Collocation methods for the solution of von-Kármán dynamic non-linear plate systems

Journal of Computational Physics

Volumn 200, Issue 2, 2004, Pages 432-461

  Yosibash, Z ^a   Kirby, R M ^b   Gottlieb, D ^c  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^b Department of Electrical and Computer Engineering   (United States)

^c BROWN UNIVERSITY   (United States)

Author keywords

Aliasing; Chebyshev collocation; Legendre collocation; Polynomial filtering; von K rm n plate model

Indexed keywords

NONLINEAR EQUATIONS; NUMERICAL METHODS; POLYNOMIALS;

ALIASING; CHEBYSHEV COLLOCATION; COLLOCATION METHOD; COLLOCATION SOLUTION; LEGENDRE COLLOCATIONS; LINEAR TERMS; NON LINEAR; PLATE MODEL; POLYNOMIAL FILTERING; VON-KÁRMÁN PLATE MODEL;

LINEAR SYSTEMS;

EID: 7244234402     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.03.018     Document Type: Article

References (20)

1. Kirby R.M. Yosibash Z. Solution of von-Kármán dynamic non-linear plate equations using a pseudo-spectral method Comput. Meth. Appl. Mech. Engrg. 193 6-8 2004 575-599
2. Lasiecka I. Uniform stabilizability of a full von Karman system with nonlinear boundary feedback SIAM J. Control Optim. 36 4 1998 1376-1422
3. Koch H. Lasiecka I. Hadamard well-posedness of weak solutions in nonlinear dynamic elasticity-full von Karman systems Progr. Nonlinear Differenatial Equations 50 2002 197-216
4. Chia Chuen-Yuan Nonlinear Analysis of Plates 1980 McGraw-Hill
5. Han W. Petyt M. Geometrically nonlinear vibration analysis of thin, rectangular plates using the hierarchical finite element method - I: The fundamental mode of isotropic plates Comp. Struct. 63 1997 295-308
6. Nath Y. Kumar S. Chebyshev series solution to non-linear boundary value problems in rectangular domain Comput. Meth. Appl. Mech. Engrg. 125 1995 41-52
7. R.E. Gordnier, R. Fithen, Coupling of a nonlinear finite element structural method with Navier-Stokes solver. AIAA2001-2853, in: 31st Fluid Dynamics Conference, June 2001
8. Gordnier R.E. Visbal M.R. Development of a three-dimensional viscous aeroelastic solver for nonlinear panel flutter J. Fluids Struct. 16 2002 497-527
9. Lagnese John E. Boundary Stabilization of Thin Plates SIAM 1989
10. Boyd J.P. Flyer N. Compatibility conditions for time-dependent partial differential equations and the rate of convergence of Chebyshev and Fourier spectral methods Comput. Meth. Appl. Mech. Engrg. 175 1999 281-309
11. Ciarlet Philippe G. Plates and Junctions in Elastic Multi-structures. An Asymptotic Analysis. RMA 14 1990 Springer Masson
12. Canuto C. Hussaini M.Y. Quarteroni A. Zang T.A. Spectral Methods in Fluid Mechanics 1987 Springer New York
13. Trefethen Lloyd N. Spectral Methods in Matlab SIAM 2000
14. Humar J.L. Dynamics of Structures 2002 A.A. Balkema Publishers
15. Szabó B.A. Babuška I. Finite Element Analysis 1991 Wiley New York
16. Karniadakis George Em Sherwin Spencer J. Spectral/hp Element Methods for CFD 1999 Oxford University Press NY, USA
17. Burden R. Faires J.D. Numerical Analysis 1993 PWS Publishing Company
18. Kreiss H.O. Lorenz J. Initial-boundary Value Problems and the Navier-Stokes Equations 1989 Academic Press
19. Strang G. Linear Algebra and Its Applications 1998 Harcourt Brace Jovanovich College Publishers
20. Gottlieb D. Hesthaven J.S. Spectral methods for hyperbolic problems J. Comput. Appl. Math. 128 1-2 2001 83-131