, Volume 54, Issue 3, pp 565–572 | Cite as

Bending of edge-bonded dissimilar rectangular plates

  • Iman Joodaky
  • Amin JoodakyEmail author


This study develops the extended Kantorovich method (EKM) to provide a closed form semi analytical solution for the bending analysis of two edge-bonded thin rectangular plates. The constituent plates could be different in thickness, length, material, loading conditions, and Winkler foundation’s stiffness. A combination of clamp, free, and simply supports are applied to the structure. The shared edge in the composite plate is assumed to be perfectly bonded. By applying the EKM together with the idea of weighted residual technique, two sets of ODEs are obtained. Bending is assumed to remain continuous on the bonded edge. The EKM procedure is modified by applying the coordinate of an arbitrary shared point in the boundary conditions for the shared edge, to relate the bending of the two plates. The ODEs are solved iteratively to obtain the deflection function in a fast convergence trend. Two examples of aluminium-steel plate and functionally graded material-steel plate are considered. The deflection results from the boundary modified EKM (BM-EKM) are in high agreement with the finite element solution results. The bending of stepped plates is a special case of the current study. The suggested BM-EKM strengthens the EKM’s ability for solving complex jointed/bonded structures in structural analyses.


Plates bending Kantorovich method Bonded plates Winkler foundation Composites Functionally graded material 


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Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Young Researchers Club, Arak BranchIslamic Azad UniversityArākIran
  2. 2.School of Mechanical EngineeringPurdue UniversityWest LafayetteUSA

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