A general degree hybrid equilibrium finite element for Kirchhoff plates

We present a family of hybrid equilibrium finite elements for the quasistatic linear elastic analysis of plates governed by Kirchhoff theory. The moments are approximated by self-balanced polynomial fields of general degree, and in order to impose strong codiffusivity, the normal boundary rotations are approximated with complete polynomials of the same degree, whereas the transverse deflections use polynomials one degree lower. Furthermore, it is also necessary to include an independent approximation of the vertex translations. We show that the triangular form of this element is stable, that is, free from spurious kinematic modes, and the formulation that we present allows these elements to be used as a standard displacement element. Examples of computed values and convergence of the solutions are presented, which demonstrate the performance of these elements. Copyright (c) 2013 John Wiley & Sons, Ltd.