Plate structural analysis based on a double interpolation element with arbitrary meshing

This paper presents the plate structural analysis based on the finite element method (FEM) using a double interpolation element with arbitrary meshing. This element used in this research is related to the first-order shear deformation theory (FSDT) and the double interpolation procedure. The first stage of the procedure is the same with the standard FEM for the quadrilateral element, but the averaged nodal gradients must be computed for the second stage of this interpolation. Shape functions established by the double interpolation procedure exhibit more continuous nodal gradients and higher-order polynomial contrast compared to the standard FEM when analysing the same mesh. Note that the total degrees of freedom (DOFs) do not increase in this procedure, and the trial solution and its derivatives are continuous across inter-element boundaries. Besides, with controlling distortion factors, the interior nodes of a plate domain are derived from a set of regular nodes. Four practical examples with good results and small errors are considered in this study for showing excellent efficiency for this element. Last but not least, this element allows us to implement the procedure in an existing FEM computer code as well as can be used for nonlinear analysis in the near future.