Abstract

One of the issues for the automotive industry is weight reduction. For this purpose, topology optimization is used for mechanical parts and usually involves a single part. Its connections to other parts are assumed to be fixed. This paper deals with a coupled topology optimization of both the structure of a part and its connections (location and number) to other parts. The present work focuses on two models of connections, namely rigid support and spring that prepares work for bolt connection. Rigid supports are modeled by Dirichlet boundary conditions while bolt-like connections are idealized and simplified as a non-local interaction to be representative enough at a low computational cost. On the other hand, the structure is modeled by the linearized elasticity system and its topology is represented by a level set function. A coupled optimization of the structure and the location of rigid supports is performed to minimize the volume of an engine accessories bracket under a compliance constraint. This coupled topology optimization (shape and connections) provides more satisfactory performance of a part than the one given by classical shape optimization alone. The approach presented in this work is therefore one step closer to the optimization of assembled mechanical systems. Thereafter, the concept of topological derivative is adapted to create an idealized bolt. The main idea is to add a small idealized bolt at the best location and to test the optimality of the solution with this new connection. The topological derivative is tested with a 3d academic test case for a problem of compliance minimization.

中文翻译：

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机械系统中连接的拓扑优化

摘要

汽车工业的问题之一是减轻重量。为此，拓扑优化用于机械零件，通常涉及单个零件。假定它与其他零件的连接是固定的。本文讨论了零件结构及其与其他零件的连接（位置和数量）的耦合拓扑优化。目前的工作集中在两种连接模型上，即刚性支撑和弹簧，这些工作为螺栓连接做准备。刚性支撑通过Dirichlet边界条件进行建模，而螺栓状连接则被理想化并简化为非局部相互作用，从而可以以较低的计算成本实现足够的代表性。另一方面，该结构由线性弹性系统建模，其拓扑结构由水平集函数表示。对结构和刚性支撑件的位置进行了耦合优化，以在顺应性约束下使发动机附件支架的体积最小化。这种耦合的拓扑优化（形状和连接）比单独的经典形状优化所提供的性能更令人满意。因此，这项工作中提出的方法离组装机械系统的优化还差了一步。此后，采用拓扑派生的概念来创建理想的螺栓。主要思想是在最佳位置添加一个小的理想化螺栓，并通过这种新连接来测试解决方案的最佳性。使用3d学术测试案例对拓扑派生进行了测试，以解决合规性最小化的问题。