RELAXATION OF PROBLEMS OF OPTIMAL STRUCTURAL DESIGN

The problem of optimal structural design is considered. The goal of de sign is to minimize an integral functional which characterized the qua lity of construction. Classes of optimal microstructures of composites made of given materials are described and analysed. The proposed meth od deals with the averaged description of minimizing sequences of mate rials layout which physically are the composites with a special micros tructure. In contrast with the known approach of the G-closure descrip tion, the suggested procedure does not require the description of the full variety of effective properties of an arbitrary composite, but in stead selects the class of structures which are the only candidates to optimal design. The approach is illustrated by the structural design problems of conducting and elastic composites.