A semi-analytical study on static behavior of thin skew plates on Winkler and Pasternak foundations

• Highly accurate results with a fast convergence using Extended Kantorovich Method.
• Studying boundary conditions comprehensively.
• Comparing effects of different foundation types and stiffness on the results.
• Studying role of the skew plate׳s angle on deflection and stress results.
• This study also covers rectangular plates when the skew angle is equaled to zero.

This study presents a semi analytical closed-form solution for governing equations of thin skew plates with various combination of clamp, free and simply supports subjected to uniform loading rested on the elastic foundations of Winkler and Pasternak. The governing forth-order partial differential equation (PDE) of two-variable function of deflection, w(X,Y), is defined in Oblique coordinates system. Application of EKM together with the idea of weighted residual technique, converts the forth-order governing equation to two ODEs in terms of X and Y in Oblique coordinates. Both resulted ODEs, are then solved iteratively in a closed-form manner with a very fast convergence. Finally deflection function is obtained. It is shown that some parameters such as angle of skew plate and stiffness of elastic foundation have an important effect on the results. Also it is investigated that shear stresses exist considerably in skew plates comparing to the corresponding rectangular plates. Comparisons of the deflection and stresses at the various points of the plates show very good agreement with results of other analytical and numerical analyses.