Continuum Topology Optimization of Buckling-Sensitive Structures

Two formulations for continuum topology optimization of structures taking buckling considerations into account are developed, implemented, and compared. In the first, the structure undergoing a specified loading is modeled as a hyperelastic continuum at finite deformations, and is optimized to maximize the minimum critical buckling load. In the second, the structure under a similar loading is modeled as linear elastic, and the critical buckling load is computed with linearized buckling analysis. Specific issues addressed include usage of suitable “mixing rules'', a node-based design variable formulation, techniques for eliminating regions devoid of structural material from the analysis problem, and consistent design sensitivity analysis. The performance of the formulations is demonstrated on the design of different structures. When problems are solved with moderate loads and generous material usage constraints, designs using compression and tension members are realized. Alternatively, when fairly large loads together with very stringent material usage constraints are imposed, structures utilizing primarily tension members result. Issues that arise when designing very light structures with stringent material usage constraints are discussed along with the importance of considering potential geometrical instabilities in the concept design of structural systems.