A piecewise linear finite element method for the buckling and the vibration problems of thin plates
A piecewise linear finite element method for the buckling and the vibration problems of thin plates
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DOI：
10.1090/s0025-5718-09-02228-5
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发表时间：
2009-02
期刊：
影响因子：
--
通讯作者：
D. Mora;R. Rodríguez
中科院分区：
文献类型：
--
作者：
D. Mora;R. Rodríguez
本文的目的是分析一种逼近薄板屈曲和振动问题的分段线性有限元方法。该方法基于Kirchhoff-Love模型弯矩公式的协调离散化。分析仅限于简单连接的多边形固支板，不一定是凸板。证明了该方法对两个谱问题都是以最优阶收敛的，包括特征值阶的改进。通过数值实验对其性能进行了评估，并与其他低阶有限元方法进行了比较。
The aim of this paper is to analyze a piecewise linear finite element method to approximate the buckling and the vibration problems of a thin plate. The method is based on a conforming discretization of a bending moment formulation for the Kirchhoff-Love model. The analysis restricts to simply connected polygonal clamped plates, not necessarily convex. The method is proved to converge with optimal order for both spectral problems, including an improved order for the eigenvalues. Numerical experiments are reported to assess its performance and to compare it with other low-order finite element methods.