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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A priori and a posteriori analysis for a locking-free low order quadrilateral hybrid finite element for Reissner-Mindlin plates
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A priori and a posteriori analysis for a locking-free low order quadrilateral hybrid finite element for Reissner-Mindlin plates

机译:Reissner-Mindlin板的无锁低阶四边形混合有限元的先验和后验分析

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摘要

This paper proposes a quadrilateral finite element method of the lowest order for Reissner-Mindlin (R-M) plates on the basis of Hellinger-Reissner variational principle, which includes variables of displacements, shear stresses and bending moments. This method uses continuous piecewise isoparametric bilinear interpolation for the approximation of transverse displacement and rotation. The piecewise-independent shear stress/bending moment approximation is constructed by following a self-equilibrium criterion and a shear-stress-enhanced condition. A priori and reliable a posteriori error estimates are derived and shown to be uniform with respect to the plate thickness t. Numerical experiments confirm the theoretical results.
机译:本文基于Hellinger-Reissner变分原理,提出了包括位移,剪应力和弯矩在内的Reissner-Mindlin(R-M)板的最低阶四边形有限元方法。该方法使用连续的分段等参双线性插值来近似横向位移和旋转。通过遵循自平衡准则和增强剪应力的条件,构造了与分段无关的剪应力/弯矩近似值。推导出先验和可靠的后验误差估计,并显示出相对于板厚度t均匀。数值实验证实了理论结果。

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