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.

PurposeThis 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/approachThe methodology relies on the adjoint method and the variational formulation of the linearized elasticity equations in order to establish the topological sensitivity.FindingsThe numerical results prove the influence of the number and locations of the bolts which strongly influence the final optimized design of the structure.Originality/valueThis paper is the first one to study the topology optimization of bolted systems without a fixed prescribed number of bolts.