Topology optimization and diverse truss designs considering nodal stability and bar buckling

Ensuring the bar stability is crucial in truss design. However, unstable nodes lacking lateral support complicate the calculation of bar buckling lengths. bar buckling constraints make the feasible region of optimization problems concave, further complicating the solution process. Moreover, traditional truss optimization methods typically yield a single optimal result, limiting the design options available to engineers. In this study, nominal disturbing load conditions are applied to the structure to eliminate unstable nodes, thereby ensuring accurate buckling length calculations. Additionally, the advanced allowable stress iteration (AASI) approach is proposed to address truss optimization problems with bar buckling constraints. To generate geometrically diverse and structurally competitive trusses, we develop a bar-length penalty (BLP) method. To validate the effectiveness of these methods, three numerical studies are presented. The results demonstrate that the proposed AASI approach produces optimized structures free from unstable nodes and bar buckling. Compared to structures optimized using the allowable stress iteration (ASI) method, which can only optimize for a single load case, those designed with the new approach maintain bar stability under all load conditions. Compared to the traditional method of increasing the cross-sectional area of unstable bars to ensure stability, much lighter trusses can be generated while maintaining the same load-bearing capacity. By applying the proposed BLP method to penalize specific bars, it is possible to achieve optimized structures with distinct topologies, similar masses, and equivalent load-carrying capacities. The proposed methods provide valuable insights for truss optimization design.