Fracture, and particularly brittle fracture, is a good example of an instability. For a homogeneous solid, subjected to a uniform stress field, a crack may appear anywhere in the structure once the threshold stress is reached. However, once a crack has been nucleated in some place, further damage in the solid will in most cases propagate from the initial crack, and not somewhere else in the solid. In this sense fracture is an unstable process. This property makes the process extremely sensitive to any heterogeneity present in the medium, which selects the location of the first crack nucleated. In particular, fracture appears to be very sensitive to disorder, which can favor or impede local cracks. Therefore, in most realistic cases, a good description of fracture mechanics should include the effect of disorder. Recently this need has motivated work in this direction starting from the usual description of fracture mechanics. Parallel with this first trend, statistical physics underwent a very important development in the description of disordered systems. In particular, let us mention the emergence of some "new" concepts (such as fractals, scaling laws, finite size effects, and so on) in this field. However, many models considered were rather simple and well adapted to theoretical or numerical introduction into a complex body of problems. An example of this can be found in percolation theory. This area is now rather well understood and accurately described.

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas­ sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe­ matical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface A wide range of problems exists in classical and quantum physics, engi­ neering, and applied mathematics in which special functions arise. The procedure followed in most texts on these topics (e. g. , quantum mechanics, electrodynamics, modern physics, classical mechanics, etc. ) is to formu­ late the problem as a differential equation that is related to one of several special differential equations (Hermite's, Bessel's, Laguerre's, Legendre's, etc. ).

Objectives This book is used to teach vibratory mechanics to undergraduate engineers at the Swiss Federal Institute of Technology of Lausanne. It is a basic course, at the level of the first university degree, necessary for the proper comprehension of the following disciplines. Vibrations of continuous linear systems (beams, plates) random vibration of linear systems vibrations of non-linear systems dynamics of structures experimental methods, rheological models, etc. Effective teaching methods have been given the highest priority. Thus the book covers basic theories of vibratory mechanics in an ap­ propriately rigorous and complete way, and is illustrated by nume­ rous applied examples. In addition to university students, it is suitable for industrial engineers who want to strengthen or complete their training. It has been written so that someone working alone should find it easy to read. pescription The subject of the book is the vibrations of linear mechanical sys­ tems having only a finite number of degrees of freedom (ie discrete linear systems). These can be divided into the following two catego­ ries : -X- systems of solids which are considered to be rigid, and which are acted upon by elastic forces and by linear resist.ive forces (viscous damping forces). deformable continuous systems which have been made discrete. In other words, systems which are replaced (approximately) by systems having only a limited number of degrees of freedom, using digital or experimental methods.

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.

Recent advances in the field of fracture of engineering materials and structures have increasingly indicated its multidisciplinary nature. This area of research now involves scientists and engineers who work in materials science, applied mathematics and mechanics, and also computer scientists. The present volume, which contains the Proceedings of the Joint FEFG/lCF International Conference on Fracture of Engineering Materials and Structures held in Singapore from the 6th to 8th of August 1991, is a testimony of this multidisciplinary nature. This International Conference was the Second Symposium of the Far East Fracture Group (FEFG) and thus provided a unique opportunity for researchers and engineers in the Far East region to exchange and acquire knowledge of new advances and applications in fracture. The Conference was also the Inter-Quadrennial International Conference on Fracture (ICF) for 1991 and thus appealed to researchers in the international arena who wished to take advantage of this meeting to present their findings. The Conference has brought together over 130 participants from more than 24 countries, and they represented government and industrial research laboratories as well as academic institutions. It has thus achieved its objective of bringing together scientists and engineers with different backgrounds and perspectives but with . a common interest in new developments in the fracture of engineering materials and structures. This volume contains 4 keynote papers, 4 invited papers and 130 contributed papers.