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Date of Publication:2022-10-06

Journal:Lixue Xuebao/Chinese Journal of Theoretical and Applied Mechanics

Volume:53

Issue:6

Page Number:1758-1768

ISSN No.:0459-1879

Abstract:Structures that contain multiple embedded components and the host material are widely used in aerospace and other fields because of their lightweight, multi-functional, and other superior performances. Most existing topology optimization studies on multi-component structures assume the interfaces between different materials to be perfectly bonded, and thus ignore the possible interfacial failure. In this paper, we propose an efficient integrated optimization method to optimize components' shapes, layouts, and the host structural topology simultaneously, while considering the interfacial behaviors to achieve the maximum structural stiffness. First, the components' shapes and layouts are described explicitly and parameterized with the superellipse model, and the corresponding level set functions are constructed; then, combining level set topological description, the cohesive zone model and the extended finite element method (XFEM), the behaviors of interfaces that are evolving during the optimization iterations are computed on the fixed grid; further, the optimization formulation considering the interfacial behavior to achieve maximum structural stiffness is established, and the optimization problem is solved with a gradient-based algorithm with analytical sensitivities that are derived with the adjoint method. In this paper, we applied the optimization framework to design the cantilever beam and MBB beam with embedded transformable components respectively. During the optimization process, we found that the initial layouts of the components have a great influence on the final design and that may lead to undesired structures. To avoid this situation, we proposed a two-stage optimization strategy-the layouts and shapes of embedded components will be optimized first, and then the collaborative optimization will be carried out. The numerical examples show that in the optimized designs, the components together with their interfaces are usually distributed in regions that are under compression, and the optimized bonding interfaces exhibit small curvature. This result avoids the interface failure and improves the structural stiffness, and illustrates the effectiveness of the proposed optimization method. © 2021, Chinese Journal of Theoretical and Applied Mechanics Press. All right reserved.

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