Higher Order Modeling of Plates by p ‐Version of Finite Element Method

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Abstract
A new p‐version finite element based on higher order theory is developed for the two‐dimensional modeling of thin‐to‐thick plates undergoing three‐dimensional (3‐D) deformations. The special case of cylindrical bending is also considered. In each case, the displacement is expressed as the product of two functions—one in terms of the out‐of‐plane coordinate and the other in terms of in‐plane coordinates. The displacement fields are based on integrals of Legendre polynomials. The computer implementation allows arbitrary variations of p‐level in the plane of the plate and in the thickness direction up to a maximum value of 8. A number of test problems on thin‐to‐thick isotropic and orthotropic plates are considered to evaluate the performance of the proposed scheme. Convergence characteristics of pointwise values of displacement and stress, as well as that of total potential energy, are studied. The superior performance of the scheme is established by comparing the results with those in the published literature.

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