A variable order approach to improve differential quadrature accuracy in dynamic analysis

Journal of Sound and Vibration

Volumn 266, Issue 2, 2003, Pages 307-323

  Zong, Z ^a  

^a INSTITUTE OF HIGH PERFORMANCE COMPUTING   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; INTERPOLATION; LAGRANGE MULTIPLIERS; NONLINEAR EQUATIONS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS; RUNGE KUTTA METHODS;

DIFFERENTIAL QUADRATURE TECHNIQUE; DYNAMIC ANALYSIS; NUMERICAL INSTABILITY; STRING VIBRATION; VARIABLE ORDER APPROACH;

VIBRATIONS (MECHANICAL);

EID: 0141453367     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-460X(02)01307-X     Document Type: Article

References (18)

1. R. E. Bellman, B. G. Kashef, J. Casti, Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations, Journal of Computational Physics 10 (1972) 40-52.
2. C. Shu, Differential Quadrature and its Applications in Engineering, Springer, Berlin, 2000.
3. S. Moradi, F. Taheri, Differential quadrature approach for delamination buckling analysis of composites with shear deformation, American Institute of Aeronautics and Astronautics Journal 36 (1998) 1869-1873.
4. C.N. Chen, Differential quadrature finite difference method for structural mechanics problems, Communications in Numerical Methods in Engineering 17 (200) 423-441.
5. W.L. Chen, A.G. Stritz, C.W. Bert, High-accuracy plane stress and plate elements in the quadrature element method, International Journal of Solids and Structures 37 (2000) 627-647.
6. F. Civian, C.M. Sliepcevich, Differential quadrature for multidimensional problems, Journal of Mathematical Analysis and Applications 101 (1984) 423-443.
7. J.R. Quan, C.T. Chang, New insights in solving distributed system equations by the quadrature methods-I, Computers and Chemical Engineering 13 (1989) 779-788.
8. J.R. Quan, C.T. Chang, New insights in solving distributed system equations by the quadrature methods-II, Computers and Chemical Engineering 13 (1989) 1017-1024.
9. C.W. Bert, M. Malik, The differential quadrature method for irregular domains and application to plate vibration, International Journal of Mechanical Sciences 38 (1996) 589-606.
10. C.W. Bert, M. Malik, Differential quadrature method in computational mechanics: a review, Applied Mechanics Reviews 49 (1996) 1-28.
11. H. Zengh, C.W. Bert, A differential quadrature analysis of vibration for rectangular stiffened plates, Journal of Sound and Vibration 241 (2001) 247-252.
12. T.C. Fung, Solving initial value problems by differential quadrature method-Part 2: second- and higher-order equations, International Journal of Numerical Methods in Engineering 50 (2001) 1429-1454.
13. C. Shu, W. Kha, Numerical simulation of natural convection in a square cavity by SIMPLE-generalized differential quadrature method, Computers and Fluids 31 (2002) 209-226.
14. C. Shu, W. Chen, H. Xue, H. Du, Numerical study of grid distribution effect on accuracy of DQ analysis of beams and plates by error estimation of derivative approximation, International Journal in Numerical Methods in Engineering 51 (2001) 159-179.
15. G.D. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, Clarendon Press, Oxford, 1985.
16. S. Adjerid, J.E. Flaherty, Amoving finite element method with error estimation and refinement for one-dimensional time dependent partial differential equations, SIAM Journal of Numerical Analysis 23 (1986) 778-795.
17. K.E. Atkinson, An Introduction to Numerical Analysis, 2nd Edition, Wiley, New York, 1989.
18. M.H.Carpenter, D. Gottlieb, S. Abarbanel, Time-stable boundary-conditions for finite-difference schemes solving hyperbolic systems-methodology and application to high-order compact schemes, Journal of Computational Physics 111 (2) (1994) 220-236.