Shape Design Sensitivity Analysis And Optimization Using The Boundary Element Method

This book investigates the various aspects of shape optimization of two dimensional continuum structures, including shape design sensitivity analysis, structural analysis using the boundary element method (BEM), and shape optimization implementation. The book begins by reviewing the developments of shape optimization, followed by the presentation of the mathematical programming methods for solving optimization problems. The basic theory of the BEM is presented which will be employed later on as the numerical tool to provide the structural responses and the shape design sensitivities. The key issue of shape optimization, the shape design sensitivity analy sis, is fully investigated. A general formulation of stress sensitivity using the continuum approach is presented. The difficulty of the modelling of the ad joint problem is studied, and two approaches are presented for the modelling of the adjoint problem. The first approach uses distributed loads to smooth the concentrated adjoint loads, and the second approach employs the singu larity subtraction method to remove the singular boundary displacements and tractions from the BEM equation. A novel finite difference based approach to shape design sensitivity is pre sented, which overcomes the two drawbacks of the conventional finite difference method. This approach has the advantage of being simple in concept, and eas ier implementation. A shape optimization program for two-dimensional continuum structures is developed, including structural analysis using the BEM, shape design sensitiv ity analysis, mathematical programming, and the design boundary modelling.

This volume presents and discusses recent advances in boundary element methods and their solid mechanics applications. It illustrates these methods in their latest forms, developed during the last five to ten years, and demonstrates their advantages in solving a wide range of solid mechanics problems.

This book is motivated largely by a desire to solve shape optimization prob lems that arise in applications, particularly in structural mechanics and in the optimal control of distributed parameter systems. Many such problems can be formulated as the minimization of functionals defined over a class of admissible domains. Shape optimization is quite indispensable in the design and construction of industrial structures. For example, aircraft and spacecraft have to satisfy, at the same time, very strict criteria on mechanical performance while weighing as little as possible. The shape optimization problem for such a structure consists in finding a geometry of the structure which minimizes a given functional (e. g. such as the weight of the structure) and yet simultaneously satisfies specific constraints (like thickness, strain energy, or displacement bounds). The geometry of the structure can be considered as a given domain in the three-dimensional Euclidean space. The domain is an open, bounded set whose topology is given, e. g. it may be simply or doubly connected. The boundary is smooth or piecewise smooth, so boundary value problems that are defined in the domain and associated with the classical partial differential equations of mathematical physics are well posed. In general the cost functional takes the form of an integral over the domain or its boundary where the integrand depends smoothly on the solution of a boundary value problem.

This volume contains edited papers from IABEM-90, the 1990 Symposium of the Interna tional Association for Boundary Element Methods (IABEM). As stated in the By-Laws of the Association, the purposes of IABEM are: 1. to promote the international exchange of technical information related to the devel opment and application of boundary-integral equation (BIE) formulations and their numerical implementation to problems in engineering and science, commonly referred to as the boundary element method (BEM); 2. to promote research and development activities for the advancement of boundary integral equation methods and boundary element solution algorithms; 3. to foster closer personal relationships within the BEM community of researchers. The objectives of the Symposium, in line with those of the Association, was to provide a forum where the two "souls" of the Association, i. e. , (i) mathematical foundations and numerical aspects, and (ii) engineering applications could be integrated. We believe that the first aspect has been neglected in too many of the BEM Symposia held in the past, which, with a few exceptions (notably, the IUTAM Symposia on the subject) have emphasized the practical aspects of the method. As a consequence, we have tried to give a stronger emphasis to the more theoretical issues: this is attested for instance, by the fact that the two general lectures were given by Prof. Gaetano Fichera, of the University of Rome "La Sapienza," and Prof.

Extensive numerical methods for computing design sensitivity are included in the text for practical application and software development. The numerical method allows integration of CAD-FEA-DSA software tools, so that design optimization can be carried out using CAD geometric models instead of FEA models. This capability allows integration of CAD-CAE-CAM so that optimized designs can be manufactured effectively.

Proceedings of the IUTAM Symposium held in Cracow, Poland, 24-27 September 2002

With the advent of powerful computers and novel mathematical programming techniques, the multidisciplinary field of optimization has advanced to the stage that quite complicated systems can be addressed. The conference was organized to provide a platform for the exchanging of new ideas and information and for identifying areas for future research. The contributions covered both theoretical techniques and a rich variety of case studies to which optimization can be usefully applied.

Originating from the 42nd conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM), the research presented in this book consist of high quality papers that report on advances in techniques that reduce or eliminate the type of meshes associated with such methods as finite elements or finite differences.