Some Problems of Structural Optimization

Abstract

Here we discuss global features of optimally assembled bodies and various formulations of optimization problems. So far, we have mainly discussed the best microstructures of composites. Now we comment on the optimal layout of these composites in an optimally designed body. According to our main concept, the optimal composites have a quasiperiodic structure that varies smoothly with the stress field (see, for example, (Armand et al., 1984)). In dealing with composites, we assume that the scale of the periodicity cells is so small that the external field can be treated as homogeneous, hence the composite is represented by its effective tensor. We keep this concept, but now we consider variation in the effective tensor.