A finite element method for the buckling problem of simply supported Kirchhoff plates
A finite element method for the buckling problem of simply supported Kirchhoff plates
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DOI：
10.1016/j.cam.2015.02.018
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发表时间：
2015-10
期刊：
影响因子：
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通讯作者：
Felipe Millar;D. Mora
中科院分区：
文献类型：
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作者：
Felipe Millar;D. Mora
本文的目的是建立一种有限元方法来逼近简支基尔霍夫板在一般平面应力张量作用下的屈曲问题。我们引入一个辅助变量w:= Δ u （u表示板的位移）来写出谱问题的变分公式。我们提出了问题的一致性离散化，其中的未知数由分段线性和连续有限元近似。我们证明了所得到的格式提供了谱的正确近似，并证明了特征函数的最优阶误差估计和特征值的双阶误差估计。最后，给出了一些数值实验来支持我们的理论结果。
The aim of this paper is to develop a finite element method to approximate the buckling problem of simply supported Kirchhoff plates subjected to general plane stress tensor. We introduce an auxiliary variable w:= Δ u (with u representing the displacement of the plate) to write a variational formulation of the spectral problem. We propose a conforming discretization of the problem, where the unknowns are approximated by piecewise linear and continuous finite elements. We show that the resulting scheme provides a correct approximation of the spectrum and prove optimal order error estimates for the eigenfunctions and a double order for the eigenvalues. Finally, we present some numerical experiments supporting our theoretical results.