zbMATH — the first resource for mathematics

Stress analysis of multi-layered hollow anisotropic composite cylindrical structures using the homogenization method. (English) Zbl 1401.74010
Summary: This paper presents a general and efficient stress analysis strategy for hollow composite cylindrical structures consisting of multiple layers of different anisotropic materials subjected to different loads. Cylindrical material anisotropy and various loading conditions are considered in the stress analysis. The general stress solutions for homogenized hollow anisotropic cylinders subjected to pressure, axial force, torsion, shear and bending are presented with explicit formulations under typical force and displacement boundary conditions. The stresses and strains in a layer of the composite cylindrical structures are obtained from the solutions of homogenized hollow cylinders with effective material properties and discontinuous layer material properties. Effective axial, torsional, bending and coupling stiffness coefficients taking into account material anisotropy are also determined from the strain solutions for the hollow composite cylindrical structures. Examples show that the material anisotropy may have significant effects on the effective stiffness coefficients in some cases. The stress analysis method is demonstrated with an example of stress analysis of a 22-layer composite riser, and the results are compared with numerical solutions. This method is efficient for stress analysis of thin-walled or moderately thick-walled hollow composite cylindrical structures with various multiple layers of different materials or arbitrary fiber angles because no explicit interfacial continuity parameters are required. It provides an efficient and easy-to-use analysis tool for assessing hollow composite cylindrical structures in engineering applications.

74A10 Stress
74S30 Other numerical methods in solid mechanics (MSC2010)
74E10 Anisotropy in solid mechanics
74A40 Random materials and composite materials
Full Text: DOI
[1] Lekhnitskii S.G.: Theory of Elasticity of an Anisotropic Body. Mir Publishers, Moscow (1981)
[2] Jolicoeur C., Cardou A.: Analytical solution for bending of coaxial orthotropic cylinders. J. Eng. Mech. ASCE 120, 2556–2574 (1994) · doi:10.1061/(ASCE)0733-9399(1994)120:12(2556)
[3] Chouchaoui C.S., Ochoa O.O.: Similitude study for a laminated cylindrical tube under tensile, torsion, bending, internal and external pressure. Part I: governing equations. Compos. Struct. 44, 221–229 (1999) · doi:10.1016/S0263-8223(98)00068-3
[4] Chouchaoui C.S., Parks P., Ochoa O.O.: Similitude study for a laminated cylindrical tube under tensile, torsion, bending, internal and external pressure. Part II: scale models. Compos. Struct. 44, 231–236 (1999) · doi:10.1016/S0263-8223(98)00069-5
[5] Wild P.M., Vickers G.W.: Analysis of filament-wound cylindrical shells under combined centrifugal, pressure and axial loading. Compos. Part A Appl. S. 28, 47–55 (1997) · doi:10.1016/S1359-835X(96)00093-0
[6] Parnas L., Katirci N.: Design of fiber-reinforced composite pressure vessels under various loading conditions. Compos. Struct. 58, 83–95 (2002) · doi:10.1016/S0263-8223(02)00037-5
[7] Verijenko V.E., Adali S., Tabakov P.Y.: Stress distribution in continuously heterogeneous thick laminated pressure vessels. Compos. Struct. 54, 371–377 (2001) · doi:10.1016/S0263-8223(01)00112-X
[8] Xia M., Takayanagi H., Kemmochi K.: Bending behavior of filament-wound fiber-reinforced sandwich pipes. Compos. Struct. 56, 201–210 (2002) · doi:10.1016/S0263-8223(01)00181-7
[9] Stroh A.N.: Dislocations and cracks in anisotropic elasticity. Philos. Mag. 3, 625–646 (1958) · Zbl 0080.23505 · doi:10.1080/14786435808565804
[10] Ting T.C.T.: Anisotropic Elasticity: Theory and Applications. Oxford Science Publications, New York (1996) · Zbl 0883.73001
[11] Kollár L.P., Springer G.S.: Stress analysis of anisotropic laminated cylinders and cylindrical segments. Int. J. Solids Struct. 29, 1499–1517 (1992) · Zbl 0760.73048 · doi:10.1016/0020-7683(92)90130-L
[12] Kollár L.P., Patterson J.M., Springer G.S.: Composite cylinders subjected to hygrothermal and mechanical loads. Int. J. Solids Struct. 29, 1519–1534 (1992) · Zbl 0825.73424 · doi:10.1016/0020-7683(92)90131-C
[13] Bhaskar K., Varadan T.K.: Exact elasticity solution for laminated anisotropic cylindrical shells. J. Appl. Mech. ASME 60, 41–47 (1993) · Zbl 0800.73226 · doi:10.1115/1.2900777
[14] Xia M., Takayanagi H., Kemmochi K.: Analysis of multi-layered filament-wound composite pipes under internal pressure. Compos. Struct. 53, 483–491 (2001) · doi:10.1016/S0263-8223(01)00061-7
[15] Xia M., Kemmochi K., Takayanagi H.: Analysis of filament-wound fiber-reinforced sandwich pipe under combined internal pressure and thermomechanical loading. Compos. Struct. 51, 273–283 (2001) · doi:10.1016/S0263-8223(00)00137-9
[16] Bakaiyan H., Hosseini H., Ameri E.: Analysis of multi-layered filament-wound composite pipes under combined internal pressure and thermomechanical loading with thermal variations. Compos. Struct. 88, 532–541 (2009) · doi:10.1016/j.compstruct.2008.05.017
[17] Calhoglu H., Ergun E., Demirdag O.: Stress analysis of filament-wound composite cylinders under combined internal pressure and thermal loading. Adv. Compos. Lett. 17, 13–21 (2008)
[18] Tarn J.Q., Wang Y.M.: Laminated composite tubes under extension, torsion, bending, shearing and pressuring: a state space approach. Int. J. Solids Struct. 38, 9053–9075 (2001) · Zbl 1037.74016 · doi:10.1016/S0020-7683(01)00170-6
[19] Tarn J.Q.: A state space formalism for anisotropic elasticity. Part II: cylindrical anisotropy. Int. J. Solids Struct. 39, 5157–5172 (2002) · Zbl 1087.74509 · doi:10.1016/S0020-7683(02)00412-2
[20] Panda S.C., Natarajan R.: Finite element analysis of laminated composite plates. Int. J. Numer. Methods Eng. 14, 69–79 (1979) · Zbl 0394.73073 · doi:10.1002/nme.1620140106
[21] Karan S.S., Sorem R.M.: Curved shell elements based on hierarchical p-approximation in the thickness direction for linear static analysis of laminated composites. Int. J. Numer. Methods Eng. 29, 1391–1420 (1990) · Zbl 0731.73081
[22] Buragohain D.N., Ravichandran P.K.: Modified 3-dimensional finite-element for general and composite shells. Comput. Struct. 51, 289–298 (1994) · Zbl 0900.73723 · doi:10.1016/0045-7949(94)90336-0
[23] ABAQUS Analysis User’s Manual, Version 6.11 (2011)
[24] Lomakin E.V.: Torsion of cylindrical bodies with varying strain properties. Mech. Solids 43, 502–511 (2008) · doi:10.3103/S0025654408030217
[25] Babuška I.: Homogenization approach in engineering. Lect. Notes Econ. Math. Syst. 134, 137–153 (1976) · doi:10.1007/978-3-642-85972-4_8
[26] Sanchez-Palencia E.: Homogenization method for the study of composite media. Lect. Notes Math. 985, 192–214 (1983) · Zbl 0525.73006 · doi:10.1007/BFb0062368
[27] Sanchez-Palencia E.: Homogenization in mechanics. A survey of solved and open problems. Rend. Sem. Mat. Univ. Politec. Torino 44, 1–45 (1986) · Zbl 0615.73009
[28] Hashin Z.: Analysis of composite materials–a survey. J. Appl. Mech. ASME 50, 481–505 (1983) · Zbl 0542.73092 · doi:10.1115/1.3167081
[29] Charalambakis, N.: Homogenization techniques and micromechanics. A survey and perspectives. Appl. Mech. Rev. 63, 030803-1–10 (2010)
[30] Enie R.B., Rizzo R.R.: Three-dimensional laminate moduli. J. Compos. Mater. 14, 150–154 (1970)
[31] Pagano N.J.: Exact moduli of anisotropic laminates. In: Sendeckyj, G.P. (eds) Mechanics of Composite Materials, pp. 23–44. Academic Press, New York (1974)
[32] Sun C.T., Li S.: Three-dimensional effective elastic constants for thick laminates. J. Compos. Mater. 22, 629–639 (1988) · doi:10.1177/002199838802200703
[33] Chen H.J., Tsai S.W.: Three-dimensional effective moduli of symmetric laminates. J. Compos. Mater. 30, 906–917 (1996) · doi:10.1177/002199839603000803
[34] Sun, X.S., Chen, Y., Tan, V.B.C., Jaiman, R.K., Tay, T.E.: Homogenization and stress analysis of multi-layered composite offshore production risers. J. Appl. Mech. Trans. ASME 81, 031003 (2013). doi: 10.1115/1.4024695
[35] Soden P.D., Hinton M.J., Kaddour A.S.: Lamina properties, lay-up configurations and loading conditions for a range of fibre-reinforced composite laminates. Compos. Sci. Technol. 58, 1011–1022 (1998) · doi:10.1016/S0266-3538(98)00078-5
[36] Chen, Y., Tan, L.B., Jaiman, R.K., Sun, X.S., Tay T.E., Tan, V.B.C.: Global-local analysis of a full-scale composite riser during vortex-induced vibration. In: Proceedings of the 32nd International Conference on Offshore Mechanics and Arctic Engineering (OMAE 2013), OMAE2013-11632 (2013)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.