Abstract
Structural components such as shell with arbitrarily supported boundary condition and angle-ply material configuration require an efficient theory to accurately predict its three-dimensional (3D) deformations and stresses. Here, a generalized 3D solution using the multiterm extended Kantorovich method (EKM) is presented for a cylindrical shell panel. In this work, the governing equation of the problem is obtained using the mixed type Reissner’s principle from shell equilibrium and constitutive relations in the cylindrical coordinate system. Further, two sets of simultaneous ordinary differential equations (ODEs) are obtained iteratively by applying the EKM. This reduction in partial differential equations to ODEs has highly increased the accuracy and convergence of the process. This solution has provided very accurate results with just two terms in the series (multiterm) expansion, and results are obtained after just one or two iteration steps for angle-ply laminates. Transverse stresses including boundary effects have been accurately predicted by presently developed solution in and around the vicinity of the clamped edge where a 3D finite element (FE) fails otherwise.
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References
Piggott, M.R., Zhang, W.: Fracture toughness of angle ply laminates. ESIS Publ. 32, 445–454 (2003)
Alipour, M.M.: An analytical approach for bending and stress analysis of cross/angle-ply laminated composite plates under arbitrary non-uniform loads and elastic foundations. Arch. Civ. Mech. Eng. 16(2), 193–210 (2016)
Chen, W.Q., Lee, K.Y.: State-space approach for statics and dynamics of angle-ply laminated cylindrical panels in cylindrical bending. Int. J. Mech. Sci. 47(3), 374–87 (2005)
Kant, T.: A critical review and some results of recently developed refined theories of fiber-reinforced laminated composites and sandwiches. Compos. Struct. 23(4), 293–312 (1993)
Wu, C.P., Chiu, K.H., Wang, Y.M.: A review on the three-dimensional analytical approaches of multilayered and functionally graded piezoelectric plates and shells. Comput. Mater. Continua. 8(2), 93–132 (2008)
Qatu, M.S., Asadi, E., Wang, W.: Review of recent literature on static analyses of composite shells: 2000–2010. Open J. Compos. Mater. 2(03), 61 (2012)
Benjeddou, A.: Advances in piezoelectric finite element modeling of adaptive structural elements: a survey. Comput. Struct. 76(1–3), 347–63 (2000)
Carrera, E.: Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking. Arch. Comput. Method E 10(3), 215–96 (2003)
Liew, K.M., Zhao, X., Ferreira, A.J.: A review of meshless methods for laminated and functionally graded plates and shells. Compos. Struct. 93(8), 2031–41 (2011)
Wu, C.P., Liu, Y.C.: A review of semi-analytical numerical methods for laminated composite and multilayered functionally graded elastic/piezoelectric plates and shells. Compos. Struct. 147, 1–5 (2016)
Ren, J.G.: Exact solutions for laminated cylindrical shells in cylindrical bending. Compos. Sci. Technol. 29(3), 169–87 (1987)
Varadan, T.K., Bhaskar, K.: Bending of laminated orthotropic cylindrical shells—an elasticity approach. Compos. Struct. 17(2), 141–56 (1991)
Bhaskar, K., Varadan, T.K.: Exact elasticity solution for laminated anisotropic cylindrical shells. J. Appl. Mech. 60(1), 41–7 (1993)
Bhaskar, K., Varadan, T.K.: A benchmark elasticity solution for an axisymmetrically loaded angle-ply cylindrical shell. Compos. Eng. 3(11), 1065–73 (1993)
Hawkes, T.D., Soldatos, K.P.: Three-dimensional axisymmetric vibrations of orthotropic and cross-ply laminated hollow cylinders. AIAA J. 30(4), 1089–98 (1992)
Jiarang, F., Hongyu, S.: Exact solution for laminated continuous open cylindrical shells. Appl. Math. Mech. 18(11), 1073–86 (1997)
Chen, W.Q.: Free vibration analysis of laminated piezoceramic hollow spheres. J. Acoust. Soc. Am. 109(1), 41–50 (2001)
Chen, W.Q., Wang, Y.F., Cai, J.B., Ye, G.R.: Three-dimensional analysis of cross-ply laminated cylindrical panels with weak interfaces. Int. J. Solids Struct. 41(9–10), 2429–46 (2004)
Yan, W., Ying, J., Chen, W.Q.: The behavior of angle-ply laminated cylindrical shells with viscoelastic interfaces in cylindrical bending. Compos. Struct. 78(4), 551–9 (2007)
Lü, C.F., Lim, C.W., Xu, F.: Stress analysis of anisotropic thick laminates in cylindrical bending using a semi-analytical approach. J. Zhejiang Univ.-Sci. A 8(11), 1740–5 (2007)
Alibeigloo, A.: Static and vibration analysis of axi-symmetric angle-ply laminated cylindrical shell using state space differential quadrature method. Int. J. Pres. Ves. Pip. 86(11), 738–47 (2009)
Sheng, H.Y., Ye, J.Q.: A three-dimensional state space finite element solution for laminated composite cylindrical shells. Comput. Method Appl. M 192(22–24), 2441–59 (2003)
Kapuria, S., Kumari, P.: Multiterm extended Kantorovich method for three-dimensional elasticity solution of laminated plates. J. Appl. Mech. 79(6), 061018(1-9) (2012)
Kapuria, S., Kumari, P.: Extended Kantorovich method for coupled piezoelasticity solution of piezolaminated plates showing edge effects. Proc. R. Soc. A-Math. Phys. 469(2151), 20120565 (2013)
Kumari, P., Susanta, B., Santosh, K.: Coupled three-dimensional piezoelasticity solution for edge effects in Levy-type rectangular piezolaminated plates using mixed field extended Kantorovich method. Compos. Struct. 140, 491–505 (2016)
Kumari, P., Singh, A., Rajapakse, R.K., Kapuria, S.: Three-dimensional static analysis of Levy-type functionally graded plate with in-plane stiffness variation. Compos. Struct. 168, 780–91 (2017)
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)
Kumari, P., Kapuria, S., Rajapakse, R.K.: Three-dimensional extended Kantorovich solution for Levy-type rectangular laminated plates with edge effects. Compos. Struct. 107, 167–76 (2014)
Xu, K., Noor, A.K., Tang, Y.Y.: Three-dimensional solutions for coupled thermoelectroelastic response of multilayered plates. Comput. Method Appl. M 126(3–4), 355–71 (1995)
Dumir, P.C., Dube, G.P., Kapuria, S.: Exact piezoelastic solution of simply-supported orthotropic circular cylindrical panel in cylindrical bending. Int. J. Solids Struct. 34(6), 685–702 (1997)
ABAQUS/STANDARD. User’s manual. Version 6.9-1 (2009)
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Kar, S., Kumari, P. A 3D solution for angle-ply cylindrical shell panel supported arbitrarily on its boundaries using extended Kantorovich method. Int J Adv Eng Sci Appl Math 12, 51–64 (2020). https://doi.org/10.1007/s12572-020-00267-5
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DOI: https://doi.org/10.1007/s12572-020-00267-5