Topology Optimization of Adhesively Bonded Double Lap Joint

In this paper, a one-dimensional mathematical model of stress state is proposed for a symmetrical double-shear adhesive joint with doublers having varying thicknesses along the joint length. This model is an extension of the classical Holland–Reissner model. Due to geometrical symmetry, load-carrying plates do not bear bending, but doublers are subjected to bending due to the eccentricity of the applied load. The suggested mathematical model is used to solve the problem of topological optimization of doubler shape and to find the length of the adhesive film with soft and rigid adhesives used in the same joint. The doubler shape is described by reducing doubler thickness along the joint length using the Fourier series with cosines. The optimization problem requires finding doubler length and Fourier coefficients, and both joint length and doubler cross-sectional area can be selected as the objective function. Constraints are applied on maximum stress in the adhesive film, stress in doublers, and minimum and maximum doubler thickness. The direct problem of determining the joint stress state at given geometrical parameters is solved using the method of finite differences. The optimization problem is solved using a genetic algorithm. To improve the convergence of this method, an island model of genetic algorithm is used. The distinctive feature of the suggested algorithm model is that mutations occur more often and with greater dispersion in one of the “islands” compared to the other two “islands.” Such a solution ensures both the quickness of evolution selection and the stability of the obtained results. Two model problems are solved.