Minimum-weight design with piecewise constant specific stiffness

Much of the literature on minimum-weight design is concerned with structures with continuously varying dimensions. Structures of this kind achieve an absolute minimum of weight and thereby provide a useful standard of comparison, but their manufacturing cost is prohibitive in most applications. As a step toward the establishment of optimality conditions for more practical structures, the present paper discusses optimal design of sandwich beams and frames with segmentwise constant cross sections. Optimality is shown to require that the mean square stress in the face sheets has the same value for all segments. The use of the optimality condition is illustrated by examples.