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 T3γ_s, 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.

本文介绍了一般的变分原理，为开发简单有效的三角形元素（在角节点处只有一个位移和两次旋转）以基于一阶Reissner-Mindlin板建模薄板到厚板提供了理论支持理论。根据运动学变量（横向位移w和旋转βx和βy）以及独立的横向剪切应变（γx和γy），该函数是修改后的Hellinger-Reissner混合表达式。）。混合配方的五个独立变量的近似值考虑了对现有的2D Timoshenko梁和诸如T3γs之类_的三角形元素的累积知识，MITC3，DKT，DST，DKMT。当前的混合变分支持不仅对于通常基于假定的自然应变公式为上述现有元素提供独特的理论支持，而且还可以提出新的简单有效的元素（在这里称为BAK1，BAK2和BAK3）。本文包括对非常薄和非常厚的板，位移，弯曲力矩和剪力的收敛，对于圆形和简单支撑的正方形板的补丁测试以及考虑规则和不规则网格的s范收敛测试的详细介绍。 。对于具有边界层效应的情况，也要考虑剪切力的分布。