Improvement of the Results of Finite Element Method in Plate Analysis Using Mesh Sizing Modifying Function

Abstract

In the finite element methods (FEM), the mesh dimension, and the number of elements can affect the responses of structures. In this paper, a procedure is proposed to modify the stiffness matric of the plate element based on the mesh geometry and mesh size for reducing the central deflection error. For this purpose, the modifying coefficients are defined for the bending and shear stiffness matrices. The sensitivity of coefficients is investigated when the thickness of the plate element, the mesh dimension, and also the type of supports vary. The analysis results prove that the values of the bending coefficient have more effect in comparison to the shear coefficient. Finally, a function is proposed to determine the bending and shear matric coefficients based on the values of the exact displacements. Various numerical studies indicate that the modifying function has significantly improved the performance of the plate element, especially for the plates with irregular and large mesh dimensions.