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Acta Mechanica
Erschienen in: Acta Mechanica 2/2020

08.01.2020 | Review and Perspective in Mechanics

Methods and guidelines for the choice of shell theories

verfasst von: Marco Petrolo, Erasmo Carrera

Erschienen in: Acta Mechanica | Ausgabe 2/2020

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Abstract

This paper provides an overview of the modeling approaches adopted over the years to develop shell theories for composite structures. Furthermore, it presents a method to assess any structural theory concerning the accuracy and computational efficiency and trigger informed decisions on the structural theory to use for a given problem. This method exploits the synergies between the Carrera unified formulation and the axiomatic/asymptotic method. Typical outcomes are the best theory diagrams or the estimation of accuracy of a theory as compared to quasi-3D solutions. The proposed framework can be useful to provide guidelines on the construction of structural theories and can serve as a trainer for the deep learning of neural networks.
Nächster Artikel Effectiveness of the segment method in absolute and joint coordinates when modelling risers
Literatur
1.
Cauchy, A.L.: Sur l’équilibre et le mouvement d’une plaque solide. Exerc. Mat. 3, 328–355 (1828)
2.
Poisson, S.D.: Memoire sur l’équilibre et le mouvement des corps elastique. Mem. R. Acad. Sci. Inst. Fr. 8, 357–570 (1829)
3.
Love, A.E.H.: The Mathematical Theory of Elasticity, 4th edn. Cambridge University Press, Cambridge (1927)MATH
4.
Kirchhoff, G.: Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. Journal für reine und angewandte Mathematik 40, 51–88 (1850)MathSciNet
5.
Reissner, E.: The effect of transverse shear deformation on the bending of elastic plates. J. Appl. Mech. 12, 69–76 (1945)MathSciNetMATH
6.
Mindlin, R.D.: Influence of rotatory inertia and shear in flexural motions of isotropic elastic plates. J. Appl. Mech. 18, 1031–1036 (1951)MATH
7.
Ambartsumian, S.A.: Nontraditional theories of shells and plates. Appl. Mech. Rev. 55(5), R35–R44 (2002)
8.
Carrera, E.: Theories and finite elements for multilayered, anisotropic, composite plates and shells. Arch. Comput. Methods Eng. 9(2), 87–140 (2002)MathSciNetMATH
9.
Lekhnitskii, S.G.: Strength calculation of composite beams. Vestnik inzhen i tekhnikov 9 (1935)
10.
Hildebrand, F.B., Reissner, E., Thomas, G.B.: Notes on the foundations of the theory of small displacements of orthotropic shells. NACA TN-1833 (1949)
11.
Koiter, W.T.: A consistent first approximation in the general theory of thin elastic shells. In: Proceedings of the Symposium on the Theory of Thin Elastic Shells, August 1959, North-Holland, Amsterdam, pp. 12–23 (1959)
12.
Ambartsumian, S.A.: Contributions to the theory of anisotropic layered shells. Appl. Mech. Rev. 15, 245–249 (1962)
13.
Pagano, N.J.: Exact solutions for composite laminates in cylindrical bending. J. Compos. Mater. 3(3), 398–411 (1969)
14.
Leissa, A.W.: Vibration of shells. NASA-SP-288, LC-77-186367 (1973)
15.
Grigolyuk, E.I., Kulikov, G.M.: General directions of the development of theory of shells. Mech. Compos. Mater. 24, 231–241 (1988)
16.
Kapania, K.: A review on the analysis of laminated shells. ASME J. Press. Vessel Technol. 111(2), 88–96 (1989)
17.
Noor, A.K., Burton, W.S.: Assessment of computational models for multilayered composite shells. Appl. Mech. Rev. 43(4), 67–97 (1989)
18.
Touratier, M.: A generalization of shear deformation theories for axisymmetric multilayered shells. Int. J. Solids Struct. 29(11), 1379–1399 (1992)MATH
19.
Vasil’ev, V.V., Lur’e, S.A.: On refined theories of beams, plates, and shells. J. Compos. Mater. 26(4), 546–557 (1992)
20.
Reddy, J.N., Robbins, D.H.: Theories and computational models for composite laminates. Appl. Mech. Rev. 47(6), 147–165 (1994)
21.
Washizu, K.: Variational Methods in Elasticity and Plasticity. Pergamon, Oxford (1968)MATH
22.
Carrera, E., Petrolo, M.: Guidelines and recommendation to construct theories for metallic and composite plates. AIAA J. 48(12), 2852–2866 (2010)
23.
Carrera, E., Petrolo, M.: On the effectiveness of higher-order terms in refined beam theories. J. Appl. Mech. 78, 021013 (2011)
24.
Gol’denweizer, A.L.: Theory of Thin Elastic Shells. International Series of Monographs in Aeronautics and Astronautics. Pergamon Press, New York (1961)MATH
25.
Cicala, P.: Systematic Approximation Approach to Linear Shell Theory. Levrotto e Bella, Torino (1965)
26.
Reddy, J.N.: Exact solutions of moderately thick laminated shells. Journal of Eng. Mech. 110(5), 794–809 (1984)
27.
Ren, J.G.: Exact solutions for laminated cylindrical shells in cylindrical bending. Compos. Sci. Technol. 29(3), 169–187 (1987)
28.
Reddy, J.N., Liu, C.F.: A higher-order shear deformation theory of laminated elastic shells. Int. J. Eng. Sci. 23(3), 319–330 (1985)MATH
29.
Wu, C.P., Liu, C.C.: Stress and displacement of thick doubly curved laminated shells. J. Eng. Mech. 120(7), 1403–1428 (1994)
30.
Leissa, A.W., Chang, J.D.: Elastic deformation of thick, laminated composite shells. Compos. Struct. 35(2), 153–170 (1996)
31.
Shu, X.P.: A refined theory of laminated shells with higher-order transverse shear deformation. Int. J. Solids Struct. 34(6), 673–683 (1997)MATH
32.
Wang, X., Wang, C., Yu, Z.Y.: An analytic method for interlaminar stress in a laminated cylindrical shell. Mech. Adv. Mater. Struct. 9(2), 119–131 (2002)
33.
Oktem, A.S., Chaudhuri, R.A.: Fourier analysis of thick cross-ply Levy type clamped doubly-curved panels. Compos. Struct. 80(4), 489–503 (2007)
34.
Noor, A.K., Rarig, P.L.: Three-dimensional solutions of laminated cylinders. Comput. Methods Appl. Mech. Eng. 3(3), 319–334 (1974)MATH
35.
Varadan, T.K., Bhaskar, K.: Bending of laminated orthotropic cylindrical shells—an elasticity approach. Compos. Struct. 17, 141–156 (1991)
36.
Fan, J., Zhang, J.: Analytical solutions for thick, doubly curved, laminated shells. J. Eng. Mech. 118(7), 1338–1356 (1992)
37.
Bhimaraddi, A., Chandrashekhara, K.: Three-dimensional elasticity solution for static response of simply supported orthotropic cylindrical shells. Compos. Struct. 20(4), 227–235 (1992)
38.
Wu, C.P., Lo, J.Y.: Three-dimensional elasticity solutions of laminated annular spherical shells. J. Eng. Mech. 126(8), 882–885 (2000)
39.
Kumari, P., Kar, S.: Static behavior of arbitrarily supported composite laminated cylindrical shell panels: an analytical 3D elasticity approach. Compos. Struct. 207, 949–965 (2019)
40.
Khare, R.K., Rode, V., Garg, A.K., John, S.P.: Higher-order closed-form solutions for thick laminated sandwich shells. J. Sandw. Struct. Mater. 7(4), 335–358 (2005)
41.
Garg, A.K., Khare, R.K., Kant, T.: Higher-order closed-form solutions for free vibration of laminated composite and sandwich shells. J. Sandw. Struct. Mater. 8(3), 205–235 (2006)
42.
Biglari, H., Jafari, A.A.: High-order free vibrations of doubly-curved sandwich panels with flexible core based on a refined three-layered theory. Compos. Struct. 92(11), 2685–2694 (2010)
43.
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. 94(2), 494–500 (2012)
44.
Hosseini-Hashemi, S., Atashipour, S.R., Fadaee, M., Girhammar, U.A.: An exact closed-form procedure for free vibration analysis of laminated spherical shell panels based on Sanders theory. Arch. Appl. Mech. 82(7), 985–1002 (2012)MATH
45.
Mantari, J.L., Guedes Soares, C.: Analysis of isotropic and multilayered plates and shells by using a generalized higher-order shear deformation theory. Compos. Struct. 94(8), 2640–2656 (2012)
46.
Hwu, C., Hsu, H.W., Lin, Y.H.: Free vibration of composite sandwich plates and cylindrical shells. Compos. Struct. 171, 528–537 (2017)
47.
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. 75, 357–376 (2013)
48.
Jin, G., Ye, T., Chen, Y., Su, Z., Yan, Y.: An exact solution for the free vibration analysis of laminated composite cylindrical shells with general elastic boundary conditions. Compos. Struct. 106, 114–127 (2013)
49.
Ye, T., Jin, G., Chen, Y., Ma, X., Su, Z.: Free vibration analysis of laminated composite shallow shells with general elastic boundaries. Compos. Struct. 106, 470–490 (2013)
50.
Qu, Y., Meng, G.: Dynamic analysis of composite laminated and sandwich hollow bodies of revolution based on three-dimensional elasticity theory. Compos. Struct. 112, 378–396 (2014)
51.
Jin, G., Ye, T., Shi, S.: Three-dimensional vibration analysis of isotropic and orthotropic open shells and plates with arbitrary boundary conditions. Shock Vib. 2015, 896204 (2015)
52.
Li, H., Pang, F., Wang, X., Du, Y., Chen, H.: Free vibration analysis for composite laminated doubly-curved shells of revolution by a semi analytical method. Compos. Struct. 201, 86–111 (2018)
53.
Zhong, R., Tang, J., Wang, A., Shuai, C., Wang, Q.: An exact solution for free vibration of cross-ply laminated composite cylindrical shells with elastic restraint ends. Comput. Math. Appl. 77(3), 641–661 (2019)MathSciNet
54.
Poore, A.L., Barut, A., Madenci, E.: Free vibration of laminated cylindrical shells with a circular cutout. J. Sound Vib. 312(1), 55–73 (2008)
55.
Shakouri, M., Kouchakzadeh, M.A.: Analytical solution for vibration of generally laminated conical and cylindrical shells. Int. J. Mech. Sci. 131–132, 414–425 (2017)
56.
Castro, S.G.P., Donadon, M.V.: Assembly of semi-analytical models to address linear buckling and vibration of stiffened composite panels with debonding defect. Compos. Struct. 160, 232–247 (2017)
57.
Kargarnovin, M.H., Hashemi, M.: Free vibration analysis of multilayered composite cylinder consisting fibers with variable volume fraction. Compos. Struct. 94(3), 931–944 (2012)
58.
Lopatin, A.V., Morozov, E.V.: Fundamental frequency of the laminated composite cylindrical shell with clamped edges. Int. J. Mech. Sci. 92, 35–43 (2015)
59.
Nasihatgozar, M., Khalili, S.M.R., Fard, K.M.: General equations for free vibrations of thick doubly curved sandwich panels with compressible and incompressible core using higher order shear deformation theory. Steel Compos. Struct. 24(2), 151–176 (2017)
60.
Wu, C.P., Chiu, K.H.: RMVT-based meshless collocation and element-free Galerkin methods for the quasi-3D free vibration analysis of multilayered composite and FGM plates. Compos. Struct. 93(5), 1433–1448 (2011)
61.
Sofiyev, A.H.: Application of the first order shear deformation theory to the solution of free vibration problem for laminated conical shells. Compos. Struct. 188, 340–346 (2018)
62.
Singh, A.V., Kumar, V.: Vibration of laminated shallow shells on quadrangular boundary. J. Aerosp. Eng. 9(2), 52–57 (1996)
63.
Singh, A.V., Shen, L.: Free vibration of open circular cylindrical composite shells with point supports. J. Aerosp. Eng. 18(2), 120–128 (2005)
64.
Zhao, X., Liew, K.M., Ng, T.Y.: Vibration analysis of laminated composite cylindrical panels via a meshfree approach. Int. J. Solids Struct. 40(1), 161–180 (2003)MATH
65.
Ye, T., Jin, G., Su, Z., Jia, X.: A unified Chebyshev–Ritz formulation for vibration analysis of composite laminated deep open shells with arbitrary boundary conditions. Arch. Appl. Mech. 84, 441–471 (2017)MATH
66.
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. 109, 150–168 (2014)
67.
Song, X., Han, Q., Zhai, J.: Vibration analyses of symmetrically laminated composite cylindrical shells with arbitrary boundaries conditions via Rayleigh–Ritz method. Compos. Struct. 134, 820–830 (2015)
68.
69.
Jin, G., Su, Z., Ye, T., Jia, X.: Three-dimensional vibration analysis of isotropic and orthotropic conical shells with elastic boundary restraints. Int. J. Mech. Sci. 89, 207–221 (2014)
70.
Yang, C., Jin, G., Zhang, Y., Liu, Z.: A unified three-dimensional method for vibration analysis of the frequency-dependent sandwich shallow shells with general boundary conditions. Appl. Math. Model. 66, 59–76 (2019)MathSciNet
71.
Singh, A.V.: Free vibration analysis of deep doubly curved sandwich panels. Comput. Struct. 73(1), 385–394 (1999)MATH
72.
Hemmatnezhad, M., Rahimi, G.H., Tajik, M., Pellicano, F.: Experimental, numerical and analytical investigation of free vibrational behavior of GFRP-stiffened composite cylindrical shells. Compos. Struct. 120, 509–518 (2015)
73.
Xie, X., Zheng, H., Jin, G.: Integrated orthogonal polynomials based spectral collocation method for vibration analysis of coupled laminated shell structures. Int. J. Mech. Sci. 98, 132–143 (2015)
74.
Qu, Y., Hua, H., Meng, G.: A domain decomposition approach for vibration analysis of isotropic and composite cylindrical shells with arbitrary boundaries. Compos. Struct. 95, 307–321 (2013)
75.
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. 98, 169–191 (2013)
76.
Guo, J., Shi, D., Wang, Q., Tang, J., Shuai, C.: Dynamic analysis of laminated doubly-curved shells with general boundary conditions by means of a domain decomposition method. Int. J. Mech. Sci. 138–139, 159–186 (2018)
77.
Alibeigloo, A.: Static and vibration analysis of axi-symmetric angle-ply laminated cylindrical shell using state space differential quadrature method. Int. J. Press. Vessels Pip. 86(11), 738–747 (2009)
78.
Lakshminarayana, H.V., Dwarakanath, K.: Free vibration characteristics of cylindrical shells made of composite materials. J. Sound Vib. 154(3), 431–439 (1992)MATH
79.
Zhu, J.: Free vibration analysis of multilayered composite plates and shells with the natural approach. Comput. Methods Appl. Mech. Eng. 130(1), 133–149 (1996)MathSciNetMATH
80.
Bardell, N.S., Dunsdon, J.M., Langley, R.S.: Free and forced vibration analysis of thin, laminated, cylindrically curved panels. Compos. Struct. 38(1), 453–462 (1997)
81.
Park, T., Kim, K., Han, S.: Linear static and dynamic analysis of laminated composite plates and shells using a 4-node quasi-conforming shell element. Compos. Part B Eng. 37(2), 237–248 (2005)
82.
Nguyen-Van, H., Mai-Duy, N., Tran-Cong, T.: Free vibration analysis of laminated plate/shell structures based on FSDT with a stabilized nodal-integrated quadrilateral element. J. Sound Vib. 313(1), 205–223 (2008)
83.
Nguyen-Van, H., Mai-Duy, N., Karunasena, W., Tran-Cong, T.: Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell element with in-plane rotations. Comput. Struct. 89(7), 612–625 (2011)
84.
Chakravorty, D., Bandyopadhyay, J.N., Sinha, P.K.: Finite element free vibration analysis of point supported laminated composite cylindrical shells. J. Sound Vib. 181(1), 43–52 (1995)MATH
85.
Ram, K.S.S., Babu, T.S.: Free vibration of composite spherical shell cap with and without a cutout. Comput. Struct. 80(23), 1749–1756 (2002)
86.
Han, S.C., Choi, S., Chang, S.Y.: Nine-node resultant-stress shell element for free vibration and large deflection of composite laminates. J. Aerosp. Eng. 19(2), 103–120 (2006)
87.
Jayasankar, S., Mahesh, S., Narayanan, S., Padmanabhan, Chandramouli: Dynamic analysis of layered composite shells using nine node degenerate shell elements. J. Sound Vib. 299(1), 1–11 (2007)
88.
Pinto Correia, I.F., Mota Soares, C.M., Mota Soares, C.A., Herskovits, J.: Analysis of laminated conical shell structures using higher order models. Compos. Struct. 62(3), 383–390 (2003)
89.
Khare, R.K., Kant, T., Garg, A.K.: Free vibration of composite and sandwich laminates with a higher-order facet shell element. Compos. Struct. 65(3), 405–418 (2004)
90.
Khare, R.K., Garg, A.K., Kant, T.: Free vibration of sandwich laminates with two higher-order shear deformable facet shell element models. J. Sandw. Struct. Mater. 7(3), 221–244 (2005)
91.
Kumar, A., Bhargava, P., Chakrabarti, A.: Vibration of laminated composite skew hypar shells using higher order theory. Thin Walled Struct. 63, 82–90 (2013)
92.
Thakur, S.N., Ray, C.: An accurate \(\text{ C }^0\) finite element model of moderately thick and deep laminated doubly curved shell considering cross sectional warping. Thin Walled Struct. 94, 384–393 (2015)
93.
Thakur, S.N., Ray, C., Chakraborty, S.: A new efficient higher-order shear deformation theory for a doubly curved laminated composite shell. Acta Mech. 228(1), 69–87 (2017)MathSciNetMATH
94.
Dau, F., Polit, O., Touratier, M.: An efficient \(\text{ C }^1\) finite element with continuity requirements for multilayered/sandwich shell structures. Comput. Struct. 82(23), 1889–1899 (2004)
95.
Yamamoto, T., Yamada, T., Matsui, K.: A quadrilateral shell element with degree of freedom to represent thickness–stretch. Comput. Mech. 59(4), 625–646 (2017)MathSciNetMATH
96.
Paccola, R.R., Sampaio, M.S.M., Coda, H.B.: Continuous stress distribution following transverse direction for FEM orthotropic laminated plates and shells. Appl. Math. Model. 40(15), 7382–7409 (2016)MathSciNetMATH
97.
Parisch, H.: A critical survey of the 9-node degenerated shell element with special emphasis on thin shell application and reduced integration. Computer Methods in Applied Mechanics and Engineering 20(3), 323–350 (1979)MATH
98.
Sze, K.Y., Yao, L.Q., Pian, T.H.H.: An eighteen-node hybrid-stress solid-shell element for homogenous and laminated structures. Finite Elem. Anal. Des. 38(4), 353–374 (2002)MATH
99.
Fiolka, M., Matzenmiller, A.: On the resolution of transverse stresses in solid-shells with a multi-layer formulation. Commun. Numer. Methods Eng. 23(4), 313–326 (2007)MATH
100.
Shiri, S., Naceur, H.: Analysis of thin composite structures using an efficient hex-shell finite element. J. Mech. Sci. Technol. 27(12), 3755–3763 (2013)
101.
Rah, K., Van Paepegem, W., Habraken, A.M., Degrieck, J.: A mixed solid-shell element for the analysis of laminated composites. Int. J. Numer. Methods Eng. 89(7), 805–828 (2012)MathSciNetMATH
102.
Kwon, Y.W.: Analysis of laminated and sandwich composite structures using solid-like shell elements. Appl. Compos. Mater. 20(4), 355–373 (2013)
103.
104.
Jabareen, M., Mtanes, E.: A solid-shell Cosserat point element for the analysis of geometrically linear and nonlinear laminated composite structures. Finite Elem. Anal. Des. 142, 61–80 (2018)MathSciNet
105.
Leonetti, L., Nguyen-Xuan, H.: A mixed edge-based smoothed solid-shell finite element method (MES–FEM) for laminated shell structures. Compos. Struct. 208, 168–179 (2019)
106.
Ko, Y., Lee, Y., Lee, P.S., Bathe, K.J.: Performance of the MITC3+ and MITC4+ shell elements in widely-used benchmark problems. Comput. Struct. 193, 187–206 (2017)
107.
Rama, G., Marinkovic, D., Zehn, M.: High performance 3-node shell element for linear and geometrically nonlinear analysis of composite laminates. Compos. Part B Eng. 151, 118–126 (2018)
108.
Ho-Nguyen-Tan, T., Kim, H.G.: A new strategy for finite-element analysis of shell structures using trimmed quadrilateral shell meshes: a paving and cutting algorithm and a pentagonal shell element. Int. J. Numer. Methods Eng. 114(1), 1–27 (2018)MathSciNet
109.
Wisniewski, K., Turska, E.: Improved nine-node shell element MITC9i with reduced distortion sensitivity. Comput. Mech. 62(3), 499–523 (2018)MathSciNetMATH
110.
Carrera, E., Cinefra, M., Lamberti, A., Petrolo, M.: Results on best theories for metallic and laminated shells including layer-wise models. Compos. Struct. 126, 285–298 (2015)
111.
Petrolo, M., Carrera, E.: Best theory diagrams for multilayered structures via shell finite elements. Adv. Model. Simul. Eng. Sci. 6(4), 1–23 (2019)
112.
Carrera, E., Miglioretti, F., Petrolo, M.: Computations and evaluations of higher-order theories for free vibration analysis of beams. J. Sound Vib. 331(19), 4269–4284 (2012)
113.
Carrera, E.: Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking. Arch. Comput. Methods Eng. 10(3), 216–296 (2003)MathSciNetMATH
114.
Vetyukov, Y.: Hybrid asymptotic-direct approach to the problem of finite vibrations of a curved layered strip. Acta Mech. 223(2), 371–385 (2012)MathSciNetMATH
115.
Kraus, H.: Thin elastic shells. John Wiley & Sons, Hoboken (1967)MATH
116.
Reddy, J.N.: A simple higher-order theory for laminated composite plates. J. Appl. Mech. 51(4), 745–752 (1984)MATH
117.
Endo, M.: An alternative first-order shear deformation concept and its application to beam, plate and cylindrical shell models. Compos. Struct. 146, 50–61 (2016)
118.
Wang, Q., Shao, D., Qin, B.: A simple first-order shear deformation shell theory for vibration analysis of composite laminated open cylindrical shells with general boundary conditions. Compos. Struct. 184, 211–232 (2018)
119.
Huang, N.N.: Influence of shear correction factors in the higher-order shear deformation laminated shell theory. Int. J. Solids Struct. 31, 1263–1277 (1994)MATH
120.
Thakur, S.N., Ray, C., Chakraborty, S.: Response sensitivity analysis of laminated composite shells based on higher-order shear deformation theory. Arch. Appl. Mech. 88(8), 1429–1459 (2018)
121.
Wu, C.P., Liu, C.C.: A local high-order deformable theory for thick laminated cylindrical shells. Compos. Struct. 29(1), 69–87 (1994)
122.
Shah, P.H., Batra, R.C.: Stress singularities and transverse stresses near edges of doubly curved laminated shells using TSNDT and stress recovery scheme. Eur. J. Mech. A/Solids 63, 68–83 (2017)MathSciNetMATH
123.
Shah, P.H., Batra, R.C.: Stretching and bending deformations due to normal and shear tractions of doubly curved shells using third-order shear and normal deformable theory. Mech. Adv. Mater. Struct. 25(15–16), 1276–1296 (2018)
124.
Khalili, S.M.R., Tafazoli, S., Fard, K.M.: Free vibrations of laminated composite shells with uniformly distributed attached mass using higher order shell theory including stiffness effect. J. Sound Vib. 330(26), 6355–6371 (2011)
125.
Desai, P., Kant, T.: On numerical analysis of axisymmetric thick circular cylindrical shells based on higher order shell theories by segmentation method. J. Sandw. Struct. Mater. 17(2), 130–169 (2015)
126.
Rabinovitch, O., Frostig, Y.: High-order analysis of unidirectional sandwich panels with flat and generally curved faces and a “soft” core. J. Sandw. Struct. Mater. 3(2), 89–116 (2001)
127.
Frostig, Y., Phan, C.N., Kardomateas, G.A.: Free vibration of unidirectional sandwich panels, part I: compressible core. J. Sandw. Struct. Mater. 15(4), 377–411 (2013)
128.
Punera, D., Kant, T.: Elastostatics of laminated and functionally graded sandwich cylindrical shells with two refined higher order models. Compos. Struct. 182, 505–523 (2017)
129.
Zhen, W., Wanji, C.: A global-local higher order theory for multilayered shells and the analysis of laminated cylindrical shell panels. Compos. Struct. 84(4), 350–361 (2008)
130.
Ossadzow, C., Touratier, M.: An improved shear-membrane theory for multilayered shells. Compos. Struct. 52(1), 85–95 (2001)
131.
Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Polit, O.: Analysis of laminated shells by a sinusoidal shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations. Compos. Part B Eng. 42(5), 1276–1284 (2011)
132.
Mantari, J.L., Oktem, A.S., Guedes Soares, C.: Bending and free vibration analysis of isotropic and multilayered plates and shells by using a new accurate higher-order shear deformation theory. Compos. Part B Eng. 43(8), 3348–3360 (2012)
133.
Thai, H.T., Vo, T.P., Bui, T.Q., Nguyen, T.K.: A quasi-3D hyperbolic shear deformation theory for functionally graded plates. Acta Mech. 225(3), 951–964 (2014)MathSciNetMATH
134.
Sayyad, A.S., Ghugal, Y.M.: Static and free vibration analysis of laminated composite and sandwich spherical shells using a generalized higher-order shell theory. Compos. Struct. 219, 129–146 (2019)
135.
Carrera, E.: Historical review of zig–zag theories for multilayered plates and shells. Appl. Mech. Rev. 56, 287–308 (2003)
136.
Ambartsumian, S.A.: On a general theory of anisotropic shells. J. Appl. Math. Mech. 22(2), 305–319 (1958)MathSciNet
137.
Murakami, H.: Laminated composite plate theory with improved in-plane response. J. Appl. Mech. 53, 661–666 (1986)MATH
138.
Grigorenko, YaM., Vasilenko, A.T.: Taking account of nonuniformity of transverse displacement deformation in thickness in layered shells. Sov. Appl. Mech. 13(10), 989–994 (1977)
139.
Rasskazov, A.O.: Theory of multilayer orthotropic shallow shells. Sov. Appl. Mech. 12(11), 1131–1136 (1976)MATH
140.
Piskunov, V.G., Rasskazov, A.A.: Investigation of stress–strained state of tapered orthotropic shells and plates on the basis of second order shear theory. Int. Appl. Mech. 34(8), 798–806 (1998)MATH
141.
Whitney, J.M.: The effect of transverse shear deformation on the bending of laminated plates. J. Compos. Mater. 3(3), 534–547 (1969)
142.
Rath, B.K., Das, Y.C.: Vibration of layered shells. J. Sound Vib. 28(4), 737–757 (1973)MATH
143.
Soldatos, K.P., Timarci, T.: A unified formulation of laminated composite, shear deformable, five-degrees-of-freedom cylindrical shell theories. Composite Structures 25(1), 165–171 (1993)
144.
Kumar, A., Chakrabarti, A., Bhargava, P.: Vibration of laminated composites and sandwich shells based on higher order zigzag theory. Eng. Struct. 56, 880–888 (2013)
145.
Kumar, A., Chakrabarti, A., Bhargava, P.: Finite element analysis of laminated composite and sandwich shells using higher order zigzag theory. Compos. Struct. 106, 270–281 (2013)
146.
Ahmed, A., Kapuria, S.: A four-node facet shell element for laminated shells based on the third order zigzag theory. Compos. Struct. 158(1), 112–127 (2016)
147.
Coda, H.B., Paccola, R.R., Carrazedo, R.: Zig–Zag effect without degrees of freedom in linear and non linear analysis of laminated plates and shells. Compos. Struct. 161, 32–50 (2017)
148.
Hsu, T.M., Wang, J.T.: Rotationally symmetric vibrations of orthotropic layered cylindrical shells. J. Sound Vib. 16(4), 473–487 (1971)MATH
149.
Cheung, Y.K., Wu, C.I.: Free vibrations of thick, layered cylinders having finite length with various boundary conditions. J. Sound Vib. 24(2), 189–200 (1972)MATH
150.
Robbins Jr., D.H., Reddy, J.N.: Modelling of thick composites using a layerwise laminate theory. Int. J. Numer. Methods Eng. 36(4), 655–677 (1993)MATH
151.
Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells. Theory and Analysis, 2nd edn. CRC Press, Boca Raton (2004)MATH
152.
Dasgupta, A., Huang, K.H.: A layer-wise analysis for free vibrations of thick composite spherical panels. J. Compos. Mater. 31(7), 658–671 (1997)
153.
Yaqoob Yasin, M., Kapuria, S.: An efficient layerwise finite element for shallow composite and sandwich shells. Compos. Struct. 98, 202–214 (2013)MATH
154.
Guo, Y., Ruess, M.: A layerwise isogeometric approach for NURBS-derived laminate composite shells. Compos. Struct. 124, 300–309 (2015)
155.
Khan, K., Patel, B.P., Nath, Y.: Dynamic characteristics of bimodular laminated panels using an efficient layerwise theory. Compos. Struct. 132, 759–771 (2015)
156.
Marjanović, M., Vuksanović, D.: Free vibrations of laminated composite shells using the rotation-free plate elements based on Reddy’s layerwise discontinuous displacement model. Compos. Struct. 156, 320–332 (2016)
157.
Kulikov, G.M., Plotnikova, S.V.: Strong sampling surfaces formulation for layered shells. Int. J. Solids Struct. 121, 75–85 (2017)
158.
Li, D.H., Zhang, F.: Full extended layerwise method for the simulation of laminated composite plates and shells. Comput. Struct. 187, 101–113 (2017)
159.
Naumenko, K., Eremeyev, V.A.: A layer-wise theory of shallow shells with thin soft core for laminated glass and photovoltaic applications. Compos. Struct. 178, 434–446 (2017)
160.
Reissner, E.: On a mixed variational theorem and on shear deformable plate theory. Int. J. Numer. Methods Eng. 23(2), 193–198 (1986)MATH
161.
Reissner, E.: On a certain mixed variational theorem and on laminated elastic shell theory. In: Elishakoff, I., Irretier, H. (eds.) Refined Dynamical Theories of Beams, Plates and Shells and Their Applications, pp. 17–27. Springer, Berlin (1987)
162.
Bhaskar, K., Varadan, T.K.: Reissner’s new mixed variational principle applied to laminated cylindrical shells. J. Press. Vessel Technol. 114(1), 115–119 (1992)
163.
Carrera, E.: Developments, ideas and evaluations based upon the Reissner’s mixed variational theorem in the modeling of multilayered plates and shells. Appl. Mech. Rev. 54, 301–329 (2001)
164.
Fettahlioglu, O.A., Steele, C.R.: Asymptotic solutions for orthotropic non-homogeneous shells of revolution. J. Appl. Mech. 44, 753–758 (1974)MATH
165.
Berdichevsky, V.L.: Variational-asymptotic method of shell theory construction. PMM 43, 664–667 (1979)
166.
Lee, C., Hodges, D.H.: Dynamic variational-asymptotic procedure for laminated composite shells—part I: low-frequency vibration analysis. J. Appl. Mech. 76(1), 011002 (2008)
167.
Lee, C.Y., Hodges, D.H.: Asymptotic construction of a dynamic shell theory: finite-element-based approach. Thin Walled Struct. 47(3), 256–270 (2009)
168.
Louhghalam, A., Igusa, T., Tootkaboni, M.: Dynamic characteristics of laminated thin cylindrical shells: asymptotic analysis accounting for edge effect. Compos. Struct. 112, 22–37 (2014)
169.
Wu, C.P., Tarn, J.Q., Chi, S.M.: Three-dimensional analysis of doubly curved laminated shells. J. Eng. Mech. 122(5), 391–401 (1996)
170.
Wu, C.P., Tarn, J.Q., Chen, P.Y.: Refined asymptotic theory of doubly curved laminated shells. J. Eng. Mech. 123(12), 1238–1246 (1997)
171.
Wu, C.P., Hung, Y.C.: Asymptotic theory of laminated circular conical shells. Int. J. Eng. Sci. 37(8), 977–1005 (1999)MATH
172.
Wu, C.P., Chi, Y.W.: Asymptotic solutions of laminated composite shallow shells with various boundary conditions. Acta Mech. 132(1), 1–18 (1999)MathSciNetMATH
173.
Akhmedov, N.K., Sofiyev, A.H.: Asymptotic analysis of three-dimensional problem of elasticity theory for radially inhomogeneous transversally-isotropic thin hollow spheres. Thin Walled Struct. 139, 232–241 (2019)
174.
Ciarlet, P.G., Lods, V.: Asymptotic analysis of linearly elastic shells. I. Justification of membrane shell equations. Arch. Ration. Mech. Anal. 136(2), 119–161 (1996)MathSciNetMATH
175.
176.
Tovstik, P.E.: On the asymptotic nature of approximate models of beams, plates, and shells. Vestn. St. Petersb. Univ. Math. 40(3), 188–192 (2007)MathSciNetMATH
177.
Vetyukov, Y., Staudigl, E., Krommer, M.: Hybrid asymptotic-direct approach to finite deformations of electromechanically coupled piezoelectric shells. Acta Mech. 229(2), 953–974 (2018)MathSciNetMATH
178.
Prulière, E.: 3D simulation of laminated shell structures using the proper generalized decomposition. Compos. Struct. 117, 373–381 (2014)
179.
Bognet, B., Leygue, A., Chinesta, F.: Separated representations of 3D elastic solutions in shell geometries. Adv. Model. Simul. Eng. Sci. 1(1), 4 (2014)
180.
Vidal, P., Gallimard, L., Polit, O.: Shell finite element based on the proper generalized decomposition for the modeling of cylindrical composite structures. Comput. Struct. 132, 1–11 (2014)
181.
Vidal, P., Gallimard, L., Polit, O.: Multiresolution strategies for the modeling of composite shell structures based on the variable separation method. Int. J. Numer. Methods Eng. 117(7), 778–799 (2019)MathSciNet
182.
Carrera, E.: The effects of shear deformation and curvature on buckling and vibrations of cross-ply laminated composite shells. J. Sound Vib. 150(3), 405–433 (1991)
183.
Carrera, E.: A study of transverse normal stress effect on vibration of multilayered plates and shells. J. Sound Vib. 225(5), 803–829 (1999)
184.
Carrera, E.: A Reissner’s mixed variational theorem applied to vibration analysis of multilayered shell. J. Appl. Mech. 66(1), 69–78 (1999)
185.
Carrera, E.: Multilayered shell theories accounting for layerwise mixed description, part 1: governing equations. AIAA J. 37(9), 1107–1116 (1999)
186.
Carrera, E.: Multilayered shell theories accounting for layerwise mixed description, part 2: numerical evaluations. AIAA J. 37(9), 1117–1124 (1999)
187.
Brank, B., Carrera, E.: Multilayered shell finite element with interlaminar continuous shear stresses: a refinement of the Reissner–Mindlin formulation. Int. J. Numer. Methods Eng. 48(6), 843–874 (2000)MATH
188.
Brank, B., Carrera, E.: A family of shear-deformable shell finite elements for composite structures. Comput. Struct. 76(1), 287–297 (2000)
189.
Carrera, E.: On the use of the Murakami’s zig–zag function in the modeling of layered plates and shells. Comput. Struct. 82(7), 541–554 (2004)
190.
Carrera, E., Giunta, G.: Exact, hierarchical solutions for localized loadings in isotropic, laminated, and sandwich shells. J. Press. Vessel Technol. 131(4), 041202 (2009)
191.
Cinefra, M., Carrera, E.: Shell finite elements with different through-the-thickness kinematics for the linear analysis of cylindrical multilayered structures. Int. J. Numer. Methods Eng. 93(2), 160–182 (2013)MathSciNetMATH
192.
Carrera, E., Cinefra, M., Petrolo, M., Zappino, E.: Finite Element Analysis of Structures Through Unified Formulation. Wiley, Chichester (2014)MATH
193.
Cinefra, M., Chinosi, C., Della Croce, L., Carrera, E.: Refined shell finite elements based on RMVT and MITC for the analysis of laminated structures. Compos. Struct. 113, 492–497 (2014)
194.
Cinefra, M., Valvano, S.: A variable kinematic doubly-curved MITC9 shell element for the analysis of laminated composites. Mech. Adv. Mater. Struct. 23(11), 1312–1325 (2016)
195.
Carrera, E., Pagani, A., Valvano, S.: Shell elements with through-the-thickness variable kinematics for the analysis of laminated composite and sandwich structures. Compos. Part B Eng. 111, 294–314 (2017)
196.
Li, G., Carrera, E., Cinefra, M., de Miguel, A.G., Pagani, A., Zappino, E.: An adaptable refinement approach for shell finite element models based on node-dependent kinematics. Compos. Struct. 210, 1–19 (2019)
197.
Bathe, K.J., Dvorkin, E.N.: A formulation of general shell elements—the use of mixed interpolation of tensorial components. Int. J. Numer. Methods Eng. 22(3), 697–722 (1986)MATH
198.
Petrolo, M., Lamberti, A.: Axiomatic/asymptotic analysis of refined layer-wise theories for composite and sandwich plates. Mech. Adv. Mater. Struct. 23(1), 28–42 (2016)
199.
Cinefra, M.: Free-vibration analysis of laminated shells via refined MITC9 elements. Mech. Adv. Mater. Struct. 23(9), 937–947 (2016)
200.
Petrolo, M., Carrera, E.: On the use of neural networks to evaluate performances of shell models for composites. Adv. Model. Simul. Eng. Sci. (in Press)
201.
Petrolo, M., Carrera, E.: Best structural theories for free vibrations of sandwich composites via machine learning. In: Proceedings of the ASME 2019 International Mechanical Engineering Congress and Exposition IMECE2019
Metadaten
Titel
Methods and guidelines for the choice of shell theories
verfasst von
Marco Petrolo
Erasmo Carrera
Publikationsdatum
08.01.2020
Verlag
Springer Vienna
Erschienen in
Acta Mechanica / Ausgabe 2/2020
Print ISSN: 0001-5970
Elektronische ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-019-02601-w

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