Optimal Design and Relaxation of Variational Problems. I

摘要

The focus of this three-part paper is the interrelation between structural design optimization, relaxation of variational problems, and homogenization. Our principal contribution is a set of methods for computing examples. From one point of view we obtain explicitly the relaxed form of certain variational problems; the same ideas in different language lead to algorithms for resolving questions of structural optimization. Our primary attention is devoted to certain model problems in two dimensions, but the approach is explained in more general terms. Part one states that optimal design chooses the shape of a structure to maximize its strength, thus making the most efficient possible use of the material available. Keywords: reprints.