On the connection between some linear triangular Reissner-Mindlin plate bending elements

We consider three triangular plate bending elements for the Reissner-Mindli n model. The elements are the MIN3 element of Tessler and Hughes [19], the stabilized MITC3 element of Brezzi, Fortin and Stenberg [5] and the T3BL el ement of Xu, Auricchio and Taylor [2, 17, 20]. We show that the bilinear fo rms of the stabilized MITC3 and MIN3 elements are equivalent and that their implementation may be simplified by using numerical integration of reduced order. The T3BL element is shown to be essentially the same as the MIN3 an d stabilized MITC3 elements with reduced integration. We finally introduce a general stabilized finite element formulation which covers all three meth ods. For this class of methods we prove the stability and optimal convergen ce properties.