Topological sensitivity analysis with respect to a small idealized bolt

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.