Anti-optimization versus probability in an applied mechanics problem: Vector uncertainty

In this study probabilistic and nonprobabilistic anti-optimization approach es are, contrasted to evaluate their relative advantages and disadvantages while solving a mechanical problem in presence of vector uncertainty. The d ifferent cases that are analyzed in probabilistic setting that deal with ei ther uniform or generic probability density functions for the uncertain var iables varying in a rectangular domain. This case has been compared with in terval analysis. a particular case of anti-optimization. The presence of a convex, smooth boundary of the uncertain domain has been also considered fo r comparing results obtained with these two alternative methods. It is show n that in case of vector uncertainty the anti-optimization method yields th e same solution for the design problem as is provided by means of more comp lex probabilistic considerations.