Optimization design of graded cellular structure based on the homogenization approach

Subjects: Mechanics >> Applied Mechanics submitted time 2022-12-21 Cooperative journals: 《应用力学学报》

陈炼雄 肖奥宇 刘辉

Abstract：

Cellular structures have attracted increasing attention in modern industry because of their excellent properties such as light weight and high specific strength.The rapid development of additive manufacturing technology makes it possible to fabricate cellular structures with complex configurations,which further promotes the progress of cellular structure design methods.There are two main methods of cellular structure design:the scale-separated approach and the scale-related approach.Based on the idea of scale-separated approach and computational homogenization method,this paper develops a multi-scale optimization design method for stochastic(two kinds of Voronoi-shaped)and non-stochastic(box-shaped)graded cellular structures.This method mainly containsthree steps,i.e.,the modeling and analysis of microstructure on the microscale(including the generation of microstructural geometry,calculation of equivalent physical quantities,and establishment of mapping relationship between geometric parameters and physical quantities),optimization of the macrostructure on the macroscale,and reconstruction of the graded cellular structure on the full-scale.This proposed scale-separated method has high computational efficiency and ensures the connectivity of the microstructure perfectly.The full-scale finite element model of the obtained cellular structure is established by using the triangle-fitting mesh division.The size effect analysis and the three-point bending beam numerical experiment of the cellular structures are carried out by taking the box-shaped graded cellular structure and two kinds of Voronoi-shaped graded cellular structure as examples,which verify the effectiveness of the proposed method and the superiority of the obtained graded cellular structure.The results show that the bearing capacity and the ductility of the graded cellular structure are better than the single-scale structure with little stiffness loss.

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