Issue 29

F. Tornabene et alii, Frattura ed Integrità Strutturale, 29 (2014) 251-265; DOI: 10.3221/IGF-ESIS.29.22 264 variational) formulation based approaches. Although it seems that DQM has been widely developed for several engineering problems, some aspects are still in a developing stage (e.g. boundary conditions in a domain decomposition approach using 1 C conditions). In a future paper the authors want to expose in detail the boundary conditions implementation from the mathematical point of view, giving all the formulae in discrete form. Moreover, the numerical results will be compared to classical FEM and SEM solutions. A CKNOWLEDGEMENTS he authors want to thank the School’s Central Library “Gian Paolo Dore” and the Engineering and Architecture’s Library “Giovanni Michelucci” for providing some of the books, theses and articles that were used and cited in the manuscript. The research topic is one of the subjects of the Center of Study and Research for the Identification of Materials and Structures (CIMEST)-”M. Capurso” of the University of Bologna (Italy). R EFERENCES [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. T