Evidence theory-based reliability optimization for cross-scale topological structures with global stress, local displacement, and micro-manufacturing constraints

Abstract

An uncertainty-oriented cross-scale topology optimization model with global stress reliability constraint, local displacement constraint, and micro-manufacturing control based on evidence theory is presented. The model is oriented to two-dimensional porous material structure, which concurrently designs the material distribution of both the macrostructure and the cell microstructure. During the optimization process, the homogenization method is used to solve the equivalent elastic modulus of the cell microstructure, which is then endowed to the macro-elements for subsequent analysis. The local stress constraints are converted to a global constraint by P-norm to reduce the computational consumption. Considering the uncertainty factors, the evidence theory is utilized to process the uncertainty parameters and evaluate the reliability of the structural strength performance. Minimum length-scale constraint is imposed on the cell microstructure by a density projection method for better manufacturability. Three numerical examples are presented to illustrate the availability of the proposed model.