The substructuring‐based topology optimization for maximizing the first eigenvalue of hierarchical lattice structure

Abstract

SummaryThis work presents a generalized substructuring‐based topology optimization method for the design hierarchical lattice structures to maximize the first eigenvalue. In this method, the macrostructure is assumed to be composed of substructures with a common artificial lattice geometry pattern. And two different yet connected scales are considered through a lattice geometry feature parameter. The feature parameter, which can control the material distribution of the substructure, determines the relative density of corresponding substructure. Each substructure is condensed into a super‐element to obtain the associated density‐related matrices. A surrogate model using cubic spline interpolation has been particularly built to map the density to stiffness and mass matrices of condensed super‐elements. The derivatives of super‐element matrices to the associated densities can be evaluated efficiently and accurately. Here, an augmented penalized density for this surrogate model is introduced. And the conventional optimality criteria method is selected as updating method of the density design variables. Numerical examples under two lattice patterns of substructures are shown to validate the correctness and superiority of this substructure‐based topology optimization method.