Lightweight topology optimization of graded lattice structures with displacement constraints based on an independent continuous mapping method

• Published in: Acta mechanica Sinica Vol. 38; no. 4
• Main Authors: Wei, Nan, Ye, Hongling, Zhang, Xing, Wang, Weiwei, Sui, Yunkang
• Format: Journal Article
• Language: English
• Published: Beijing The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences 01.04.2022; Springer Nature B.V
• Edition: English ed.
• Subjects: Classical and Continuum Physics; Computational Intelligence; Continuity (mathematics); Design optimization; Displacement; Elastic properties; Engineering; Engineering Fluid Dynamics; Interpolation; Lattice design; Lightweight; Mapping; Mathematical analysis; Optimization; Optimization models; Polynomials; Quadratic programming; Research Paper; Sensitivity analysis; Strain; Theoretical and Applied Mechanics; Topology optimization; Unit cell; Topology optimization; Displacement constraints; Graded lattice structures; ICM method; Effective properties
• ISSN: 0567-7718; 1614-3116
• DOI: 10.1007/s10409-021-09047-x

This paper presents a novel topology optimization method to design graded lattice structures to minimize the volume subject to displacement constraints based on the independent continuous mapping (ICM) method. First, the effective elastic properties of graded unit cells are analyzed by the strain energy-based homogenization method. A surrogate model using quartic polynomial interpolation is built to map the independent continuous topological variable to the effective elastic matrix of the unit cell and set up the relationship between the macroscale structure and microscale unit cells. Second, a lightweight topology optimization model is established, which can be transformed into an explicitly standard quadratic programming problem by sensitivity analysis and solved by dual sequential quadratic programming. Third, several numerical examples demonstrate that graded lattice structures have a better lightweight effect than uniform lattice structures, which validates the effectiveness and feasibility of the proposed method. The results show that graded lattice structures become lighter with increasing displacement constraints. In addition, some diverse topological configurations are obtained. This method provides a reference for the graded lattice structure design and expands the application of the ICM method.