Topological optimization of a symmetric single-lap adhesive joint

The profile optimization problem for layers overlapped with an interjacent adhesive layer is considered. The joint is considered according to the Volkersen model, according to which the base layers are considered as rods that act only in stress-strain, and the adhesive layer acts only in shear. The aim of the optimization is to design a joint structure of minimum mass under the strength restrictions for the adhesive layer and the minimally allowable base layer thickness. The base layers profile is described by a Fourier series expansion. The direct stress state problem for the joint of variable thickness rods is solved by the finite difference method. The optimization problem is reduced to the problem of determining Fourier series coefficients and the joint length. A genetic optimization algorithm was used. The model problem is solved.