Topological optimization of a symmetrical adhesive joint. Island model of genetic algorithm

Abstract

Modern additive technologies make it possible to create structures of variable thickness and of any shape. Thus, designers face problems of optimal design of a new type, and these are problems of topological optimization. Such problems are to determine the optimal form of the structure or the optimal distribution of material over the structure. As a rule, the criterion of optimality is the mass of the structure. However, the structure must retain its bearing capacity under a certain load. The symmetric two-shear adhesive joint of the main plate with two overlays of the same shape on both sides is the object of study in this article. The main goal of this study was to determine the optimal form of overlays with variable thicknesses under certain restrictions. The main restriction is the strength of the structure. Furthermore, additional restrictions are imposed on the minimum and maximum thickness of the overlay. Therefore, the solution to the problem is presented in the form of a set of the following tasks: building a mathematical model of the adhesive joint, building a numerical solution to the primal problem using the finite difference method, and building a genetic optimization algorithm. In the presented article, to improve the convergence of the genetic algorithm is proposed to use an island model that consists of several populations. The main feature of the proposed model of the genetic algorithm lies in the fact that on one of the "islands" mutations occur more frequently and with higher dispersion than on the other two "islands". On the one hand, this decision ensures a high rate of evolutionary selection, and on the other hand, the stability of the results is achieved. Several modeling problems are solved in this article. The main results of this research include the following: nonlinear dependence of the overlay length on the applied load was determined; restrictions on the minimum thickness of the overlay, which cause the appearance of a certain “plateau” at the edge of the overlay, the thickness of which is equal to the minimum allowable were defined.

Keywords

• constrained optimization
• finite difference method
• genetic algorithm