Static analysis of shear-deformable shells of revolution via G.D.Q. method

Structural Engineering and Mechanics

Volumn 19, Issue 4, 2005, Pages 459-475

  Artioli, Edoardo ^a   Viola, Erasmo ^a,b  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b Structural Mechanics   (Italy)

Author keywords

Generalized differential quadrature; Numerical method; Shell of revolution; Static analysis

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY ELEMENT METHOD; ELASTICITY; FOURIER TRANSFORMS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; SHEAR DEFORMATION; STRAIN;

GENERALIZED DIFFERENTIAL QUADRATURE; SHELL OF REVOLUTION; STATIC ANALYSIS; STRESS PATTERNS;

SHELLS (STRUCTURES);

EID: 17044383899     PISSN: 12254568     EISSN: None     Source Type: Journal    
DOI: 10.12989/sem.2005.19.4.459     Document Type: Article

References (24)

1. Bellman, R. and Casti, J. (1971), "Differential quadrature and long-term integration", J. Mathematics Analytic Applications, 34, 235-238.
2. Bellman, R., Kashef, B. and Casti, J. (1972), "Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations", J. of Computational Physics, 10(1), 40-52.
3. Bellomo, N. (1997), "Nonlinear models and problems in applied sciences from differential quadrature to generalized collocation methods", Mathematical and Computer Modelling, 26(4), 13-34.
4. Bert, C.W. and Malik, M. (1996), "Differential quadrature method in computational mechanics: a review", Appl. Mech. Rev., 49, 1-27.
5. Bert, C.W. and Malik, M. (1996), "Free vibration analysis of thin cylindrical shells by the differential quadrature method", J. of Pressure Vessel Technology, 118, 1-12.
6. Gould, P.L. (1999), Analysis of Shells and Plates, Upper Saddle River, Prentice Hall.
7. Gould, P.L. and Sen, S.K. (1971), "Refined mixed method finite elements for shells of revolution", Proc. Air Force third Conference on matrix methods in structural mechanics, AFB Ohio.
8. Jiang, W. and Redekop, D. (2002), "Polar axisymmetric vibration of a hollow toroid using the differential quadrature method", J. Sound Vib., 251(4), 761-765.
9. Kim, J.G. and Kim, Y.Y. (2000), "A higher-order hybrid-mixed harmonic shell-of-revolution element", Comput. Meth. Appl. Mech. Eng., 182, 1-16.
10. Krysl, P. and Belytschko, T. (1996), "Analysis of thin shells by the element-free Galerkin method", Int. J. Solids Struct., 33(20-22), 3057-3080.
11. Kunieda, H. (1984), "Flexural axisymmetric free vibrations of a spherical dome: exact results and approximate solutions", J. Sound Vib., 92(1), 1-10.
12. Liu, Y. (1998), "Analysis of shell-like structures by the boundary element method based on 3-D elasticity: Formulation and verification", Int. J. Numer. Meth. Eng., 41, 541-558.
13. Luah, M.H. and Fan, S.C. (1990), "New spline finite element for analysis of shells of revolution", J. Eng. Mech., ASCE, 116(3), 709-725.
14. Mirfakhraei, P. and Redekop, D. (1998), "Buckling of circular cylindrical shells by the Differential Quadrature Method", Int. J. of Pressure Vessels and Piping, 75, 347-353.
15. Mizusawa, T. (1988), "Application of spline strip method to analyse vibration of open cylindrical shells", Int. J. Numer. Meth. Eng., 26, 663-676.
16. Prato, C. (1969), "Shell finite element method via Reissner's principle", Int. J. Solids Struct., 5, 1119-1133.
17. Reddy, J.N. (1984), Energy and Variational Methods in Applied Mechanics, John Wiley & Sons.
18. Redekop, D. and Xu, B. (1999), "Vibration analysis of toroidal panels using the differential quadrature method", Thin Walled Structures, 34, 217-231.
19. Reissner, E. (1946), "Stresses and small displacements of shallow spherical shells - Part II", J. Mathematics Physics, 25, 80-85.
20. Shu, C. and Richards, B.E. (1992), "Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations", Int. J. Numer. Meth. Eng., 15, 791-798.
21. Viola, E. and Artioli, E. (2004), "The G.D.Q. method for the harmonic dynamic analysis of rotational shell structural elements", Structural Engineering and Mechanics, 17(6), 789-817.
22. Viola, E., Sgallari, F. and Artioli, E. (2003), "Computational efficiency of the Generalized Differential Quadrature method in the elastic analysis of shells of revolution", Technical Report, DISTART, University of Bologna, Italy.
23. Wu, C.P. and Lee, C.Y. (2001), "Differential quadrature solution for the free vibration analysis of laminated conical shells with variable stiffness", Int. J. Mech. Sci., 43, 1853-1869.
24. Yang, H.T.Y., Saigal, S., Masud, A. and Kapania, R.K. (2000), "A survey of recent shell finite elements", Int. J. Numer. Meth. Eng., 47, 101-127.