Topological sensitivity analysis with respect to a small idealized bolt

Abstract

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.

Topology optimization of three-dimensional structures subject to self-weight loading

“…Thus, the topological derivative method has applications in many different fields. For a complete review of the topological derivative method and the most recent developments in this area, see the special issue on the topological derivative method and its applications in computational engineering recently published in the Engineering Computations Journal (Novotny et al ., 2022), covering various topics ranging from new theoretical developments (Amstutz, 2022; Baumann and Sturm, 2022; Delfour, 2022) to applications in structural and fluid dynamics topology optimization (Kliewe et al ., 2022; Romero, 2022; Santos and Lopes, 2022), geometrical inverse problems (Bonnet, 2022; Canelas and Roche, 2022; Fernandez and Prakash, 2022; Le Louër and Rapún, 2022a, b), synthesis and optimal design of metamaterials (Ferrer and Giusti, 2022; Yera et al ., 2022), fracture mechanics modelling (Xavier and Van Goethem, 2022), up to industrial applications (Rakotondrainibe et al ., 2022) and experimental validation of the topological derivative method (Barros et al ., 2022).…”

On the robustness of the topological derivative for Helmholtz problems and applications

“…The number of articles has increased tremendously, so that seeking a complete list of references is inordinate. See the special issue on the topological derivative method and its applications in computational engineering, recently published in the Engineering Computations Journal (Novotny, Giusti and Amstutz, 2022), covering various topics ranging from new theoretical developments (Amstutz, 2022;Baumann and Sturm, 2022;and Delfour, 2022) to applications in structural and fluid dynamics topology optimization (Kliewe, Laurain and Schmidt, 2022;Romero, 2022;and Santos and Lopes, 2022), geometrical inverse problems (Bonnet, 2022;Canelas and Roche, 2022;Fernandez and Prakash, 2022;Le Louër and Rapún, 2022a,b), synthesis and optimal design of metamaterials (Ferrer and Giusti, 2022;Yera et al, 2022), fracture mechanics modelling (Xavier and Van Goethem, 2022), up to industrial applications (Rakotondrainibe, Allaire and Orval, 2022) and experimental validation of the topological derivative method (Barros et al, 2022).…”

General prediction model of residual pretightening force of bolt group with one-step and multi-step pretightening and analysis of influencing factors from the perspective of elastic interaction

“…However, there is inevitably elastic interaction between bolts during the assembly process of bolts (Bickford and Nassar, 1998), which makes the applied bolt pretightening force difficult to achieve the desired effect, resulting in uneven stress distribution, fatigue strength (Leray et al. , 2008) and other mechanical properties of the connection system, and ultimately affecting the connection performance of the overall system (Allaire et al. , 2022).…”

“…It is widely used because of its convenient use, easy disassembly and replacement and good connection performance. However, there is inevitably elastic interaction between bolts during the assembly process of bolts (Bickford and Nassar, 1998), which makes the applied bolt pretightening force difficult to achieve the desired effect, resulting in uneven stress distribution, fatigue strength (Leray et al, 2008) and other mechanical properties of the connection system, and ultimately affecting the connection performance of the overall system (Allaire et al, 2022). Therefore, in order to improve the performance of bolt connection system and predict the distribution of residual pretightening force of bolt group, the research on the general prediction model of residual pretightening force of bolt group of connection structure considering elastic interaction has great engineering application value and academic significance.…”