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Integrated topology optimization of multi-component structures considering connecting interface behavior

机译：考虑连接接口行为的多组件结构的集成拓扑优化

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It is often highly desirable to simultaneously optimize the layout of embedded functional components and the topology of the host structure supporting these components to achieve the best overall performance while still ensuring the structural integrity. We propose a topology optimization framework to account for connecting interface behaviors between the components and the host structure. Here we treat the connecting interfaces with the cohesive zone model to reflect the adhesively bonded interface behaviors. A conforming mesh in conjunction with interface elements is employed to discretize the evolving structure while accounting for the strong discontinuity of displacement field across the material interfaces. To give a clear representation of structural boundaries and the connecting interfaces, we also suggest a multi-material interpolation model in the level set framework, which can conveniently define the connecting interface locations and describe multi-material distribution without redundant phase in the design domain. The objective function is defined as the sum of the strain energy and the work done by the traction on the connecting interface, and the evolution velocities of the level set and the embedded components are treated as design variables. These design variables are updated with the MMA optimizer on the basis of adjoint-variable sensitivity analysis. This optimization formulation allows multiple constraints and mixed design variables (i.e level set design variables and components' design variables) to be easily handled in level set based optimization. The design is advanced by the Hamilton-Jacobi equation with the velocity design variables as input. Numerical examples demonstrate the validity and applicability of the proposed method. (C) 2018 Elsevier B.V. All rights reserved.
机译：人们通常非常希望同时优化嵌入式功能组件的布局和支持这些组件的主机结构的拓扑，以实现最佳的总体性能，同时又要确保结构的完整性。我们提出一种拓扑优化框架，以解决组件和主机结构之间的接口行为连接问题。在这里，我们用内聚区模型处理连接界面，以反映粘合界面的行为。结合界面元素的贴合网格用于离散化演化结构，同时考虑了跨材料界面的位移场的强烈不连续性。为了清楚地表示结构边界和连接界面，我们还建议在级别集框架中使用多材料插值模型，该模型可以方便地定义连接界面位置并描述多材料分布，而在设计域中没有多余的阶段。目标函数定义为应变能和连接界面上的牵引力所完成的功的总和，并且将水平集和嵌入式组件的演化速度视为设计变量。这些设计变量会在伴随变量敏感性分析的基础上使用MMA优化器进行更新。这种优化公式允许在基于水平集的优化中轻松处理多个约束和混合的设计变量（即，水平集设计变量和组件的设计变量）。通过Hamilton-Jacobi方程将速度设计变量作为输入来推进设计。数值算例表明了该方法的有效性和适用性。 （C）2018 Elsevier B.V.保留所有权利。

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