Structural optimization under uncertainty in loading directions: Benchmark results

In this paper, using a recently developed unified approach, benchmark results are presented for structural optimization when the only source of uncertainty is the variability of the applied load directions. The worst-load-direction oriented framework can be applied to a broad class of engineering optimization problems. In each case, the central element of the solution searching algorithm is a standard multi-load structure optimization problem, which using an appropriate method, can be solved within reasonable time. The varying load directions are handled by additional linear or nonlinear relations, which describe the allowable perturbations of the nominal load directions. The result of the optimization is a performance measure minimal design which is invariant to the investigated uncertainty type and satisfies the response constraints. In order to illustrate the viability and efficiency of the approach, problem-specific models, algorithms and detailed benchmark results are presented for volume minimization of 2D continuum structures with compliance constraints and weight minimization of 2D truss structures with displacement and stress constraints. In each case, the computational cost of the proposed approach is comparable with its fixed load direction oriented equivalent because the worst-load-direction identification process is searching on the space of allowable direction perturbations, which generally means an easier and smaller computational problem than the standard multi-load structure optimization.