The complex method applied to optimal truss configuration

Abstract The Complex Method of Box is applied to the determination of optimal member sizes and geometric configuration for minimum weight of 3-dimensional truss structures. Design constraints include bounds on member size, joint coordinates, member stresses, Euler buckling and joint displacements. The displacement method of structural analysis is used and the system is assumed to be linearly elastic. Statically indeterminate structures under multiple loading conditions can be optimized and the sizing as well as the geometric design variables may be linked. Limited topological changes are permitted for designs which have small member forces. The design spaces for sizing and geometric variables are separated. Geometry is modified by the Complex Method and member sizes by stress ratio and a scaling procedure for stiffness. The method is applied to two numerical examples from the literature. Results indicate favourable design improvements and rates of convergence. Substantial additional improvement resulting from member deletion is demonstrated.