The Temperature Stresses in the Adhesive Joint of Two Coaxial Tubes. Refined Theory.

Abstract An analytical solution for the problem of determining the stress-strain state of an adhesive joint of two cylindrical shells caused by temperature loads is developed. The model assumes that the adhesive layer works on displacement and tear-off. The values of the shear stress through the thickness of the adhesive layer are assumed to vary linearly. The two-parameter Vlasov-Pasternak model on an elastic foundation is used to characterize the normal stresses in the adhesive layer. The suggested method enables the fulfilment of the boundary conditions at the unloaded interface of the adhesive layer while providing a highly accurate representation of the stress state within the adhesive layer. The solution to the issue is derived in an analytical format. The issue is simplified to a system of ordinary differential equations and is addressed using the matrix method. Satisfaction of the boundary conditions leads to a system of nineteen linear equations with nineteen unknown coefficients. The model problem was solved.