考虑界面力学性能的组件及结构的协同优化

Multi-component structures with multiple embedded functional components and supporting structures are widely used in aerospace and other fields due to their excellent characteristics such as lightweight and multi-function. Most of the existing research on the topological optimization of multi-component structures is based on the ideal interface assumption, ignoring the possible damage at the material connection interface. In this paper, for a structure containing multiple embedded functional components, considering the mechanical properties of the connection interface, the shape and layout of the components and the topology of the supporting material are co-optimized to achieve excellent load-bearing performance of the multi-component structure. Firstly, based on the super-ellipse model, an explicit parametric description of the shape and layout of the embedded components is carried out, and its level set function expression is constructed; then, combined with the level set topological description of the components and the supporting material, the cohesive zone model and the extended finite element method (XFEM), the mechanical properties of the structure topology and the connection interface that continuously evolve with the optimization iteration are accurately described under a fixed grid; further, a topological optimization formulation for multi-component structures considering the interface mechanical properties in the level set method framework is established, the analytical sensitivity is derived based on the adjoint variable method and a gradient optimization algorithm is used to solve the optimization problem. In this paper, this optimization framework is used to co-optimize the cantilever beam and MBB beam of the embedded components respectively. During the optimization process, it is found that the initial layout of the components has a great influence on the final design and may lead to an unfavorable structure. To avoid this situation, a two-stage optimization strategy is proposed in this paper, that is, first optimize the layout and shape of the components, and then carry out the co-optimization of the structure and the embedded components. The numerical results show that in the optimization results, the functional components and the interface are usually distributed in the area where the structure is under compressive stress, and the optimal shape of the connection interface appears as a smooth curve with a small curvature. This design avoids tensile and shear damage at the interface and effectively improves the load-bearing capacity of the structure. At the same time, it also shows the effectiveness of the topological optimization method considering the mechanical properties of the connection interface proposed in this paper.

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.