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

Abstract

Summary This 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.

Data-driven multiscale design of cellular composites with multiclass microstructures for natural frequency maximization

“…This underlines the importance of combining different classes to accommodate various local property requirements. In contrast, using a single predefined microstructure design concept for the whole structure, which is very common in existing literature [17,28,30], will be suboptimal for general design cases.…”

“…Most existing data-driven multiscale TO methods are based on the framework of variable-density cellular structure design [27][28][29][30][31]. In this framework, the full structure is assumed to be composed of the same form (class) of microstructures with varying density (volume fraction) of the solid materials.…”

“…In this framework, the full structure is assumed to be composed of the same form (class) of microstructures with varying density (volume fraction) of the solid materials. A surrogate model can be trained to approximate the relation between the volume fraction and the homogenized stiffness tensor of the microstructure, such as neural network [29], scaling law model [27,28], and diffuse approximation [30]. Using this surrogate model to replace the material law, elemental volume fraction can be used as the only design variable in the multiscale design without the need to perform on-the-fly homogenization and nested optimization.…”

GM-TOuNN: Graded Multiscale Topology Optimization using Neural Networks

“…This leads to a significant reduction in computational cost ( [28]) since homogenization is not needed within the optimization loop. However, restricting the design to a single microstructure can significantly reduce performance ( [29]). To further improve the performance of GM-TO, without substantially increasing the computational cost, one can use a finite number of graded microstructures.…”

Decomposition and optimization of linear structures using meta models

“…In the context of multi-scale optimization, the connection of the macro and micro scale of the structure is sometimes replaced by meta models to reduce the computational cost. In Wu et al (2019) and Wu et al (2020) a substructuring technique for hierarchical lattice structures was used to estimate the mass and the stiffness matrix of microstructures. For this purpose, a regression model based on a reduced basis description was established, where the microstructure properties are determined by samples of parametrized unit cells.…”