An improved quadrilateral finite element for analysis of thin plates

A review of 4-node, 12 degrees-of-freedom quadrilateral elements for thin plates is presented. An improved thin plate element based on the Discrete Kirchhoff Assumptions, called IDKQ, is discussed. The formulation is based on a coordinate transformation technique which involves the imposition of the Discrete Kirchhoff Assumptions at the center and mid-side nodes of the 9-node Lagrangean isoparametric plate element denoted as QUAD9. The element IDKQ passes the patch test and it appears to be accurate. Based on the numerical results from a set of standard test problems, this new formulation is shown to be an improvement over the earlier attempts to formulate a compatible and computationally efficient finite element for thin plates analysis.