Abstract
A general quadrilateral finite element for thin and moderately thick plates is described. The element is not derived from the traditional variational principles, but is rather based on a “free formulation”, which satisfies the mathematical convergence requirements. The transverse displacement is expanded in a set of fundamental rigid-body and constant curvature modes plus a set of higher order modes. There is no additional expansion for the shear deformations, these are accounted for in a special way using the local equilibrium equations, kinematics, and the constitutive relations for shear. Many of the difficulties encountered in connection with the normal elements based on Reissner theory are avoided by using the present formulation. Very good results have been obtained for thin and thick plates of various geometries.
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