Cite this article as:

Barulina M. A. Application of Generalized Differential Quadrature Method to Two-dimensional Problems of Mechanics. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2018, vol. 18, iss. 2, pp. 206-216. DOI: https://doi.org/10.18500/1816-9791-2018-18-2-206-216

Language: 
Russian
Heading: 
Mechanics
UDC: 
51.74

Application of Generalized Differential Quadrature Method to Two-dimensional Problems of Mechanics

Authors: 
Barulina Marina A. , Institute of Precision Mechanics and Control, Russian Academy of Sciences, 24, Rabochaya str., 410028, Saratov, Russia , marina@ibarulina.ru
Abstract: 
The application of the generalized differential quadrature method to the solution of two-dimensional problems of solid mechanics is discussed by an example of the sample analysis of vibrations o f a rectangular plate under various types of boundary cond itions. The dif ferential quadrature method (DQM) is known as an effective method for resolving differential equations, both ordinary an d partial. The main problems while using DQM, as well as other q u adrature methods, are choosing the distribution for construction of the points grid and d etermination of the weight coefficients, and incorporarting boundary conditions in the resolving system of linear algebraic equations. In the present study a generalized approach to accounting the boundary conditions is proposed and a universal algorithm for the composition of a resolving algebraic system is given. In the paper it is shown by an example of model analysis of a rectangular plate vibrations that the DQM allows us to effectively resolve two-dimensional problems of solid mechanics gaining an acceptable accuracy with a relatively small number of points on the grid. The latter is provided by the aid of the classical non-uniform Chebyshev – Gauss – Lobatto distribution and generalized approach to accounting of the boundary conditions.
Key words: 
differential quadrature method, numer i cal methods, differential equations, eigenfrequencies, rectangular plate
DOI: 
https://doi.org/10.18500/1816-9791-2018-18-2-206-216
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