Bending Analysis of Thin Skew Plates Using Extended Kantorovich Method

An accurate approximate closed-form solution is presented for bending of thin skew plates with clamped edges subjected to uniform loading using the extended Kantorovich method (EKM). Successive application of EKM together with the idea of weighted residual technique (Galerkin method) converts the governing forth-order partial differential equation (PDE) to two separate ordinary differential equations (ODE) in terms of oblique coordinates system. The obtained ODE systems are then solved iteratively with very fast convergence. In every iteration step, exact closed-form solutions are obtained for two ODE systems. It is shown that some parameters such as angle of skew plate have an important effect on results. It is shown that the method provides sufficiently accurate results not only for deflections but also for stress components. Comparison of the deflection and stresses at various points of the plates show very good agreement with results of other analytical and numerical analyses. Also, it has been shown that for skew angle less than 30° this method provides more accurate results and when the skew angle becomes greater than 30°, results gradually begin to deviate from those reported using other methods or by finite element softwares.