Uncertainty‐oriented double‐scale topology optimization with macroreliability limitation and micromanufacturing control

Abstract

AbstractThis article proposes an uncertainty‐oriented double‐scale topology optimization method considering macroreliability limitation and micromanufacturing control. The procedure combines the homogenization method to solve the equivalent elastic property of the microstructure, the feature distance theory to evaluate reliability, a density projection for manufacturability control, and the solid isotropic material with penalization model to suppress intermediate density. To coupling the micro–macro scale, the equivalent elastic property of the cell microstructure is evaluated by the numerical homogenization method and then endowed to the macroelement for finite element analysis. Uncertainty factors existed in optimization parameters are evaluated by the interval convex set model. By utilizing the interval parameter vertex method and the feature distance theory, the reliability of displacement constraint in the optimization model is evaluated and constrained. In terms of length scale control, the microdensity design variables are projected by a threshold function to obtain a clear microstructure that satisfies the preset minimum length scale constraint. Finally, three numerical examples are presented to illustrate the effect of micromanufacturing control, as well as the necessity of considering parameter uncertainty.