Anti-Optimization Versus Probability in an Applied Mechanics Problem: Vector Uncertainty

Abstract

In this study probabilistic and nonprobabilistic anti-optimization approaches are contrasted to evaluate their relative advantages and disadvantages while solving a mechanical problem in presence of vector uncertainty. The different cases that are analyzed in probabilistic setting that deal with either uniform or generic probability density functions for the uncertain variables varying in a rectangular domain. This case has been compared with interval analysis, a particular case of anti-optimization. The presence of a convex, smooth boundary of the uncertain domain has been also considered for comparing results obtained with these two alternative methods. It is shown that in case of vector uncertainty the anti-optimization method yields the same solution for the design problem as is provided by means of more complex probabilistic considerations. [S0021-8936(00)03103-2]