The two-parameter elastic foundation model used for the computation of the glued connection stressed state

Mathematics. Physics. Mechanics


Kurennov S. S.

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



This article is dedicated to the development of the method of calculation of adhesive joints. Here is proposed to model the adhesive layer with a two-parameter model of the elastic foundation.
Here is given an analytical model for calculation of the stress-strain state of a three-layer beam. Connecting layer is simulated by the two-parameter elastic foundation, bearing layers are considered as the beams of Timoshenko.
The problem is reduced to a system of differential equations which is solved by matrix method.
The new model of the adhesive joint allows more accurate simulation of the stress state in the neighborhood of the boundary points of the connection, in the most loaded areas.
The technique, proposed here, can be developed for a multi-layer joints.
To determine the stress state of the adhesive joint here was used a multi-parameter Vlasov-Pasternak elastic foundation model, which takes into account the relative shifts of the layers and their derivatives.


single lap joint, analytical solution, adhesive joints, Timoshenko beam


  1. Goland M., Reissner E. The stresses in Cemented Joints, J. App. Mech., 1944, vol. 11, pp.A11-A27.
  2. Hart-Smith, L.J. Adhesive-Bonded Single-Lap Joints, Douglas Aircraft Co., NASA Langley Report CR 112236, 1973, 37 p.
  3. Rzhanitsyn A.R. Sostavnye sterzhni i plastiny (Compound rods and plates), Moscow, Stroiizdat, 1986, 316 p.
  4. Chen W.T., Nelson C.W. Thermal stress in bonded joints, IBM Journal of Research and Development, 1979,vol. 23 no.2,pр. 179-188.
  5. Luo Q., Tong L. Fully-coupled nonlinear analysis of single lap adhesive joints, International Journal of Solids and Structures, 2007, vol. 44, pp. 2349-2370.
  6. Luo Q., Tong L. Analytical solutions for adhesive composite joints considering large deflection and transverse shear deformation in adherends, International Journal of Solids and Structures, 2008, vol. 45, pp. 5914–5935.
  7. Sandu M., Sandu A., Constantinescu D.M., Strength of adhesively bonded single strapped joints loaded in tension. Proceedings of the Romanian Academy, 2010,Series A, vol. 11(4), pp. 371-379.
  8. Artyukhin Yu.P. Vestnik Kazanskogo universiteta, 1975, no. 11, pp. 136–148.
  9. Zhao B., Lu Z-H., Lu Y-N. Closed-form solutions for elastic stress–strain analysis in unbalanced adhesive single-lap joints considering adherend deformations and bond thickness, International Journal of Adhesion & Adhesives, 2011, vol. 31, pp. 434–445.
  10. Pasternak P.L. Osnovy novogo metoda rascheta fundamentov na uprugom osnovanii pri pomoshhi dvuh kojefficientov posteli (Basis of new method of calculation of foundations on the elastic foundation through two subgrade resistance coefficients), Moscow, Gosstojizdat, 1954, 56 p.

Download — informational site MAI

Copyright © 2000-2022 by MAI