES
 Index
Product information
 Title: Boundary Element Techniques in Engineering
 Author(s):
 Release date: January 2016
 Publisher(s): Newnes
 ISBN: 9781483102566
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