Topology Optimization of Geometrically Nonlinear Structures Based on a Self-Adaptive Material Interpolation Scheme

In this paper, a simple and effective self-adaptive material interpolation scheme is proposed to solve the numerical instability problem, which may occur in topology optimization considering geometrical nonlinearity when using density-based method. The primary concept of the proposed method revolves around enhancing the deformation resistance of minimum-density or intermediatedensity elements, thus avoiding numerical instability due to excessive distortion of these elements. The proposed self-adaptive material interpolation scheme is based on the power law method, and the stiffness of minimum-density or intermediate-density elements can be adjusted by a single parameter, α. During the optimization process, the parameter α will be changed according to an adaptive adjustment strategy to ensure that elements within the design domain are not excessively distorted, while the mechanical behavior of the structure can be approximated with acceptable accuracy. Numerical examples of minimizing compliance and maximizing displacement of structure are given to prove the validity of the proposed self-adaptive material interpolation scheme.