Topological optimization hybrid algorithm for the adhesive joint

Abstract

The subject of this study is a topological optimization algorithm for a lapped symmetric adhesive joint. The purpose of this research is to create a hybrid optimization algorithm that combines the advantages of a genetic algorithm and a particle swarm algorithm and, at the same time, reduces the time required to solve the problem. Task: to create a methodology for solving the optimization problem for a symmetric double-sided lapped adhesive joint, which consists of a main plate and two patches (the main plate has a constant thickness, and the thickness of the patches varies along the length of the joint, this is required to reduce the stress concentration in the joint and reduce its weight) with satisfaction of the optimality criterion, namely, to minimize the mass of the structure with the strength and thickness restrictions for the patch. The optimization problem is that we must find the optimal patch form, namely, the length of the patch and the thickness-on-length dependence for the patch. Methods: the modified Goland-Reissner model was used to describe the deflected mode of the joint. The finite difference method was used to solve the direct stress state problem for the structure. For the numerical solution of the optimization problem, a combination of the multi-population model of the genetic optimization algorithm and the particle swarm algorithm was used. To improve the performance of the genetic algorithm, a multi-population model with migration of the best individuals between populations was applied. The introduction of individuals from other populations into the population avoids homogenization of the genotype in a separate population and premature stopping of the optimization process. To describe the shape of the patch, the Fourier series expansion of the patch thickness dependence was used. Results: A hybrid algorithm is proposed based on the sequential application of a genetic algorithm and a particle swarm algorithm for three populations of solutions. The particle swarm algorithm makes it possible to improve the value of the objective function achieved at the previous stage by 20%. Conclusions: the scientific novelty lies in the improvement of the optimization algorithm compared with the known ones. To reduce the calculation time, a one-dimensional adhesive joint stress state mathematical model was used in this paper. The methods used made it possible to create a combined topological optimization algorithm that combines the advantages of both methods and allows us to find a solution to the problem quite quickly. The Python program run time is only a few minutes.

Keywords

• adhesive joint
• genetic algorithm
• particle swarm optimization
• finite difference method
• topology optimization