On the formulation and evaluation of old and new efficient low order triangular plate bending elements with shear effects

This paper deals with the presentation of a general, variational principle as theoretical support for the development of simple and efficient triangular elements having only one displacement and two rotations at the corner nodes to model thin to thick plates based on the first order Reissner- Mindlin plate theory. The functional is a modified Hellinger–Reissner mixed expression in terms of the kinematic variables (transverse displacement w and rotations βx and βy), and independent transverse shear strains (γx and γy). The approximations of the five independent variables of the mixed formulation take into account the accumulated knowledge on existing performing 2D Timoshenko beams and triangular elements such as T3γs, MITC3, DKT, DST, DKMT. The present mixed variational support is useful, not only to give a unique theoretical support to the above existing elements, usually based on assumed natural strain formulations, but it allows also to propose new simple and efficient elements, here called BAK1, BAK2 and BAK3. The paper includes a detailed presentation of results of patch tests for very thin and very thick plates, for convergence of displacements, bending moments and shear forces, for clamped circular and simply supported square plates and for s-norm convergence tests considering regular and irregular meshes. Shear force distribution is also considered for situations with boundary layer effects.