A Plate Bending Kirchhoff Element Based on Assumed Strain Functions

Journal of Solid Mechanics

مقاله 14، دوره 12، شماره 4، اسفند 2020، صفحه 935-952   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.22034/jsm.2020.1901430.1601

نویسندگان

F Boussem^{* 1}؛ L Belounar²

¹Biskra University, BP145 Biskra 07000, Algeria

²NMISSI Laboratory, Biskra University, BP145 Biskra 07000, Algeria

چکیده

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.              

کلیدواژه‌ها

Strain approach؛ Plate bending؛ Kirchhoff plate theory؛ Higher-order strain field؛ Free vibration

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