Optimum shape design of structures under uncertain loadings 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 displacements and strain energies 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 expected values of strain energy densities are uniform on every boundary element.