Topics in Boundary Element Research - Böcker

As the Boundary Element Method develops into a tool of engineering analysis more effort is dedicated to studying new applications and solving different problems. This book contains chapters on the basic principles of the technique, time dependent problems, fluid mechanics, hydraulics, geomechanics and plate bending. The number of non-linear and time dependent problems which have become amenable to solution using boundary elements have induced many researchers to investigate in depth the basis of the method. Chapter 0 of this book presents an ap­ proach based on weighted residual and error approximations, which permits easy construction of the governing boundary integral equations. Chapter I reviews the theoretical aspects of integral equation formulations with emphasis in their mathematical aspects. The analysis of time dependent problems is presented in Chap. 2 which describes the time and space dependent integral formulation of heat conduction problems and then proposes a numerical procedure and time marching algorithm. Chapter 3 reviews the application of boundary elements for fracture mechanics analysis in the presence of thermal stresses. The chapter presents numerical results and the considerations on numerical accuracy are of interest to analysts as well as practising engineers.

The application of BEM in all fields of engineering and science has progressed at an accelerate rate since the first book on the method appeared in the late seventies. In particular the advantages of BEM for potential problems are essential to solve a whole range of electrical engineering problems. Previous volumes in this series have focussed on the state of the art in other fields while this volume discusses only problems related to electrical engineering. The book reviews a series of important applications such as the design of semiconductor devices and their thermal analysis. The following two chapters concentrate on the study of galvanic corrosion and cathodic protection. Chapter 4 deals with the design of capacitance transducers. The next three chapters concentrate on the applications of the method to simulate electrochemical problems with special reference to Plating Process. The last chapter in the book discusses the case of inverse problems in electrical engineering and presents some applications including their use in tomography.

As the Boundary Element Method develops into a tool of engineering analysis more effort is dedicated to studying new applications and solving different problems. This book contains chapters on the basic principles of the technique, time dependent problems, fluid mechanics, hydraulics, geomechanics and plate bending. The number of non-linear and time dependent problems which have become amenable to solution using boundary elements have induced many researchers to investigate in depth the basis of the method. Chapter 0 of this book presents an ap­ proach based on weighted residual and error approximations, which permits easy construction of the governing boundary integral equations. Chapter I reviews the theoretical aspects of integral equation formulations with emphasis in their mathematical aspects. The analysis of time dependent problems is presented in Chap. 2 which describes the time and space dependent integral formulation of heat conduction problems and then proposes a numerical procedure and time marching algorithm. Chapter 3 reviews the application of boundary elements for fracture mechanics analysis in the presence of thermal stresses. The chapter presents numerical results and the considerations on numerical accuracy are of interest to analysts as well as practising engineers.

This series has been developed in response to the interest shown in boundary ele­ ments by scientists and engineers. Whilst Volume 1 was dedicated to basic principles and applications, this book is concerned with the state of the art in the solution of time-dependent problems. Since papers have recently been published on this im­ portant topic it is time to produce a work of a more permanent nature. The volume begins with a chapter on the Fundamentals of Boundary Integral Equation Methods in Elastodynamics. After reviewing the basic equations of elasto­ dynamics, the wave equation and dynamic reciprocal theorems are stated and the direct and indirect boundary element formulations are presented. Eigenvalue problems are discussed together with the case of the Fourier transformations. Several applications illustrate the effectiveness of the technique for engineering. Chapter 2 examines some of the various boundary integral equation formulations available for elastodynamic problems. In particular the displacement-traction for­ mulation is compared with the displacement-potential case. The special character­ istics of the elastodynamics fundamental solutions are discussed in detail and a criti­ cal comparison with the elastostatics case is presented. While the chapter is not meant to be a complete review of the work in the field, the original presentation of the problem and the suggestions for further work make an important contribu­ tion to the development of the method.

Past volumes of this series have concentrated on the theoretical and the more formal aspects of the boundary element method. The present book instead stresses the computational aspects of the technique and its applications with the objective of facilitating the implementation of BEM in the engineering industry and its better understanding in the teaching and research environments. The book starts by discussing the topics of convergence of solutions, application to nonlinear problems and numerical integration. This is followed by a long chapter on the computational aspects of the method, discussing the different numerical schemes and the way in which influence functions can be computed. Three separate chapters deal with important techniques which are related to classical boundary elements, namely the edge method, multigrid schemes and the complex variable boundary element approach. The last two chapters are of special interest as they present and explain in detail two FORTRAN codes which have numerous applications in engineering, i.e. a code for the solution of potential problems and another for elastostatics. Each sub­ routine in the programs is listed and explained. The codes follow the same format as the ones in the classical book "The Boundary Element Method for Engineers" (by C. A. Brebbia, Computational Mechanics Publications, first published in 1978) but are more advanced in terms of elements and capabilities. In particular the new listings deal with symmetry, linear elements for the two dimensional elasticity, some mixed type of boundary conditions and the treatment of infinite regions.

The first volume of this series dealt with the Basic Principles of Boundary Elements, while the second concentrated on time dependent problems and Volume three on the Computational Aspects of the method. This volume studies the applications of the method to a wide variety of geomechanics problems, most of which are ideally suited for boundary elements demonstrating the potentiality of the technique. Chapter 1 deals with the application of BEM to three dimensional elastody­ namics soil-structure interaction problems. It presents detailed formulations for rigid, massless foundations of arbitrary shape both in the frequency and time domains. The foundations are assumed to be resting on a linearly elastic, homogeneous, isotropic half-space and be subjected to externally applied loads on obliquely incident body. The chapter reviews the major advances in soil foundation interaction presents a series of numerical results and stresses the practical application of BEM, pointing out the high accuracy and efficiency of the technique, even when using coarse mesh discretizations.

General Applications of BEM to electromagnetic problems are comparatively new although the method is ideally suited to solve these problems, which usually involve unbounded domains. The present volume comprises contributions by eminent researchers working on applications of boundary elements in electromagnetic problems. The volume deals with the solutions of Maxwell's equation for three-dimensional as well as two-dimensional cases. It also discusses combination of BEM with FEM particularly in the case of saturated media. Some chapters specifically deal with the design of electromagnetic devices. The book is essential reading to those engineers and scientists, who are interested in the state of the art for electrical and electromagnetic application of boundary elements. It is also an important reference for those engineers who are working on the design of electromagnetic components many of which can be advantageously carried out using BEM.

The Boundary Element Method has now become a powerful tool of engineering analysis and is routinely applied for the solution of elastostatics and potential problems. More recently research has concentrated on solving a large variety of non-linear and time dependent applications and in particular the method has been developed for viscous fluid flow problems. This book presents the state of the art on the solution of viscous flow using boundary elements and discusses different current approaches which have been validated by numerical experiments. . Chapter 1 of the book presents a brief review of previous work on viscous flow simulation and in particular gives an up-to-date list of the most important BEM references in the field. Chapter 2 reviews the governing equations for general viscous flow, including compressibility. The authors present a compre­ hensive treatment of the different cases and their formulation in terms of boundary integral equations. This work has been the result of collaboration between Computational Mechanics Institute of Southampton and Massa­ chusetts Institute of Technology researchers. Chapter 3 describes the gen­ eralized formulation for unsteady viscous flow problems developed over many years at Georgia Institute of Technology. This formulation has been extensively applied to solve aer09ynamic problems.