Simultaneous Topology, Shape and Size Optimisation of 2D Trusses with Practical Constraints

Abstract

This study introduces a novel optimisation methodology for 2D trusses, based on genetic algorithms. It combines topology, shape and size optimisation into a single procedure, while bridging the gap to practical application. This is achieved by including Eurocode EN 1993‐1‐1 deflection and capacity checks, using discrete section sizes from a commercial catalogue, and allowing the user to control the number of truss connections, which directly affects cost, complexity and buildability. Members meeting at acute angles, crossing in the truss plane, or forming tightly bunched nodes are penalised against. The objective function, consisting of truss weight and several penalty terms, is highly nonlinear and discontinuous, requiring novel techniques for robust convergence. ‘Advanced mutations’ are introduced to facilitate escape from local minima, together with suitable cross‐over operations. Additionally, penalty severity increases dynamically as the algorithm progresses, improving both stability and constraint satisfaction in the final solution.