Bücher von C. A. Brebbia

The boundary element method (BEM) is now a well-established numerical technique which provides an efficient alternative to the prevailing finite difference and finite element methods for the solution of a wide range of engineering problems. The main advantage of the BEM is its unique ability to provide a complete problem solution in terms of boundary values only, with substantial savings in computer time and data preparation effort. An initial restriction of the BEM was that the fundamental solution to the original partial differential equation was required in order to obtain an equivalent boundary in­ tegral equation. Another was that non-homogeneous terms accounting for effects such as distributed loads were included in the formulation by means of domain integrals, thus making the technique lose the attraction of its "boundary-only" character. Many different approaches have been developed to overcome these problems. It is our opinion that the most successful so far is the dual reciprocity method (DRM), which is the subject matter of this book. The basic idea behind this approach is to employ a fundamental solution corresponding to a simpler equation and to treat the remaining terms, as well as other non-homogeneous terms in the original equation, through a procedure which involves a series expansion using global approximating functions and the application of reciprocity principles.

Over a period of several years the field of probabilistic mechanics and com­ putational mechanics have progressed vigorously, but independently. With the advent of powerful computational hardware and the development of novel mechanical techniques, the field of stochastic mechanics has progressed in such a manner that the inherent uncertainty of quite complicated systems can be addressed. The first International Conference on Computational Stochastic Mechanics was convened in Corfu in September 1991 in an ef­ fort to provide a forum for the exchanging of ideas on the current status of computational methods as applied to stochastic mechanics and for identi­ fying needs for further research. The Conference covered both theoretical techniques and practical applications. The Conference also celebrated the 60th anniversary of the birthday of Dr. Masanobu Shinozuka, the Sollenberger Professor of Civil Engineering at Princeton University, whose work has contributed in such a great measure to the development of Computational Stochastic Mechanics. A brief sum­ mary of his career and achievements are given in the Dedication. This book comprises some of the papers presented at the meeting and cov­ ers sections on Theoretical Reliability Analysis; Damage Analysis; Applied Reliability Analysis; Theoretical Random Vibrations; Stochastic Finite Ele­ ment Concept; Fatigue and Fracture; Monte Carlo Simulations; Earthquake Engineering Applications; Materials; Applied Random Vibrations; Applied Stochastic Finite Element Analysis, and Flow Related Applications and Chaotic Dynamics. The Editors hope that the book will be a valuable contribution to the grow­ ing literature covering the field of Computational Stochastic Mechanics.

This book comprises an edited version of the Proceedings of the 2nd Interna­ tional Conference on Applications of Supercomputers in Engineering which took place at the Massachusetts Institute of Technology, Cambridge, USA during August 1991. The Conference was organized by the Wessex Insti­ tute of Technology, Southampton, UK with the support of the International Society for Boundary Elements. The first International Conference on Ap­ plications of Supercomputers in Engineering held in Southampton, UK in September 1989 was a very successful meeting and the resulting Conference Proceedings are now widely distributed throughout the world. The revolutionary aspects of the next generation of computers are now fully recognised by many engineers and scientists. Vector and parallel computers form the basis of the computing power needed to address the complex prob­ lems with which engineers are faced. The new machines not only increase the size of the problems which can be solved, but also require a different computational approach to obtain the most efficient results.

As the Boundary Element Method develops into a tool of engineering analysis more effort is dedicated to studying new applications and solving different problems. 2 which describes the time and space dependent integral formulation of heat conduction problems and then proposes a numerical procedure and time marching algorithm.

VI SOCRATES: I think that we ought to stress that we will write only about things that we have first hand experience in, in a coherent way that will be useful to engineers and other scientists and stressing the formulation without being too mathematical.