Form Finding of Sparse Structures with Continuum Topology Optimization

A continuum topology optimization methodology suitable for finding optimal forms of large-scale sparse structures is presented. Since the need to avoid long compressive spans can be critical in determining the optimal form of such structures, a formulation is used wherein the structure is modeled as a linear elastic continuum subjected to design loads, and optimized in form to maximize the minimum critical buckling load. Numerical issues pertinent to accurate solution of the linearized buckling eigenvalue problem and accurate design sensitivity analysis are discussed. The performance of the proposed design formulation is demonstrated on a few problems designed to find optimal forms of a canyon bridge, long-span bridges, and an electrical transmission tower. In all cases, very credible structural forms are obtained with the proposed design formulation. The results of the design examples solved are typically superior structural forms with regard to buckling stability than those obtained to minimize the mean structural compliance.