Adaptive member adding for truss topology optimization: application to elastic design

Abstract

This paper provides a rigorous and computationally efficient means of identifying compliance-based optimal truss topologies from high-resolution ground structures—problems involving over 30 million potential elements can be solved in under 1 h on a typical laptop. The adaptive ‘member adding’ approach is shown to provide significant savings in computational time and memory usage compared to directly solving the full optimization problem, whilst obtaining the same optimal solution; this paper presents the first application of this powerful principle to the well-known linear-elastic design problem. The computational advantages are particularly notable for multiple load-case problems, as the numerical structure of these cannot be effectively exploited without understanding of the physical nature of the problem. For such cases, the member adding process reduces the computational time required from approximately O(m2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(m^2)$$\\end{document} to O(m), where m is the number of potential elements; here, the time required is reduced by a factor of up to 60 for the relatively small problems that could be solved with both approaches. By using the member adding approach, compliance-optimized structures are obtained at a significantly higher resolution than has previously been possible. The findings of this paper have the potential to deliver a step change in the size of problems that can be solved in compliance-based truss topology optimization, and an accompanying Python code is provided to facilitate this.