Bending Analysis of Thin Skew Plates Using Extended Kantorovich Method

Abstract

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.

Asymptotic Approach to Oblique Cross-Sectional Analysis of Beams

“…Several such studies can be seen in the literature [15,16], and to date analysis of skew plates has followed a similar approach [17][18][19]. A large body of literature on skew plates involves the usage of an unskewed plate theory (Love-Kirchhoff or Reissner-Mindlin) along with a transformation of the coordinate and variable to an axis system that describes the plate.…”

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

“…All these applications of EKM, are devoted and restricted to the problems in the Cartesian and Polar coordinate systems. The authors of the present paper, for the first time applied EKM in oblique coordinate system for bending of skew plates under clamp boundary conditions without considering foundations and stress analysis [14]. Based on the other solution methods, several research have studied bending, buckling, vibration and other analysis for skew plates in term of oblique coordinate system [15][16][17][18][19][20].…”

Asymptotic Approach to Oblique Cross-Sectional Analysis of Beams

“…Several such studies can be seen in the literature, 9,10 and to date analysis of skew plates has followed a similar approach. [11][12][13] In light of these studies it is important to note that the current analysis of oblique sections does not involve any transformations or adaptation of results from the existing VAM procedure (which goes into VABS) for orthogonal sections. The analysis for oblique cross sections will be carried out independently, from first principles.…”