Calculation of the stress state of а glue joint of rectangular plates with different widths

Аuthors

Kurennov S. S.^*, Tanchik E. V.

National Aerospace University «Kharkov Aviation Institute», KhAI, 17, Chkalova St., Kharkiv, 61070, Ukraine

*e-mail: ss_kurennov@mail.ru

Abstract

The article is devoted to the issue of the dayconcerning calculation of the stress state of the overlapping glue jointin two-dimensional formulation. The purpose of the work is to solve the problem of glue jointstress state of symmetrical rectangular plates with different width under longitudinal load. For the first time we obtained the solution of the problem in analytical form. To build the solution we used simplified Volkersentwo-dimensional model, according to which connecting layers are considered to be rigid in transverse direction. The hypothesis of the plates rigidness in transverse direction was implemented earlier for creation refined theory of beams. The author developed this theory for connection of two plates. The outer layers work only in tension and compression in the longitudinal direction and shift. The adhesive layer is a shear layer. The stresses assumed to be constant over the thickness of the glued layers. The stresses in the adhesive layer are proportional to the difference between the displacements of the outer layers. Due to joint symmetry and imposed stiffness layers hypothesis, there is no movements of layers in the transverse direction. In the gluing area, the stress state is described by a system of two, second order partial differential equations with respect to the longitudinal movements of the outer layers. Outside the gluing area the movements of a wider layer are described by a second order partial differential equations with respect to the longitudinal displacements. Solution of the equations is build as a series expansion in the eigen functions. Eigen values are found fr om homogeneous boundary conditions at the lateral sides of the connection and the conjugation conditions on the lim it of the bonding domain and the outer edge of wider plates. The corresponding eigen functions are not orthogonal. Coefficients of the series are found from the orthogonality condition of the residual vector of boundary conditions to the eigenfunctionsvectors.

The model problem is solved, and the obtained data was compared with calculations based on implementation of the finite elements method. Calculations have shown that the accuracy of the method is sufficient for designing such connections.

Keywords:

glue joint, analytical solution, two-dimensional model

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