Comparisons of optimality criteria for minimum-weight dual material structures

A criterion established by Prager for minimum-weight design of structures, using different materials for tension and compression members, referred to here as bi-material structures, appears to have been completely overlooked in the literature. Cantilever and simply supported beam designs are analyzed to compare the result of applying this criterion with the conditions established by Michell in his groundbreaking paper on structural optimization. Surprisingly, for statically determinate bi-material structures, Michellʹs original conditions for minimum volume, also ensure minimum weight. However, for statically indeterminate structures, Michellʹs criterion does not give least weight unless the ratio, of yield stress to density, is the same for tension and compression members. For statically indeterminate cantilever design cases analyzed in this paper, the weight differences between those satisfying Michellʹs and Pragerʹs conditions are shown to be very small, even when the ratio of yield stress to density tension differs by a factor of 7 between the tension and compression members. This allows the selection of alternative structural layouts for other attributes than minimum weight.