摘要
This paper presents a low order stabilized hybrid quadrilateral finite element method for ReissnerMindlin plates based on Hellinger-Reissner variational principle,which includes variables of displacements,shear stresses and bending moments.The approach uses continuous piecewise isoparametric bilinear interpolations for the approximations of the transverse displacement and rotation.The stabilization achieved by adding a stabilization term of least-squares to the original hybrid scheme,allows independent approximations of the stresses and moments.The stress approximation adopts a piecewise independent 4-parameter mode satisfying an accuracy-enhanced condition.The approximation of moments employs a piecewise-independent 5-parameter mode.This method can be viewed as a stabilized version of the hybrid finite element scheme proposed in [Carstensen C,Xie X,Yu G,et al.A priori and a posteriori analysis for a locking-free low order quadrilateral hybrid finite element for Reissner-Mindlin plates.Comput Methods Appl Mech Engrg,2011,200:1161-1175],where the approximations of stresses and moments are required to satisfy an equilibrium criterion.A priori error analysis shows that the method is uniform with respect to the plate thickness t.Numerical experiments confirm the theoretical results.
This paper presents a low order stabilized hybrid quadrilateral finite element method for Reissner- Mindlin plates based on Hellinger-Reissner variational principle, which includes variables of displacements, shear stresses and bending moments. The approach uses continuous piecewise isoparametric bilinear interpolations for the approximations of the transverse displacement and rotation. The stabilization achieved by adding a stabilization term of least-squares to the original hybrid scheme, allows independent approximations of the stresses and moments. The stress approximation adopts a piecewise independent 4-parameter mode satisfying an accuracy-enhanced condition. The approximation of moments employs a piecewise-independent 5-parameter mode. This method can be viewed as a stabilized version of the hybrid finite element scheme proposed in [Carstensen C, Xie X, Yu G, et al. A priori and a posteriori analysis for a locking-free low order quadrilateral hybrid finite element for Reissner-Mindlin plates. Comput Methods Appl Mech Engrg, 2011, 200： 1161-1175], where the approximations of stresses and moments are required to satisfy an equilibrium criterion. A priori error analysis shows that the method is uniform with respect to the plate thickness t. Numerical experiments confirm the theoretical results.
基金
supported by National Natural Science Foundation of China (Grant Nos. 11171239 and 11226333)
Scientific Research Foundation for the Returned Overseas Chinese Scholars and Foundation for Excellent Young Scholars of Sichuan University (Grant No. 2011SCU04B28)
