A Plate Bending Kirchhoff Element Based on Assumed Strain Functions

F. Boussem, L. Belounar
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引用次数: 6

Abstract

To investigate static and free vibration for thin plate bending structures, a four-node quadrilateral finite element is proposed in this research paper. This element has been formulated by using both the assumptions of thin plates theory (Kirchhoff plate theory) and strain approach. The suggested element which possesses only three degrees of freedom (one transverse displacement and two normal rotations) at each of four corner nodes is based on assumed higher-order functions for the various components of strain field that satisfies the compatibility equation. The displacement functions of the developed element are obtained by integrating the assumed strains functions and satisfy the exact representation of the rigid body modes. Several numerical tests in both static and free vibration analysis are presented to assess the performance of the new element. The obtained results show high solution accuracy, especially for coarse meshes, of the developed element compared with analytical and other numerical solutions available in the literature.
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基于假设应变函数的板弯曲Kirchhoff单元
为了研究薄板弯曲结构的静振动和自由振动问题,提出了一种四节点四边形有限元方法。该元素是用薄板理论(基尔霍夫板理论)和应变方法的假设来表示的。所建议的单元在满足相容性方程的应变场各分量的假设高阶函数的基础上,在每个角节点上仅具有三个自由度(一个横向位移和两个法向旋转)。开发单元的位移函数通过对假定的应变函数进行积分得到,满足刚体模态的精确表示。在静态和自由振动分析中,给出了几个数值试验来评估新单元的性能。所得结果表明,与现有的解析解和其他数值解相比,所开发的单元具有较高的解精度,特别是对于粗网格。
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