C. A. Brebbia

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. We should write with integrity and honesty, giving reference to other authors where reference is due, but avoiding mentioning everybody just to be certain that our book is widely advertised. Above all, the book should be clear and useful. PLATO: I think we should include a good discussion of fundamental ideas, of how integral equations are formed, pointing out that they are like two dimensional shadows of three dimensional objects, ... SOCRATES: Stop there! Remember you are not 'the' Plato! PLATO: Sorry, I was carried away. ARISTOTLE: I think that the book should have many applications so that the reader can learn by looking at them how to use the method. SOCRATES: I agree. But we should be careful. It is easy to include many illustra­ tions and examples in a book in order to disguise its meagre contents. All examples should be relevant. ARISTOTLE: And we should also include a full computer program to give the reader if so he wishes, a working experience of the technique.

The advent of rapid, reliable and cheap computing power over the last decades has transformed many, if not most, fields of science and engineering. The multidisciplinary field of optimization is no exception. First of all, with fast computers, researchers and engineers can apply classical optimization methods to problems of larger and larger size. In addition, however, researchers have developed a host of new optimization algorithms that operate in a rather different way than the classical ones, and that allow practitioners to attack optimization problems where the classical methods are either not applicable or simply too costly (in terms of time and other resources) to apply. This book is intended as a course book for introductory courses in stochastic optimization algorithms (in this book, the terms optimization method and optimization algorithm will be used interchangeably), and it has grown from a set of lectures notes used in courses, taught by the author, at the international master programme Complex Adaptive Systems at Chalmers University of Technology in Goteborg, Sweden.Thus, a suitable audience for this book are third and fourth-year engineering students, with a background in engineering mathematics (analysis, algebra, and probability theory) as well as some knowledge of computer programming.

The increasing size and complexity of new structural forces in engineering have made it necessary for designers to be aware of their dynamic behaviour. Dynamics is a subject which has traditionally been poorly taught in most engineering courses. This book was conceived as a way of providing engineers with a deeper knowledge of dynamic analysis and of indicating to them how some of the new vibrations problems can be solved. The authors start from basic principles to end up with the latest random vibration applications. The book originated 1n a week course given annually by the authors at the Computational Mechanics Centre, Ashurst Lodge, Southampton, England. Special care was taken to ensure continuity in the text and notations. Southampton 1984 CONTENTS Page Foreword Chapter 1 Introduction to Vibration 1. Introductory Remarks 1 2. Single Degree of Freedom Systems: Equations of Motion and Types of Problem 2 3. Response 6 4. General Structures: Equations of Motion 11 5. Response 15 6. Dynamic Interaction Problems 20 Chapter 2 Free Vibration, Resonance and Damping l. Introduction 25 25 2. Spring-Mass System 3. Simple Pendulum 27 4. Beam with Central Load 28 5. Rolling of a Ship 28 6. Springs in Parallel 30 7. Springs in Series 30 8. Free Vibration 31 9. Energy of Vibrating System 33 10. Damped Free Vibration 34 11. Undamped Forced Response 38 12. Damped Forced Response 39 13. Undamped Transient Vibration 42 14. Damped Transient Vibration 43 15.

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.