Development of a new quadrilateral thin plate element using area coordinates

A new quadrilateral thin plate bending element with 12 degrees of freedom, called element ACGCQ, has been developed by employing both the area coordin ates and the generalized conforming approach. The deflection field of the e lement is expressed as a polynomial, in terms of area coordinates, which is corresponding to a fourth order polynomial in terms of Cartesian coordinat es x and y. The 12 generalized conforming conditions implemented are four-p oint and four-line compatibility conditions for the deflection w, and four- line compatibility conditions for the normal slope psi (n), Since the relat ion between the area and Cartesian coordinates is linear, the formulation o f the element stiffness matrix is straight forward. Several numerical examp les were employed to test the proposed element. The results obtained show t hat it possesses the advantage of high accuracy and reliability, rapid conv ergence and insensitivity to geometric distortion. (C) 2000 Elsevier Scienc e S.A. All rights reserved.