Topology optimization incorporating external variables with metamodeling

Abstract

The objective of conventional topology optimization is to optimize the material distribution for a prescribed design domain. However, solving the topology optimization problem strongly depends on the settings specified by the designer for the shape of the design domain or their specification of the boundary conditions. This contradiction indicates that the improvement of structures should be achieved by optimizing not only the material distribution but also the additional design variables that specify the above settings. We refer to the additional design variables as external variables. This paper presents our work relating to solving the design problem of topology optimization incorporating external variables. The approach we follow is to formulate the design problem as a multi-level optimization problem by focusing on the dominance-dependence relationship between external variables and material distribution. We propose a framework to solve the optimization problem utilizing the multi-level formulation and metamodeling. The metamodel approximates the relationship between the external variables and the performance of the corresponding optimized material distribution. The effectiveness of the framework is demonstrated by presenting three examples.

Improved Efficient Projection Density Function Based on Topology Optimization

“…Just like that, for minimization weight with several constraints, Long Kai et al [6] improved capable, diagonally quadratic design. Maruyama et al [7] established a methodology of an external variable to find out the design problem of optimal topology by means of incorporating external variables, where both the external variables and the material distribution are at the same time as optimized. Zhang et al [8] used the topology optimization method by the means of moving morphable components for a rib-stiffened structure.…”