Purpose

This paper is devoted to the theoretical and numerical study of a new topological sensitivity concerning the insertion of a small bolt connecting two parts in a mechanical structure. First, an idealized model of bolt is proposed which relies on a non-local interaction between the two ends of the bolt (head and threads) and possibly featuring a pre-stressed state. Second, a formula for the topological sensitivity of such an idealized bolt is rigorously derived for a large class of objective functions. Third, numerical tests are performed in 2D and 3D to assess the efficiency of the bolt topological sensitivity in the case of no pre-stress. In particular, the placement of bolts (acting then as springs) is coupled to the further optimization of their location and to the shape and topology of the structure for volume minimization under compliance constraint.

Design/methodology/approach

The methodology relies on the adjoint method and the variational formulation of the linearized elasticity equations in order to establish the topological sensitivity.

Findings

The numerical results prove the influence of the number and locations of the bolts which strongly influence the final optimized design of the structure.

Originality/value

This paper is the first one to study the topology optimization of bolted systems without a fixed prescribed number of bolts.

中文翻译：

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小理想化螺栓的拓扑敏感性分析

目的

本文致力于对一种新的拓扑敏感性进行理论和数值研究，该敏感性涉及插入连接机械结构中两个部件的小螺栓。首先，提出了一个理想的螺栓模型，该模型依赖于螺栓两端（头部和螺纹）之间的非局部相互作用，并且可能具有预应力状态。其次，对于一大类目标函数，严格推导出这种理想化螺栓的拓扑灵敏度公式。第三，在 2D 和 3D 中进行数值测试，以评估在无预应力情况下螺栓拓扑敏感性的效率。特别是，

设计/方法/方法

该方法依赖于伴随方法和线性化弹性方程的变分公式，以建立拓扑灵敏度。

发现

数值结果证明了螺栓的数量和位置对结构的最终优化设计有很大的影响。

原创性/价值

本文是第一个研究没有固定规定数量的螺栓的螺栓系统拓扑优化的论文。