Integrated Topology Optimization of Multi-component System Considering Interface Behavior of Interconnection Based on Conforming Mesh and Interface Elements

Abstract

In integrated topology optimization of multi-component structures, the behavior of connecting interfaces between the components and host structure is a crucial issue closely related to the structural integrity. We propose a topology optimization framework to consider these interface behaviors. We treat the connecting interfaces with the cohesive zone model, which can effectively describe adhesively bonded interface behavior. The conforming mesh is adopted to discretize the evolving structure, and the interface elements are inserted to discretize the connecting interfaces. To clearly describe the structural boundaries and connecting interfaces, we also suggest a multi-material level set model. This level set model can conveniently define the locations of the connecting interfaces, and describe multi-material distribution without redundant phases. The objective function is the sum of strain energy and the work dissipated on the connecting interfaces. We treat the evolving velocities of the level set and the embedded components as design variables. The mathematical programming method (MMA in this study) is employed to obtain these design variables on the basis of adjoint-variable sensitivity analysis. With the proposed optimization formulation, multiple constraints and mixed design variables (i.e. level set design variables and components’ design variables) in level set-based optimization can be easily handled. The Hamilton-Jacobi equation is used to advance the design with the design variables as inputs. The numerical example shows the applicability and effectiveness of the proposed method.