An alternative formulation of Kirchhoffs equations is given which is amenable to a standard Co finite element discretization. In this formulation, the potential energy of the plate is formulated entirely in terms of rotations, whereas the deflections are the outcome of a subsidiary problem. The nature of the resulting equations is such that Co interpolation can be used on both rotations and deflections. In particular, general classes of triangular and quadrilateral isoparametric elements can be used in conjunction with the method. Unlike other finite element methods which are based on three-dimensional or Mindlin formulations, the present approach deals directly with Kirchhoff's equations of thin plate bending. Excellent accuracy is observed in standard numerical tests using both distorted and undistorted mesh patterns.
' 3 particularly in the early days of research on the subject. However, these elements have been found to be excessively stiff in distorted configurations. Some of these deficiencies were overcome by R a ~z a q u e ~~ by means of a technique which was subsequently shown to be equivalent to a stress-hybrid formulation of the type introduced by Pian33 and Piang and Tong.34 Here, we focus attention on displacement formulations with the conventional three degrees of freedom per node. An alternative approach which retains the classical Kirchhoff theory of plates but in conjunction with highly nonconforming C' shape functions has been developed by Bergan and coworkers.'* l4
Much of the recent work on elements based on Kirchhoffs theory has endeavored to relax the exacting normality constraint of thin plate kinematics. An example is provided by the so-called