Topology Optimization of Snapping Structures With Convex Element Constraints for Tailored Mechanical Responses

Abstract

The basic unit of snapping mechanical metamaterials is typically a bistable unit. This study proposes a systematic inverse design framework based on topology optimization for designing snapping structures with specific force‐displacement response curves. Such problems involve large deformations and complex deformation modes, which often lead to numerical instability during the optimization process. The paper proposes two improvements to address these issues. In the nonlinear finite element analysis, an improved displacement‐controlled arc‐length method is proposed. The method effectively handles the snap‐through and snap‐back behaviors exhibited by the structure during loading in the topology optimization process, while simultaneously obtaining the deformed configuration of the structure under the prescribed displacement boundary condition. Furthermore, the paper introduces convex element constraints to constrain the deformation state of elements. This approach mitigates convergence issues caused by severe compressive deformations of the elements during nonlinear topology optimization. This work contributes to the design of snapping structures by providing a stable and effective optimization framework.