Stabilization of geometrically nonlinear topology optimization by the Levenberg–Marquardt method

This paper deals with the design of compliant mechanisms in a continuum-based finite-element representation. Because the displacements of mechanisms are intrinsically large, the geometric nonlinearity is essential for designing such mechanisms. However, the consideration of the geometric nonlinearity may cause some instability in topology optimization. The problem is in the analysis part but not in the optimization part. To alleviate the analysis problem and eventually stabilize the optimization process, this paper proposes to apply the Levenberg–Marquardt method to the nonlinear analysis of compliant mechanisms.