Discontinuous Materials and Structures (Advances in Boundary Elements Ser., Vol. 5)

Research into the Boundary Element Method in all its various forms has reached a high level of maturity and it is now well established as part of the computational tool box.
The contributors to this volume focus on a class of problems where the BEM can be exploited to full effect. These involve global variations in material behaviour, where the material properties vary throughout the domain in a piecewise constant fashion, or where the variation may be adequately represented by an anisotropic elastic medium approximation.

Preface Research into the Boundary Element Method in all its various forms has reached a very mature state, and the method is now well established as a respectable resident of the computational tool box. It seems there is no field of application that cannot be tackled using this method, and in many cases it is the "method of choice". This is particularly true when the unique advantages of the technique can be exploited. The most obvious of these advantages becomes apparent in the treatment of linear material or field problems, where it can be implemented as a true "boundary" element method. In many applications one only requires the solutions on the boundary to solve the problem in hand, and in these cases the power of the method can be quite spectacular. Much of this power is retained in applications involving non-linear boundary conditions, such as thermal radiation or surface contact problems. It is only when we deal with, for example, problems involving spatial variations in material properties or viscous flow problems at non-trivial Reynolds numbers that the need for a domain mesh may detract from the method.

The focus of this volume is a class of problems that involve global variations in material behaviour, but where the material properties vary throughout the domain in a piecewise constant fashion, thereby permitting the use of a sub-structure approach, or where the variation may be adequately represented by an anisotropic elastic medium approximation, In either case, the full power of the Boundary Element Method can be exploited. If sub-structuring is to be utilised, the equations corresponding to each sub-region can then be assembled to yield the overall solution. In some cases the material behaviour in a sub-region may be non-linear, but provided a substantial proportion of the problem exhibits linear behaviour, the Boundary Element Method remains an attractive tool.

The contributions to this volume provide an illustration of the wide variety of such applications that may be treated using various forms of the Boundary Element Method. These applications range from prediction of the behaviour of micro-composite systems (Chapters 1 and 2) to analysis of macro-composite structures (Chapter 3), and in fields ranging from fluid mechanics (Chapter 4) to geomechanics (Chapter 6). The use of the anisotropic approximation is demonstrated with reference to composite laminates and rock masses in Chapters 5 and 6. The potential benefits to be gained by coupling BEM and FEM are highlighted in Chapters 6 and 7. In particular, coupling of the two methods permits certain laminated structures to be handled without recourse to the anisotropic approximation (Chapter 7).

We have deliberately avoided the use of the term "composite material" in the title of this volume in recognition of the fact that such systems are not restricted to the realm of solid mechanics. In fact there exists now a very active worldwide effort focused on the application of boundary integral equations to particle suspensions (Chapter 4). These problems are unique in that the distribution and orientation of the suspended phase changes with time. The solution must utilise algorithms for following the trajectory of each particle and to correctly model the particle-particle interactions. Mark B. Bush Perth, Australia 1999