A random sampling approach to worst-case design of structures

A random sampling approach is presented for worst-case design of structures. Uncertainties are considered in structural and material parameters, which are assumed to exist in intervals with prescribed upper and lower bounds. Constraints are given for the worst responses that are found by solving anti-optimization problems. Optimal cross-sections are then selected from the list of available sections. The regions of uncertainty of parameters are discretized into integer values to formulate the hybrid problem of optimization and anti-optimization as an integer programming problem. The accuracy of solution is defined based on the order of the objective value; hence, a random sampling approach is successfully applied to obtain optimal and anti-optimal solutions within the prescribed accuracy. It is shown in the numerical examples that a good approximate optimal solution is found by random sampling with small number of analyses.