Differential quadrature element method for buckling analysis of rectangular Mindlin plates having discontinuities

In this paper, a new solution approach, the differential quadrature element method is applied to the buckling analysis of discontinuous rectangular plates based on the Mindlin plate theory. The domain decomposition method is used to divide the solution domain into smaller elements according to the discontinuities contained in the plate. Then, differential quadrature procedures are applied to each element to formulate the discretized element governing equations. These discrete equations are then assembled into an overall equation system, using the compatibility conditions, and solved by a standard eigensolver. Detailed formulations for modeling of the plate and the compatibility conditions are derived. Convergence and comparison studies are carried out to examine the reliability and accuracy of the numerical solutions. Four rectangular Mindlin plates with different discontinuities (mixed boundary conditions and cracks) are analyzed to show the applicability and flexibility of the present methodology for solving a class of buckling problems. Due to the lack of published solutions for buckling of thick discontinuous plates and the high accuracy of the present approach, the solutions obtained may serve as benchmark values for further studies.

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