ROBUST TOPOLOGY OPTIMIZATION OF STRUCTURES CONSIDERING THE UNCERTAINTY OF SURFACE LAYER THICKNESS

For additively manufactured structure, the poor forming precision and surface roughness may cause surface layer heterogeneity, which leads to uncertain material properties and/or uncertain structure geometry. In order~to obtain a structure with less sensitive to the uncertainty, a rubost topology optimization method accounting for the uncertain surface thickness of structures is proposed, in which two key problems need to be solved to study the surface layer thickness uncertainty caused by the heterogeneity of the structure surface layer. One is accurately identifying the structure surface layer. The other is to carry out propagation analysis and stochastic response estimation of uncertainty. First of all, an erosion-based surface layer identification method is adopted to establishing the equivalent model of surface layer heterogeneity through smooth filtering based on Helmholtz partial differential equation(PDE) as well as discrete mapping based on Heaviside filtering and tanh function, which is called a two-step filtering/projection process. Secondly, while the thickness of the heterogeneous surface layer is regarded as a random variable subject to Gaussian distribution, the uncertain propagation is analyzed and the system stochastic response is predicted based on the perturbation finite element method. Taking the weighted sum of the mean value and standard deviation of structural compliance as the optimization objective, a robust topology optimization model considering the uncertainty of surface layer thickness is established, and the sensitivities of the objective function with respect to design variables are derived. Finally, several numerical examples are given to demonstrate the effectiveness of the proposed method. The numerical results show that the structural configuration with stronger uncertainty resistance can be obtained by considering the influence of surface thickness uncertainty on the structural performance during the design process, which effectively improves the robustness of the structural performance. Therefore, for additive manufacturing structures, it is of great significance to consider the influence of surface layer thickness uncertainty on structural performance in topology optimization design.