Development of a new quadrilateral thin plate element using area coordinates

Abstract

A new quadrilateral thin plate bending element with 12 degrees of freedom, called element ACGCQ, has been developed by employing both the area coordinates and the generalized conforming approach. The deflection field of the element is expressed as a polynomial, in terms of area coordinates, which is corresponding to a fourth order polynomial in terms of Cartesian coordinates x and y. The 12 generalized conforming conditions implemented are four-point and four-line compatibility conditions for the deflection w, and four-line compatibility conditions for the normal slope ψn. Since the relation between the area and Cartesian coordinates is linear, the formulation of the element stiffness matrix is straight forward. Several numerical examples were employed to test the proposed element. The results obtained show that it possesses the advantage of high accuracy and reliability, rapid convergence and insensitivity to geometric distortion.