Configuration Optimization of Trusses Subject to Strength, Displacement and Frequency Constraints

Abstract

Three-dimensional elastic trusses are designed for minimum weight, subject to constraints on member stresses, Euler buckling, joint displacements and system natural frequencies. Multiple static loading conditions are considered. The finite-element displacement method of analysis is used and eigenvalues are calculated using the subspace iteration technique. All gradient information is calculated analytically. The design problem is cast as a multilevel numerical optimization problem. The joint coordinates are treated as system variables. For each proposed configuration, the member sizes are updated as a suboptimization problem. This subproblem is efficiently solved using approximation concepts in the reciprocal variable space. The multilevel approach is shown to be an effective technique which conveniently takes advantage of the most efficient methods available for the member sizing problem. Examples are presented to demonstrate the method. The optimum configuration is shown to be strongly dependent on the constraints which are imposed on the design.