Distributed Parameter Optimal Structural Design: Some Basic Problem Formulations and their Application

As a part of the broad development that has taken place in the field of structural optimization in recent years, analytical modelling for the design of continuum structures has been extended to cover a variety of new applications. Thus there are formulations available now for the optimization with respect to various modes of response or measures of performance, for most types of structural form, to be optimal relative to material distribution, shape, choice of materials, prestress, and so on. Only a modest part out of the comprehensive list of topics is to be covered in these lectures. The reader will find a good many of the major areas of application e.g., ‘design for dynamic response,’ ‘shape design’, ‘grid optimization,’ and ‘sensitivity analysis’ — to name a few, treated in separate lectures given elsewhere within the institute. (Citations to other lectures in this collection are identified by the authors name with an asterisk attached to it.) Our effort is directed more toward an exposition of methods for the interpretation of design problems into a form convenient for analysis. This is to be done mainly within the perspective of well known results from the mathematics of optimization. The material presented here is comprised for the most part of formal problem statements, listings and interpretation of necessary conditions, and the presentation of example applications.