Optimal truss sizing based on explicit Taylor series expansions

Abstract

This paper deals with the classical structural optimization problem of minimizing the weight of a truss structure, subject to constraints on displacements and stresses. Design variables are the cross-section areas of the elements. The main theoretical result presented is that the complete Taylor series expansions of all constraint functions can be explicitly expressed, once the displacements corresponding ton specific load cases have been calculated, wheren = the number of elements. Based on this theoretical result, new explicit approximations of the constraint functions are suggested. These approximations are shown to have some interesting theoretical properties. They also seem to work very well in practice, when included in an optimization scheme.