Accurate inter-laminar recovery for plates and doubly-curved shells with variable radii of curvature using layer-wise theories

Composite Structures

Volumn 124, Issue , 2015, Pages 368-393

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

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Doubly curved shells and panels; Generalized differential quadrature method; Higher order shear deformation theory; Laminated composites; Layer wise approach

Indexed keywords

DIFFERENTIATION (CALCULUS); ELASTICITY; LAMINATING; SHEAR DEFORMATION; STATIC ANALYSIS; STRUCTURAL DESIGN;

CARRERA UNIFIED FORMULATIONS; DOUBLY CURVED LAMINATED SHELL; DOUBLY CURVED SHELLS; GENERALIZED DIFFERENTIAL QUADRATURE METHODS; HIGHER ORDER SHEAR DEFORMATION THEORY; HIGHER-ORDER FORMULATIONS; LAYER-WISE; NUMERICAL APPLICATIONS;

LAMINATED COMPOSITES;

EID: 84922351879     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2014.12.062     Document Type: Article

References (157)

1. Love A.E.H. A treatise on the mathematical theory of elasticity 1944, Dover.
2. Sokolnikoff I.S. Tensor analysis theory and applications 1951, John Wiley & Sons.
3. Sokolnikoff I.S. Mathematical theory of elasticity 1956, McGraw-Hill.
4. Saada A.S. Elasticity, theory and applications 1974, Pergamon Press.
5. Lekhnitskii S.G. Theory of elasticity of an anisotropic body 1981, Mir Publishers.
6. Mase G.T., Mase G.E. Continuum mechanics for engineers 1999, CRC Press.
7. Sanders JL. An improved first approximation theory of thin shells. NASA-TR-R24; 1959.
8. Timoshenko S., Woinowsky-Krieger S. Theory of plates and shells 1959, McGraw-Hill.
9. Flügge W. Stresses in shells 1960, Springer-Verlag.
10. Gol'denveizer A.L. Theory of elastic thin shells 1961, Pergamon Press.
11. Novozhilov V.V. Thin shell theory 1964, P. Noordhoff.
12. Ambartusumyan SA. Theory of anisotropic shells. NASA-TT-F-118; 1964.
13. Vlasov VZ. General theory of shells and its application in engineering. NASA-TT-F-99; 1964.
14. Kraus H. Thin elastic shells 1967, John Wiley & Sons.
15. Lekhnitskii S.G., Tsai S.W., Cheron T. Anisotropic plates 1968, Gordon and Breach, Science Publishers.
16. Leissa AW. Vibration of plates. NASA-SP-160; 1969.
17. Dixon SC, Hudson ML. Flutter, vibration and buckling of truncated orthotropic conical shells with generalized elastic edge restraint. NASA-TN-D-5759; 1970.
18. Leissa AW. Vibration of shells. NASA-SP-288; 1973.
19. Szilard R. Theory and analysis of plates 1974, Prentice-Hall.
20. Donnel L.H. Beams, plates and shells 1976, McGraw-Hill.
21. Calladine C.R. Theory of shell structures 1983, Cambridge University Press.
22. Gould P.L. Finite element analysis of shells of revolution 1985, Pitman Publishing.
23. Niordson F.I. Shell theory 1985, North-Holland.
24. Markuš Š. The mechanics of vibrations of cylindrical shells 1988, Elsevier.
25. Tzou H.S. Piezoelectric shells 1993, Kluwer Academic Publishers.
26. Rogacheva N.N. The theory of piezoelectric shells and plates 1994, CRC Press.
27. Kaw A.K. Mechanics of composite materials 1997, CRC Press.
28. Libai A., Simmonds J.G. The nonlinear theory of elastic shells 1998, Cambridge University Press.
29. Liew K.M., Wang C.M., Xiang Y., Kitipornchai S. Vibration of Mindlin plates 1998, Elsevier.
30. Gould P.L. Analysis of shells and plates 1999, Prentice-Hall.
31. Jones R.M. Mechanics of composite materials 1999, Taylor & Francis.
32. Reddy J.N. Theory and analysis of elastic plates 1999, Taylor & Francis.
33. Vorovich I.I. Nonlinear theory of shallow shells 1999, Springer.
34. Ciarlet P. Theory of shells 2000, Elsevier.
35. Wang C.M., Reddy J.N., Lee K.H. Shear deformable beams and plates 2000, Elsevier.
36. Ventsel E., Krauthammer T. Thin plates and shells 2001, Marcel Dekker.
37. Reddy J.N. Energy principles and variational methods in applied mechanics 2002, John Wiley & Sons.
38. Reddy J.N. Mechanics of laminated composite plates and shells 2003, CRC Press.
39. Wempner G., Talaslidis D. Mechanics of solids and shells 2003, CRC Press.
40. Qatu M.S. Vibration of laminated shells and plates 2004, Elsevier.
41. Soedel W. Vibrations of shells and plates 2004, Marcel Dekker.
42. Vinson J.R., Sierakowski R.L. The behavior of structures composed of composite materials 2004, Kluwer Academic Publishers.
43. Li H., Lam K.Y., Ng T.Y. Rotating shell dynamics 2005, Elsevier.
44. Mindlin R.D. An introduction to the mathematical theory of vibrations of elastic plates 2006, World Scientific Publishing.
45. Awrejcewicz J., Krysko V.A., Krysko A.V. Thermo-dynamics of plates and shells 2007, Springer.
46. Amabili M. Nonlinear vibrations and stability of shells and plates 2008, Cambridge University Press.
47. Chakraverty S. Vibration of plates 2009, CRC Press.
48. Chapelle D., Bathe K.J. The finite element analysis of shells - fundamentals 2011, Springer.
49. Leissa A.W., Qatu M.S. Vibrations of continuous systems 2011, McGraw-Hill.
50. Calvi G.M., Nascimbene R. Progettere i Gusci 2011, IUSS Press.
51. Tornabene F. Meccanica delle Strutture a Guscio in Materiale Composito. Il Metodo Generalizzato di Quadratura Differenziale 2012, Esculapio.
52. Tornabene F., Fantuzzi N. Mechanics of laminated composite doubly-curved shell structures. The generalized differential quadrature method and the strong formulation finite element method 2014, Esculapio. 10.14634/978-88-748-8687-6.
53. Carrera E., Brischetto S., Nali P. Plates and shells for smart structures 2011, John Wiley & Sons.
54. Carrera E. Multilayered shell theories accounting for layerwise mixed description. Part 1: Governing equations. AIAA J 1999, 37:1107-1116.
55. Carrera E. Multilayered shell theories accounting for layerwise mixed description. Part 2: Numerical evaluations. AIAA J 1999, 37:1117-1124.
56. Carrera E. Historical review of zig-zag theories for multilayered plates and shells. Appl Mech Rev 2003, 56:287-308.
57. Liew K.M., Zhao X., Ferreira A.J.M. A review of meshless methods for laminated and functionally graded plates and shells. Compos Struct 2011, 93:2031-2041.
58. Batra R.C., Xiao J. Analysis of post-buckling and delamination in laminated composite St. Venant-Kirchhoff beams using CZM and layer-wise TSNDT. Compos Struct 2013, 105:369-384.
59. Batra R.C., Xiao J. Finite deformations of curved laminated St. Venant-Kirchhoff beam using layer-wise third order shear and normal deformable beam theory (TSNDT). Compos Struct 2013, 97:147-164.
60. Boscolo M. Analytical solution for free vibration analysis of composite plates with layer-wise displacement assumptions. Compos Struct 2013, 100:493-510.
61. Hadjiloizi D.A., Kalamkarov A.L., Metti Ch., Georgiades A.V. Analysis of smart piezo-magneto-thermo-elastic composite and reinforced plates. Part I: Model development. Curved Layer Struct 2014, 1:11-31.
62. Hadjiloizi D.A., Kalamkarov A.L., Metti Ch., Georgiades A.V. Analysis of smart piezo-magneto-thermo-elastic composite and reinforced plates. Part II: Applications. Curved Layer Struct 2014, 1:32-58.
63. Mashat D.S., Carrera E., Zenkour A.M., Al Khateeb S.A. Use of axiomatic/asymptotic approach to evaluate various refined theories for sandwich shells. Compos Struct 2014, 109:139-149.
64. Naumenko K., Eremeyev V.A. A layer-wise theory for laminated glass and photovoltaic panels. Compos Struct 2014, 112:283-291.
65. Qatu M.S., Sullivan R.W., Wang W. Recent research advances on the dynamic analysis of composite shells: 2000-2009. Compos Struct 2011, 93:14-31.
66. Asadi E., Wang W., Qatu M.S. Static and vibration analyses of thick deep laminated cylindrical shells using 3D and various shear deformation theories. Compos Struct 2012, 94:494-500.
67. Liu B., Xing Y.F., Qatu M.S., Ferreira A.J.M. Exact characteristic equations for free vibrations of thin orthotropic circular cylindrical shells. Compos Struct 2012, 94:484-493.
68. Efraim E., Eisenberger M. Exact vibration frequencies of segmented axisymmetric shells. Thin Walled Struct 2006, 44:281-289.
69. Efraim E., Eisenberger M. Dynamic stiffness vibration analysis of thick spherical shell segments with variable thickness. J Mech Mater Struct 2010, 5:821-835.
70. Brischetto S., Torre R. Exact 3D solutions and finite element 2D models for free vibration analysis of plates and cylinders. Curved Layer Struct 2014, 1:59-92.
71. Fazzolari F.A., Carrera E. Advanced variable kinematics Ritz and Galerkin formulations for accurate buckling and vibration analysis of anisotropic laminated composite plates. Compos Struct 2011, 94:50-67.
72. Fazzolari F.A., Boscolo M., Banerjee J.R. An exact dynamic stiffness element using a higher order shear deformation theory for free vibration analysis of composite plate assemblies. Compos Struct 2013, 96:262-278.
73. Fazzolari F.A., Banerjee J.R. Axiomatic/asymptotic PVD/RMVT-based shell theories for free vibrations of anisotropic shells using an advanced Ritz formulation and accurate curvature descriptions. Compos Struct 2014, 108:91-110.
74. Jin G., Ye T., Jia X., Gao S. A general Fourier solution for the vibration analysis of composite laminated structure elements of revolution with general elastic restraints. Compos Struct 2014, 109(1):150-168.
75. Jin G., Ye T., Ma X., Chen Y., Su Z., Xie X. A unified approach for the vibration analysis of moderately thick composite laminated cylindrical shells with arbitrary boundary conditions. Int J Mech Sci 2013, 75:357-376.
76. Qu Y., Long X., Wu S., Meng G. A unified formulation for vibration analysis of composite laminated shells of revolution including shear deformation and rotary inertia. Compos Struct 2013, 98:169-191.
77. Natarajan S., Ferreira A.J.M., Nguyen-Xuan H. Analysis of cross-ply laminated plates using isogeometric analysis and unified formulation. Curved Layer Struct 2014, 1:1-10.
78. Sofiyev A.H., Kuruoglu N. Buckling and vibration of shear deformable functionally graded orthotropic cylindrical shells under external pressures. Thin Walled Struct 2014, 78:121-130.
79. Mohazzab A.H., Dozio L. Prediction of natural frequencies of laminated curved panels using refined 2-D theories in the spectral collocation method. Curved Layer Struct 2015, 2:1-14.
80. Tornabene F. Free vibration analysis of functionally graded conical, cylindrical and annular shell structures with a four-parameter power-law distribution. Comput Methods Appl Mech Eng 2009, 198:2911-2935.
81. Tornabene F., Viola E. Free vibrations of four-parameter functionally graded parabolic panels and shell of revolution. Eur J Mech A-Solid 2009, 28:991-1013.
82. Tornabene F., Viola E. Free vibration analysis of functionally graded panels and shells of revolution. Meccanica 2009, 44:255-281.
83. Tornabene F., Viola E., Inman D.J. 2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical and annular shell structures. J Sound Vib 2009, 328:259-290.
84. Viola E., Tornabene F. Free vibrations of three parameter functionally graded parabolic panels of revolution. Mech Res Commun 2009, 36:587-594.
85. Qu Y., Meng G. Dynamic analysis of composite laminated and sandwich hollow bodies of revolution based on three-dimensional elasticity theory. Compos Struct 2014, 112:378-396.
86. Sofiyev A.H. The influence of non-homogeneity on the frequency-amplitude characteristics of laminated orthotropic truncated conical shell. Compos Struct 2014, 107:334-345.
87. Su Z., Jin G., Shi S., Ye T. A unified accurate solution for vibration analysis of arbitrary functionally graded spherical shell segments with general end restraints. Compos Struct 2014, 111:271-284.
88. Groh R.M.J., Weaver P.M. Buckling analysis of variable angle tow, variable thickness panels with transverse shear effects. Compos Struct 2014, 107:482-493.
89. Ye T., Jin G., Chen Y., Ma X., Su Z. Free vibration analysis of laminated composite shallow shells with general elastic boundaries. Compos Struct 2013, 106:470-490.
90. Jahromi H.N., Aghdam M.M., Fallah A. Free vibration analysis of Mindlin plates partially resting on Pasternak foundation. Int J Mech Sci 2013, 75:1-7.
91. Qu Y., Long X., Li H., Meng G. A variational formulation for dynamic analysis of composite laminated beams based on a general higher-order shear deformation theory. Compos Struct 2013, 102:175-192.
92. Qu Y., Long X., Yuan G., Meng G. A unified formulation for vibration analysis of functionally graded shells of revolution with arbitrary boundary conditions. Compos Part B Eng 2013, 50:381-402.
93. Li Z.-M., Qiao P. On an exact bending curvature model for nonlinear free vibration analysis shear deformable anisotropic laminated beams. Compos Struct 2013, 108:243-258.
94. Fazzolari F.A. A refined dynamic stiffness element for free vibration analysis of cross-ply laminated composite cylindrical and spherical shallow shells. Compos Part B Eng 2014, 62:143-158.
95. Sofiyev A.H. The combined influences of heterogeneity and elastic foundations on the nonlinear vibration of orthotropic truncated conical shells. Compos Part B Eng 2014, 61:324-339.
96. Duc N.D., Quan T.Q. Transient responses of functionally graded double curved shallow shells with temperature-dependent material properties in thermal environment. Eur J Mech A/Solids 2014, 47:101-123.
97. Phung-Van P., Nguyen-Thoi T., Dang-Trung H., Nguyen-Minh N. A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) using layerwise theory based on the C0-HSDT for analyses of composite plates. Compos Struct 2014, 111:553-565.
98. Finlayson B.A., Scriven L.E. The method of weighted residual: a review. ASME Appl Mech Rev 1966, 19:735-748.
99. Bert C., Malik M. Differential quadrature method in computational mechanics. ASME Appl Mech Rev 1996, 49:1-27.
100. Shu C. Differential quadrature and its application in engineering 2000, Springer.
101. Zong Z., Zhang Y.Y. Advanced differential quadrature methods 2009, CRC Press.
102. Tornabene F., Fantuzzi N., Ubertini F., Viola E. Strong formulation finite element method based on differential quadrature: a survey. ASME Appl Mech Rev 2015, 67:020801-1-020801-55.
103. Shu C., Du H. Free vibration analysis of composites cylindrical shells by DQM. Compos Part B Eng 1997, 28B:267-274.
104. Artioli E., Gould P., Viola E. A differential quadrature method solution for shear-deformable shells of revolution. Eng Struct 2005, 27:1879-1892.
105. Viola E., Tornabene F. Vibration analysis of damaged circular arches with varying cross-section. Struct Integr Durab (SID-SDHM) 2005, 1:155-169.
106. Viola E., Tornabene F. Vibration analysis of conical shell structures using GDQ method. Far East J Appl Math 2006, 25:23-39.
107. Tornabene F. Modellazione e Soluzione di Strutture a Guscio in Materiale Anisotropo [Ph.D. thesis]. University of Bologna; 2007.
108. Tornabene F., Viola E. Vibration analysis of spherical structural elements using the GDQ method. Comput Math Appl 2007, 53:1538-1560.
109. Marzani A., Tornabene F., Viola E. Nonconservative stability problems via generalized differential quadrature method. J Sound Vib 2008, 315:176-196.
110. Tornabene F., Viola E. 2-D solution for free vibrations of parabolic shells using generalized differential quadrature method. Eur J Mech A-Solid 2008, 27:1001-1025.
111. Alibeigloo A., Modoliat R. Static analysis of cross-ply laminated plates with integrated surface piezoelectric layers using differential quadrature. Compos Struct 2009, 88:342-353.
112. Alibeigloo A., Nouri V. Static analysis of functionally graded cylindrical shell with piezoelectric layers using differential quadrature method. Compos Struct 2010, 92:1775-1785.
113. Andakhshideh A., Maleki S., Aghdam M.M. Non-linear bending analysis of laminated sector plates using generalized differential quadrature. Compos Struct 2010, 92:2258-2264.
114. Sepahi O., Forouzan M.R., Malekzadeh P. Large deflection analysis of thermo-mechanical loaded annular FGM plates on nonlinear elastic foundation via DQM. Compos Struct 2010, 92:2369-2378.
115. Tornabene F., Marzani A., Viola E., Elishakoff I. Critical flow speeds of pipes conveying fluid by the generalized differential quadrature method. Adv Theor Appl Mech 2010, 3:121-138.
116. Yas M.H., Sobhani Aragh B. Three-dimensional analysis for thermoelastic response of functionally graded fiber reinforced cylindrical panel. Compos Struct 2010, 92:2391-2399.
117. Tornabene F. 2-D GDQ solution for free vibrations of anisotropic doubly-curved shells and panels of revolution. Compos Struct 2011, 93:1854-1876.
118. Tornabene F. Free vibrations of laminated composite doubly-curved shells and panels of revolution via the GDQ method. Comput Methods Appl Mech Eng 2011, 200:931-952.
119. 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 2011, 94:186-206.
120. Tornabene F., Liverani A., Caligiana G. FGM and laminated doubly-curved shells and panels of revolution with a free-form meridian: a 2-D GDQ solution for free vibrations. Int J Mech Sci 2011, 53:446-470.
121. Zhao X., Liew K.M. Free vibration analysis of functionally graded conical shell panels by a meshless method. Compos Struct 2011, 93:649-664.
122. 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 2012, 43:1847-1872.
123. Tornabene F., Liverani A., Caligiana G. Static analysis of laminated composite curved shells and panels of revolution with a posteriori shear and normal stress recovery using generalized differential quadrature method. Int J Mech Sci 2012, 61:71-87.
124. 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 2012, 331:4848-4869.
125. Viola E., Rossetti L., Fantuzzi N. Numerical investigation of functionally graded cylindrical shells and panels using the generalized unconstrained third order theory coupled with the stress recovery. Compos Struct 2012, 3736-3758.
126. Ferreira A.J.M., Viola E., Tornabene F., Fantuzzi N., Zenkour A.M. Analysis of sandwich plates by generalized differential quadrature method. Math Prob Eng 2013, 2013:1-22. [Article ID 964367].
127. 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 2013, 3:1-25.
128. Tornabene F., Ceruti A. Mixed static and dynamic optimization of four-parameter functionally graded completely doubly-curved and degenerate shells and panels using GDQ method. Math Prob Eng 2013, 2013:1-33. [Article ID 867079].
129. 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 2013, 55:642-659.
130. 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 2013, 93:635-688.
131. Tornabene F., Viola E. Static analysis of functionally graded doubly-curved shells and panels of revolution. Meccanica 2013, 48:901-930.
132. 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 2013, 104:94-117.
133. 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 2013, 95:639-666.
134. 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 2013, 101:59-93.
135. Ferreira A.J.M., Carrera E., Cinefra M., Viola E., Tornabene F., Fantuzzi N., et al. Analysis of thick isotropic and cross-ply laminated plates by generalized differential quadrature method and a unified formulation. Compos Part B Eng 2014, 58:544-552.
136. 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 2014, 107:675-697.
137. 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 2014, 57:269-296.
138. Viola E., Rossetti L., Fantuzzi N., Tornabene F. Static analysis of functionally graded conical shells and panels using the generalized unconstrained third order theory coupled with the stress recovery. Compos Struct 2014, 112:44-65.
139. Tornabene F., Fantuzzi N., Bacciocchi M. The local GDQ method applied to general higher-order theories of doubly-curved laminated composite shells and panels: the free vibration analysis. Compos Struct 2014, 116:637-660.
140. Tornabene F., Fantuzzi N., Bacciocchi M. Free vibrations of free-form doubly-curved shells made of functionally graded materials using higher-order equivalent single layer theories. Compos Part B Eng 2014, 67:490-509.
141. Tornabene F., Fantuzzi N., Viola E., Batra R.C. Stress and strain recovery for functionally graded free-form and doubly-curved sandwich shells using higher-order equivalent single layer theory. Compos Struct 2014, 119:67-89.
142. Tornabene F, Fantuzzi N, Viola E. Inter-laminar stress recovery procedure for doubly-curved, singly-curved, revolution shells with variable radii of curvature and plates using generalized higher-order theories and the local GDQ method. Mech Adv Mater Struct; in press.
143. Tornabene F. General higher order layer-wise theory for free vibrations of doubly-curved laminated composite shells and panels. Mech Adv Mater Struct; in press.
144. Viola E., Dilena M., Tornabene F. Analytical and numerical results for vibration analysis of multi-stepped and multi-damaged circular arches. J Sound Vib 2007, 299:143-163.
145. Fantuzzi N. Generalized differential quadrature finite element method applied to advanced structural mechanics [Ph.D. thesis]. University of Bologna; 2013.
146. Viola E., Tornabene F., Fantuzzi N. Generalized differential quadrature finite element method for cracked composite structures of arbitrary shape. Compos Struct 2013, 106:815-834.
147. Viola E., Tornabene F., Ferretti E., Fantuzzi N. Soft core plane state structures under static loads using GDQFEM and cell method. CMES 2013, 94:301-329.
148. Viola E., Tornabene F., Ferretti E., Fantuzzi N. GDQFEM numerical simulations of continuous media with cracks and discontinuities. CMES 2013, 94:331-368.
149. Viola E., Tornabene F., Ferretti E., Fantuzzi N. On static analysis of plane state structures via GDQFEM and cell method. CMES 2013, 94:419-456.
150. Fantuzzi N., Tornabene F. Strong formulation finite element method for arbitrarily shaped laminated plates - I. Theoretical analysis. Adv Aircraft Space Sci 2014, 1:124-142.
151. Fantuzzi N., Tornabene F. Strong formulation finite element method for arbitrarily shaped laminated plates - II. Numerical analysis. Adv Aircraft Space Sci 2014, 1:143-173.
152. Fantuzzi N., Tornabene F., Viola E. Generalized differential quadrature finite element method for vibration analysis of arbitrarily shaped membranes. Int J Mech Sci 2014, 79:216-251.
153. Tornabene F., Fantuzzi N., Bacciocchi M. The strong formulation finite element method: stability and accuracy. Fract Struct Integr 2014, 29:251-265.
154. Fantuzzi N., Tornabene F., Viola E., Ferreira A.J.M. A strong formulation finite element method (SFEM) based on RBF and GDQ techniques for the static and dynamic analyses of laminated plates of arbitrary shape. Meccanica 2014, 49:2503-2542.
155. Fantuzzi N, Tornabene F, Viola E. Four-parameter functionally graded cracked plates of arbitrary shape: a GDQFEM solution for free vibrations. Mech Adv Mater Struct; in press. http://dx.doi.org/10.1080/15376494.2014.933992. http://dx.doi.org/10.1080/15376494.2014.933992.
156. Fantuzzi N. New insights into the strong formulation finite element method for solving elastostatic and elastodynamic problems. Curved Layer Struct 2014, 1:93-126.
157. Viola E, Tornabene F, Fantuzzi N. DiQuMASPAB software. DICAM Department, Alma Mater Studiorum, University of Bologna; 2013. http://software.dicam.unibo.it/diqumaspab-project.