用改进型广义协调元分析薄板的振动与稳定

本文在文献1]和2]的基础上,将改进型三角形广义协调元TGC-9-1应用于薄板振动和稳定分析中。推导出带有一个内部自由度(外部结点有九个自由度)的三角形板单元的协调质量矩阵和几何刚度矩阵。并通过算例表明,改进型广义协调三角形单元(TGC-9-1)具有良好的性态和更好的精度,程序简便。

Vibration and Stability Analysis of Thin Plate with Improved Generalized Conforming Element

Based on references 1] and 2] , this paper put forward a improved generalized conforming element with 10 degrees of freedom (9 external d. o. f. ), which is used for the analysis of vibration and stability of thin plate. The element used condense method dispel one internal d. o. f. and surplus 9 external d. o. f. The mass and geometric stiffness matrix of element are found. After that,the problem sum up to the generalized eigenvalue solution.Displacement field of the element have complete third order polynomal, which increase conformance and calculation precision. The final results show that the advantages of the improved element are:less d. o. f. ,higher precision solution and easyto be programmed. The element is a simple, efficient and reliable element for analysis of vibration and stability of thin plate.