New Locking-Free Mixed Method for the Reissner-Mindlin Thin Plate Model
New Locking-Free Mixed Method for the Reissner-Mindlin Thin Plate Model
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DOI：
10.1137/s0036142901385222
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发表时间：
2002-04
期刊：
影响因子：
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通讯作者：
M. Amara;D. Capatina;Amna Chatti
中科院分区：
文献类型：
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作者：
M. Amara;D. Capatina;Amna Chatti
在这里，我们感兴趣的Reissner-Mindlin模型的弯曲薄板的物理边界条件。众所周知，这个问题奇异地依赖于板的厚度\（\vareps\）。通过分解的弯矩和对偶的对称性，我们得到一个等价的混合制定的初始问题，其未知数现在属于经典的Sobolev空间。然后，我们提出了一个低阶协调有限元方法，我们获得了最佳的误差估计独立的小参数\（\vareprom。因此，该离散方法是无条件收敛且无锁定的。它直接给出了弯矩的近似值，并允许我们恢复另外两个变量，即挠度和旋转矢量。
We are interested here in the Reissner--Mindlin model for a bending thin plate with physical boundary conditions. It is well known that this problem depends singularly upon the plate's thickness \( \varepsilon \). By decomposing the bending moment and by dualizing its symmetry, we obtain an equivalent mixed formulation of the initial problem whose unknowns now belong to classical Sobolev spaces. We then propose a low-order conforming finite element method for which we obtain optimal error estimates independently upon the small parameter \( \varepsilon . \) Thus, the discrete method is unconditionally convergent and locking-free. It directly gives an approximation of the bending moment and allows us to recover the two other variables, which are the deflection and the rotation vector.