A data-driven integrated optimization method of macroscopic topology and microscopic configuration for the graded functional cellular structures

Abstract

In the topology optimization of the multiscale structure, how to ensure the connectivity between adjacent microstructures, how to control the design space of microstructures, and how to reduce the amount of calculation and improve calculation efficiency are three basic challenging issues currently faced. To this end, this paper proposes a data-driven approach to achieve the integrated optimization of macroscopic topology and microscopic configuration of the graded functional cellular structures. At the macro level, a topological description function is introduced to realize the topological control of the macrostructure. At the micro level, several cutting functions are used to realize the control of the configuration and size of the microstructure. The integrated optimization design of macro and micro cellular structures can be realized. Based on the computational homogenization method and numerical integration technology, an optimization problem independent offline microstructure database is established at the microscopic scale, where the relationship between the equivalent elastic parameters, relative pseudo-density, and design variables of the microstructure is stored. Based on this offline database, the entire topology optimization process is completed only on a macro scale, which greatly reduces the amount of calculation and improves calculation efficiency. In addition, implicit geometric modeling of full-scale cellular structures can be achieved using the reconstruction technique introduced in this work, which ensures smooth connection between adjacent microstructures. Finally, numerical examples are used to verify the effectiveness of the algorithm and the superiority of gradient cellular structures compared with single-scale structures.