Cost minimization of 2D continuum structures under stress constraints by increasing commonality in their skeletal equivalents

It is well known that, for real-life engineering problems, minimum weight does not necessarily mean minimum cost, thus it is of practical value to simultaneously achieve both layout optimization and cost minimization of a structure. Towards this direction, the present paper discusses a procedure of four steps concerning 2D continuum structures under stress constraints only. The continuum is first substituted by an equivalent skeletal structure, which is then optimized using the Sequential Quadratic Programming (SQP) technique. In the sequel the optimized structural members of equal or near-equal cross-sections are appropriately grouped and finally all optimized structural members of imposed critical minimum or near-minimum cross-section are eliminated. Both grouping and elimination procedures were based on a simple statistical manipulation. The proposed procedure was applied to four test cases, namely the short and long cantilever, the MBB beam and the L-shape beam. The conclusion of the present work was that, for 2D continuum structures under stress constraints only, the proposed procedure provided the means for both layout optimization and structural cost minimization.