Topological optimization BI-adhesive double lap adhesive joint. One-dimension model

Abstract

The aim of the article is to construct a solution to the problem of topological optimization of a symmetric two-shear and bi-adhesive joint. The one-dimensional mathematical model of the stress state of a symmetrical double-shear adhesive joint with a variable thickness of the outer substrate along the lap length is represented in the article. The proposed model is a generalization of the classical Goland-Reissner model. The proposed mathematical model is used to solve the problem of topological optimization of the outer substrate shape as well as to obtain the optimal length of the sections for the rigid and compliant adhesives. The expansion of the outer substrate thickness dependence along the adhesive joint length into a Fourier series in cosines was used to describe the shape of the outer substrate. The desired values in the optimization problem are the lengths of the adhesive joint sections with the compliant and rigid adhesives as well as the Fourier coefficients. The objective function is the cross-sectional area of the outer substrate. Restrictions are imposed on the maximum stresses in the adhesive layer and in the outer substrate. A genetic algorithm was used to solve the optimization problem. The direct problem of determining the stress state of the adhesive joint at specified parameters was solved using the finite difference method. The model problem is solved and the results of the stress state calculation are compared with the results of finite element modeling.