考虑界面力学性能的组件及结构的协同优化

马晶; 赵明宣; 王浩淼; 刘湃; 亢战

doi:10.6052/0459-1879-21-010

考虑界面力学性能的组件及结构的协同优化

doi: 10.6052/0459-1879-21-010

马晶^*,
赵明宣^†,
王浩淼^†,
刘湃^*,2), ,,
亢战^*

^*大连理工大学工业装备结构分析国家重点实验室, 辽宁大连 116024
^†上海宇航系统工程研究所, 上海 201109

基金项目: 1)国家重点研发计划(2017YFB0203604);国家自然科学基金(11902064)

详细信息

作者简介:
2)刘湃, 博士后, 主要研究方向: 结构拓扑优化. E-mail: pailiu@dlut.edu.cn

通讯作者:
刘湃

中图分类号: O346
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出版历程
- 收稿日期: 2021-01-06
- 刊出日期: 2021-06-01

INTEGRATED OPTIMIZATION OF EMBEDDED COMPONENTS AND STRUCTURE CONSIDERING MECHANICAL PROPERTIES OF CONNECTING INTERFACE

Ma Jing^*,
Zhao Mingxuan^†,
Wang Haomiao^†,
Liu Pai^{*,2)
, ,},
Kang Zhan^*

^*State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, Liaoning, China
^†Shanghai Institute of Aerospace System Engineering, Shanghai 201109, China

摘要

摘要: 包含多个内嵌功能组件及支撑结构的多组件结构因其轻量化、多功能等优良特性被广泛应用于航空航天等领域.已有的多组件结构拓扑优化研究大多基于理想界面假设,忽略了材料连接界面可能发生的破坏. 本文针对包含多个内嵌式功能性组件的结构,考虑连接界面的力学性能, 对组件的形状、布局及支撑材料的拓扑进行协同优化,以实现多组件结构的优良承载性能. 首先,基于超椭圆模型对内嵌组件的形状及布局进行显式的参数化描述,并构造其水平集函数表达; 进而,结合组件及支撑材料的水平集拓扑描述、内聚力模型及扩展有限元方法(extended finite element method, XFEM), 在固定网格下对随优化迭代不断演化的结构拓扑及连接界面的力学性能进行准确描述;进一步, 建立水平集法框架下考虑界面力学性能的多组件结构拓扑优化列式,基于伴随变量法推导解析的灵敏度并采用梯度优化算法求解优化问题.本文采用该优化框架分别对内嵌组件的悬臂梁和MBB梁进行协同优化, 在优化过程中,发现组件的初始布局对最终设计有很大的影响, 并且可能导致不良结构.为了避免此情况, 本文提出了两个阶段的优化策略,即首先对组件布局和形状进行优化, 再进行结构和内嵌组件的协同优化.数值结果显示, 在优化结果中功能性组件及界面通常分布于结构受压应力作用的区域,且连接界面最优形状呈现为曲率较小的光滑曲线,该设计避免界面发生拉伸及剪切破坏, 有效提高了结构的承载力,同时也表明了本文所提出考虑连接界面力学性能拓扑优化方法的有效性.
- 拓扑优化 /
- 内嵌式组件 /
- 连接界面 /
- 内聚力模型 /
- 扩展有限元
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.
- topology optimization /
- embedded components /
- connecting interface /
- cohesive model /
- XFEM

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