Topology optimization of functionally graded lattice structure for energy absorption

Abstract

The functionally graded lattice structure refers to a lattice structure that varies continuously in composition and structure according to space. In comparison to a homogeneous lattice structure, this type of structure possesses excellent physical characteristics such as lightweight, superior energy absorption capability, and outstanding thermal performance. As a result, it finds extensive application in various engineering design studies. In particular, research focusing on energy absorption has been extensively pursued, employing both numerical and experimental approaches. Furthermore, efforts have been made to optimize the design for maximizing performance, considering the plastic deformation of the structure and numerically interpreting the fine structure of the lattice.

However, calculating the energy absorption performance requires considering the structural yielding and performing numerical analysis of the fine structure of the lattice, which incurs high computational costs. Homogenization methods offer an effective approach to reduce the computational cost by replacing complex-shaped and multi-material microstructures with equivalent homogeneous unit cells to calculate effective material properties. Through this approach, studies on lattice structure design based on the calculation of effective properties have been conducted, primarily assuming linear properties.

In this study, we propose a design method for functionally graded lattice structures with consideration of nonlinearity by using homogenization methods. Effective material properties of lattice structures with nonlinear behavior are numerically calculated using homogenization methods. The energy absorption performance of the structure is defined as the absorbed energy before structural failure and is maximized through topology optimization. To achieve this, the failure stress of the material is imposed as a constraint in the topology optimization process.

The effectiveness of the proposed method is demonstrated through numerical examples. The optimization results are transformed into functionally graded lattice structures through reverse homogenization and validated through reinterpretation.

Furthermore, the feasibility of manufacturing the optimized functionally graded lattice structure is confirmed by converting the obtained topology optimization results into CAD format and utilizing 3D printing for actual fabrication.