Layout optimisation of frame structures with multiple constraints and geometric complexity control

A comprehensive framework for the layout optimisation of rigid-jointed frame structures is proposed, addressing multiple mechanical constraints while effectively managing geometric complexity. The constraints considered include displacement, stress, and both local and global stability. Geometric complexity is controlled by minimising low-stiffness elements and reducing the number of elements in the resulting layouts. Numerical examples demonstrate the effectiveness of the proposed method, showcasing its ability to generate optimal structural layouts with desirable mechanical performance and varying levels of geometric complexity in member connectivity. This innovative optimisation framework offers significant advantages over conventional layout optimisation approaches by ensuring both the optimality and manufacturability of frame structures, thereby facilitating their practical application.