A differential quadrature hierarchical finite element method and its application to thin plate free vibration

被引：0
作者：
Wu Y. [1 ]
Xing Y.-F. [1 ]
机构：
[1] Institute of Solid Mechanics, Beihang University (BUAA), Beijing
来源：
Zhendong Gongcheng Xuebao/Journal of Vibration Engineering | 2018年 / 31卷 / 02期
关键词：
Differential quadrature method; Hermite interpolation; Hierarchical finite element method; Vibration of thin plates;
D O I：
10.16385/j.cnki.issn.1004-4523.2018.02.019
中图分类号：
学科分类号：
摘要：
A Hermite differential quadrature hierarchical finite element method is proposed and elaborated in this paper. The geometric mapping is based on blending function interpolation, while the shape functions at the element edges are derived from Hermite interpolation bases with non-uniform distributed nodes and the internal hierarchical face functions are obtained through tensor product of one dimensional Jacobi orthogonal polynomials. The shape functions in conjunction with Gauss-Lobatto interpolation are employed in discretizing the potential functional of thin plates to obtain the element matrices. In the present elements, the DOFs (Degree of Freedoms) collocations are free at each side and inside of the element, therefore it is allowed to use elements with different order in assembly. The present elements are used in free vibration analysis of thin plate, and the results are compared with the exact solutions and the numerical results by other methods, which show the high accuracy as well as fast convergence of present elements. Moreover, the stability problems are not suffered even when the element order is very high. © 2018, Nanjing Univ. of Aeronautics an Astronautics. All right reserved.
引用
收藏
页码：343 / 351
页数：8
相关论文
共 16 条
  • [1] Courant R., Variational methods for the solution of problems of equilibrium and vibrations, Bulletin of the American Mathematical Society, 49, 1, pp. 1-23, (1943)
  • [2] Turner M.J., Stiffness and deflection analysis of complex structures, Journal of the Aeronautical Sciences, 23, 9, pp. 805-823, (1956)
  • [3] Zienkiewicz O.C., Taylor R.L., Taylor R.L., Et al., Finite Element Method: Its Basis and Fundamentals, (2013)
  • [4] Babusska I., Szabo B.A., Katz I.N., The p-version of the finite element method, Siam Journal on Numerical Analysis, 18, 3, pp. 515-545, (1981)
  • [5] Babuska I., Suri M., The p- and h-p versions of the finite element method, an overview, Computer Methods in Applied Mechanics and Engineering, 80, 1990, pp. 5-26, (1990)
  • [6] Zienkiewicz O.C., De Gago S.R.J.P., Kelly D.W., The hierarchical concept in finite element analysis, Computers & Structures, 16, 1, pp. 53-65, (1983)
  • [7] Peano A., Hierarchies of conforming finite elements for plane elasticity and plate bending, Computers & Mathematics with Applications, 2, 3, pp. 211-224, (1976)
  • [8] Bardell N.S., The application of symbolic computing to the hierarchical finite element method, International Journal for Numerical Methods in Engineering, 28, 5, pp. 1181-1204, (1989)
  • [9] Bardell N.S., Free vibration analysis of a flat plate using the hierarchical finite element method, Journal of Sound & Vibration, 151, 2, pp. 263-289, (1991)
  • [10] Liu C., Liu B., Zhao L., Et al., A differential quadrature hierarchical finite element method and its applications to vibration and bending of Mindlin plates with curvilinear domains, International Journal for Numerical Methods in Engineering, 109, 2, pp. 174-197, (2016)
12