A Gradient-Free Topology Optimization Strategy for Continuum Structures with Design-Dependent Boundary Loads

In this paper, the topology optimization of continuum structures with design-dependent loads is studied with a gradient-free topology optimization method in combination with adaptive body-fitted finite element mesh. The material-field series-expansion (MFSE) model represents the structural topology using a bounded material field with specified spatial correlation and provides a crisp structural boundary description. This feature makes it convenient to identify the loading surface for the application of the design-dependent boundary loads and to generate a body-fitted mesh for structural analysis. Using the dimension reduction technique, the number of design variables is significantly decreased, which enables the use of an efficient Kriging-based algorithm to solve the topology optimization problem. The effectiveness of the proposed method is demonstrated using several numerical examples, among which a design problem with geometry and contact nonlinearity is included.