Optimum Shape Design of Structures under Uncertain Loading by Boundary Element Method

Abstract

A structure optimized for a given determinate load is not optimum for other loads. This paper proposes a shape determination method by BEM for structures which are subjected to uncertain loads. In the case that the loads are represented by some random variables which obey certain probabilistic laws, response quantities such as displacement and strain energy can be expressed as random variables by the use of a method of "decomposition into fundamental loads". Then only several runs of analysis can give optimum shapes where the expected values of strain energy densities are uniform on every boundary element.