Reformulation of Reissner-Mindlin plate equations for computational efficiency

Finite Elements based on Reissner-Mindlin Plate Theory are becoming more popular than the ones based on Kirchoff-Poisson Plate Theory because of the obvious advantages. These advantages include applicability for a larger range of thickness and inclusion of rotary inertia in dynamics. However such formulations have been plagued by a number of computational problems like slow convergence, shear locking, rank deficiency etc. This article first points out the absence of transpose relation between the [ψ] and [∂] operator matrices in the governing differential equation [ψ][D][∂]{u} + {f} = 0 for Timoshenko beam and Reissner-Mindlin plates. Secondly, it contributes a superposition concept by which the state of stress and deformation in a general Reissner-Mindlin plate can be obtained by superposing two primitive states: Pure Shear state and Pure Moment (Bending and Twisting) state. This concept restores the above mentioned transpose relation and also eliminates the 'shear-locking' problem. (author)