The strong formulation finite element method: Stability and accuracy

Frattura ed Integrita Strutturale

Volumn 8, Issue 29, 2014, Pages 251-265

  Tornabene, Francesco ^a   Fantuzzi, Nicholas ^a   Bacciocchi, Michele ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Differential quadrature method; Finite element method; Free vibration analysis; Numerical stability; Static analysis; Strong formulation finite element method

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIATION (CALCULUS); NUMERICAL METHODS; PLATES (STRUCTURAL COMPONENTS); STATIC ANALYSIS; VIBRATION ANALYSIS;

DIFFERENTIAL QUADRATURE METHODS; FREE-VIBRATION ANALYSIS; MEMBRANES AND PLATES; NUMERICAL RESULTS; NUMERICAL SOLUTION; STRONG FORMULATIONS; STRUCTURAL COMPONENT; STRUCTURAL SYSTEMS;

FINITE ELEMENT METHOD;

EID: 84904885383     PISSN: None     EISSN: 19718993     Source Type: Journal    
DOI: 10.3221/IGF-ESIS.29.22     Document Type: Article

References (37)

1. Viola, E., Tornabene, F., Vibration analysis of damaged circular arches with varying cross-section, SID-SDHM, 1 (2005) 155-169.
2. Viola, E., Dilena, M., Tornabene, F., Analytical and numerical results for vibration analysis of multi-stepped and multi-damaged circular arches, J. Sound Vib., 299 (2007) 143-163.
3. Viola, E., Tornabene, F., Fantuzzi, N., Generalized differential quadrature finite element method for cracked composite structures of arbitrary shape, Compos. Struct., 106 (2013) 815-834.
4. Fantuzzi, N., Tornabene, F., Viola, E., Generalized Differential Quadrature Finite Element Method for Vibration Analysis of Arbitrarily Shaped Membranes, Int. J. Mech. Sci., 79 (2014) 216-251.
5. Fantuzzi, N., Tornabene, F., Strong formulation finite element method for arbitrarily shaped laminated plates - I. Theoretical analysis, Adv. Aircraft Space. Sci., 1 (2014) 125-143.
6. Fantuzzi, N., Tornabene, F., 2014, "Strong formulation finite element method for arbitrarily shaped laminated plates - II. Numerical Analysis", Adv. Aircraft Space. Sci., 1 (2014) 145-175.
7. Tornabene, F., Fantuzzi, N., Mechanics of Laminated Composite Doubly-Curved Shell Structures. The Generalized Differential Quadrature Method and the Strong Formulation Finite Element Method, Esculapio, Bologna, (2014).
8. Bellman, R., Casti, J., Differential quadrature and long-term integration, J. Math. Anal. Appl., 34 (1971) 235-238.
9. Bert, C.W., Malik, M., Differential quadrature method in computational mechanics, Appl. Mech. Rev., 49 (1996) 1-27.
10. Quan, J.R., Chang, C.T., New insights in solving distributed system equations by the quadrature method - I. Analysis, Comput. Chem. Eng., 13 (1989) 779-788.
11. Quan J.R., Chang, C.T., New insights in solving distributed system equations by the quadrature method - II. Numerical experiments, Comput. Chem. Eng., 13 (1989) 1017-1024.
12. Striz, A.G., Chen, W.L., Bert, C.W., Static analysis of structures by the quadrature element method (QEM), Int. J. Solids Struct., 31 (1994) 2807-2818.
13. Reddy, J.N., Mechanics of Laminated Composites Plates and Shells, 2nd edition, CRC Press, New York, (2004).
14. Gottlieb, D., Orszag, S.A., Numerical Analysis of Spectral Methods. Theory and Applications, CBMS-NSF Regional Conf. Ser. in Appl. Math., SIAM, (1977).
15. Boyd, J.P., Chebyshev and Fourier Spectral Methods, Dover Publications, (2001).
16. Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A., Spectral Method. Fundamentals in Single Domains, Springer, (2006).
17. Shu, C., Differential Quadrature and Its Application in Engineering, Springer, (2000).
18. Chen, C.-N., Discrete Element Analysis Methods of Generic Differential Quadratures, Springer, (2006).
19. Zong, Z., Zhang, Y.Y., Advanced Differential Quadrature Methods, CRC Press, (2009).
20. Viola, E., Tornabene, F., Dynamical analysis of spherical shell structural elements using the First Order Shear Deformation Theory, Mechanical Vibration: where do we stand?, CISM, 488 (2007) 17-41, Springer-Wien, New York.
21. Tornabene, F., 2-D GDQ solution for free vibrations of anisotropic doubly-curved shells and panels of revolution, Compos. Struct., 93 (2011) 1854-1876.
22. Tornabene, F., Free vibrations of anisotropic doubly-curved shells and panels of revolution with a free-form meridian resting on Winkler-Pasternak elastic foundations, Compos. Struct., 94 (2011) 186-206.
23. Tornabene, F., Liverani, A., Caligiana, G., Laminated composite rectangular and annular plates: a GDQ solution for static analysis with a posteriori shear and normal stress recovery, Compos. Part B Eng., 43 (2012) 1847-1872.
24. Tornabene, F., Liverani, A., Caligiana, G., General anisotropic doubly-curved shell theory: a Differential Quadrature solution for free vibrations of shells and panels of revolution with a free-form meridian, J. Sound Vib., 331 (2012) 4848-4869.
25. Tornabene, F., Ceruti, A., Free-form laminated doubly-curved shells and panels of revolution resting on Winkler- Pasternak elastic foundations: a 2-D GDQ solution for static and free vibration analysis, World J. Mech., 3 (2013) 1-25.
26. Tornabene, F., and Ceruti, A., Mixed static and dynamic optimization of four-parameter functionally graded completely doubly-curved and degenerate shells and panels using GDQ method, Math. Problem. Eng., 2013 (2013) 1-33, Article ID 867079.
27. Tornabene, F., Reddy, J.N., FGM and laminated doubly-curved and degenerate shells resting on nonlinear elastic foundations: a GDQ solution for static analysis with a posteriori stress and strain recovery, J. Indian Inst. Sci., 93 (2013) 635-688.
28. Tornabene, F., Viola, E., Static analysis of functionally graded doubly-curved shells and panels of revolution, Meccanica, 48 (2013) 901-930.
29. Tornabene, F., Viola, E., Fantuzzi, N., General higher-order equivalent single layer theory for free vibrations of doubly-curved laminated composite shells and panels, Compos. Struct., 104 (2013) 94-117.
30. Viola, E., Tornabene, F., Fantuzzi, N., General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels, Compos. Struct., 95 (2013) 639-666.
31. Viola, E., Tornabene, F., Fantuzzi, N., Static analysis of completely doubly-curved laminated shells and panels using general higher-order shear deformation theories, Compos. Struct., 101 (2013) 59-93.
32. Tornabene, F., Fantuzzi, N., Viola, E., Ferreira, A.J.M., Radial basis function method applied to doubly-curved laminated composite shells and panels with a general higher-order equivalent single layer theory, Compos. Part B Eng., 55 (2013) 642-659.
33. Tornabene, F., Fantuzzi, N., Viola, E., Carrera, E., Static analysis of doubly-curved anisotropic shells and panels using CUF approach, differential geometry and differential quadrature method, Compos. Struct., 107 (2014) 675-697.
34. Tornabene, F., Fantuzzi, N., Viola, E., Reddy, J.N., Winkler-Pasternak foundation effect on the static and dynamic analyses of laminated doubly-curved and degenerate shells and panels, Compos. Part B Eng., 57 (2014) 269-296.
35. Ding, H., Shu, C., Yeo, K.S., Xu, D., Numerical computation of three-dimensional incompressible viscous flows in the primitive variable form by local multiquadric differential quadrature method, Comput. Meth. Appl. Mech. Eng., 195 (2006) 516-533.
36. Cottrell, J.A., Hughes, T.J.R., Bazilevs, Y., Isogeometric Analysis. Toward Integration of CAD and FEA, John Wiley & Sons, (2009).
37. Reali, A., An isogeometric analysis approach for the study of structural vibrations, J. Earthq. Eng., 10 (2006) 1-30.