DOI QR코드

DOI QR Code

Deformation and stress analysis of a sandwich cylindrical shell using HDQ Method

  • Shokrollahi, Hassan (Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University)
  • Received : 2017.07.27
  • Accepted : 2018.01.29
  • Published : 2018.04.10

Abstract

In this paper, the response of a sandwich cylindrical shell over any sort of boundary conditions and under a general distributed static loading is investigated. The faces and the core are made of some isotropic materials. The faces are modeled as thin cylindrical shells obeying the Kirchhoff-Love assumptions. For the core material it is assumed to be thick and the in-plane stresses are negligible. The governing equations are derived using the principle of the stationary potential energy. Using harmonic differential quadrature method (HDQM) the equations are solved for deformation components. The obtained results primarily are compared against finite element results. Then, the effects of changing different parameters on the stress and displacement components of sandwich cylindrical shells are investigated.

Keywords

References

  1. Abouhamze, M., Aghdam, M.M. and Alijani, F. (2007), "Bending analysis of symmetrically laminated cylindrical panels using the extended Kantorovich method", Mech. Adv. Mater. Struct., 14(7), 523-530. https://doi.org/10.1080/15376490701585967
  2. Alankaya, V. and Oktem, A.S. (2016), "Static analysis of laminated and sandwich composite doubly-curved shallow shells", Steel Compos. Struct., Int. J., 20(5), 1043-1066. https://doi.org/10.12989/scs.2016.20.5.1043
  3. Allahkarami, F., Nikkhah-Bahrami, M. and Saryazdi, M.G. (2017), "Damping and vibration analysis of viscoelastic curved microbeam reinforced with FG-CNTs resting on viscoelastic medium using strain gradient theory and dqm", Steel Compos. Struct., Int. J., 25(2), 141-155.
  4. Allen, H.G. (1969), Analysis and Design of Structural Sandwich Panels, Pergamon Press Inc., Oxford, UK.
  5. Altenbach, H. (2011), "Mechanics of advanced materials for lightweight structures", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 225(11), 2481-2496. https://doi.org/10.1177/0954406211417068
  6. Altenbach, H., Altenbach, J. and Kissing, W. (2004), Mechanics of Composite Structural Elements, Springer, New York, USA.
  7. Baltacioglu, A.K., Akgoz, B. and Civalek, O. (2010), "Nonlinear static response of laminated composite plates by discrete singular convolution method", Compos. Struct., 93(1), 153-161. https://doi.org/10.1016/j.compstruct.2010.06.005
  8. Bellman, R., Kashef, B.G. and Casti, J. (1972), "Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations", J. Comput. Phys., 10(1), 4-52.
  9. Bhimaraddi, A. and Chandrashekhara, K. (1992), "Threedimensional elasticity solution for static response of simply supported orthotropic cylindrical shells", Compos. Struct., 20(4), 227-235. https://doi.org/10.1016/0263-8223(92)90028-B
  10. Bozdogan, K.B. (2012), "Differential quadrature method for free vibration analysis of coupled shear walls", Struct. Eng. Mech., Int. J., 41(1), 67-81. https://doi.org/10.12989/sem.2012.41.1.067
  11. Carrera, E. (2003), "Historical review of Zig-Zag theories for multilayered plates and shells", Appl. Mech. Rev., 56(3), 287-308. https://doi.org/10.1115/1.1557614
  12. Carrera, E. (2004), "On the use of the Murakami's zig-zag function in the modeling of layered plates and shells", Comput. Struct., 82(7-8), 541-554. https://doi.org/10.1016/j.compstruc.2004.02.006
  13. Civalek, O. (2004), "Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns", Eng. Struct., 26(2), 171-186. https://doi.org/10.1016/j.engstruct.2003.09.005
  14. Civalek, O. (2007a), "Linear vibration analysis of isotropic conical shells by discrete singular convolution (DSC)", Struct. Eng. Mech., Int. J., 25(1), 127-130. https://doi.org/10.12989/sem.2007.25.1.127
  15. Civalek O. (2007b), "A parametric study of the free vibration analysis of rotating laminated cylindrical shells using the method of discrete singular convolution", Thin-Wall. Struct., 45(7-8), 692-698. https://doi.org/10.1016/j.tws.2007.05.004
  16. Civalek, O. (2008a), "Vibration analysis of conical panels using the method of discrete singular convolution", Commun. Numer. Meth. Eng., 24(3), 169-181. https://doi.org/10.1002/cnm.961
  17. Civalek, O. (2008b), "Analysis of thick rectangular plates with symmetric cross-ply laminates based on first-order shear deformation theory", J. Compos. Mater., 42(26), 2853-2867. https://doi.org/10.1177/0021998308096952
  18. Civalek, O. and Gurses, M. (2009), "Free vibration analysis of rotating cylindrical shells using discrete singular convolution technique", Int. J. Pres. Ves. Pip., 86(10), 677-683. https://doi.org/10.1016/j.ijpvp.2009.03.011
  19. Civalek, O. and Ulker, M. (2004), "Harmonic differential quadrature (HDQ) for axisymmetric bending analysis of thin isotropic circular plates", Struct. Eng. Mech., Int. J., 17(1), 1-14. https://doi.org/10.12989/sem.2004.17.1.001
  20. Gurses, M., Civalek, O., Korkmaz, A. and Ersoy, H. (2009), "Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first-order shear deformation theory", Int. J. Numer. Meth. Eng., 79(3), 290-313. https://doi.org/10.1002/nme.2553
  21. Gurses, M., Akgoz, B. and Civalek, O. (2012), "Mathematical modeling of vibration problem of nano-sized annular sector plates using the nonlocal continuum theory via eight-node discrete singular convolution transformation", Appl. Math. Comput., 219(6), 3226-3240. https://doi.org/10.1016/j.amc.2012.09.062
  22. Hamzehkolaei, N.S., Malekzadeh, P. and Vaseghi, J. (2011), "Thermal effect on axisymmetric bending of functionally graded circular and annular plates using dqm", Steel Compos. Struct., Int. J., 11(4), 341-358. https://doi.org/10.12989/scs.2011.11.4.341
  23. Jaskula, L. and Zielnica, J. (2011), "Large displacement stability analysis of elastic-plastic unsymmetrical sandwich cylindrical shells", Thin Wall. Struct., 49(5), 611-617. https://doi.org/10.1016/j.tws.2010.09.004
  24. Librescu, L. and Hause, T. (2000), "Recent developments in the modeling and behavior of advanced sandwich constructions: a survey", Compos. Struct., 48(1-3), 1-17. https://doi.org/10.1016/S0263-8223(99)00068-9
  25. Maleki, S., Tahani, M. and Andakhshideh, A. (2012), "Static and transient analysis of laminated cylindrical shell panels with various boundary conditions and general lay-ups", ZAMM Z. Angew. Math. Mech., 92(2), 124-140. https://doi.org/10.1002/zamm.201000236
  26. Malekzadeh, P. (2009), "A two-dimensional layerwise-differential quadrature static analysis of thick laminated composite circular arches", Appl. Math. Model., 33(4), 1850-1861. https://doi.org/10.1016/j.apm.2008.03.008
  27. Mohammadimehr, M. and Shahedi, S. (2016), "Nonlinear magneto-electro-mechanical vibration analysis of doublebonded sandwich Timoshenko microbeams based on MSGT using Gdqm", Steel Compos. Struct., Int. J., 21(1), 1-36. https://doi.org/10.12989/scs.2016.21.1.001
  28. Ng, T.Y. and Lam, K.Y. (1999), "Effects of elastic foundation on the dynamic stability of cylindrical shells", Struct. Eng. Mech., Int. J., 8(2), 193-205. https://doi.org/10.12989/sem.1999.8.2.193
  29. Noor, A.K., Burton, W.S. and Bert, C.W. (1996), "Computational models for sandwich panels and shells", Appl. Mech. Rev., 49(3), 155-199. https://doi.org/10.1115/1.3101923
  30. Plantema, F.J. (1966), Sandwich Construction, John Wiley & Sons, New York, USA.
  31. Rao, T. (2002), "Study of core compression using digital image correlation (DIC)", Master of Science Dissertation; Michigan Technological University.
  32. Shu, C. (2000), Differential Quadrature and its Application in Engineering, Springer, Berlin, Germany.
  33. Shu, C. and Richards, B.E. (1992), "Application of generalized differential quadrature to solve two-dimensional incompressible Navier Stockes equations", Int. J. Numer. Meth. Fl., 15(7), 791-798. https://doi.org/10.1002/fld.1650150704
  34. Soedel, W. (2004), Vibrations of Shells and Plates, Marcel Dekker Inc., New York, USA.
  35. Striz, A.G., Wang, X. and Bert, C.W. (1995), "Harmonic differential quadrature method and applications to analysis of structural components", Act. Mech., 111(1-2), 85-94. https://doi.org/10.1007/BF01187729
  36. Tornabene, F., Liverani, A. and Caligiana, G. (2012), "Static analysis of laminated composite curved shells and panels of revolution with aposteriori shear and normal stress recovery using generalized differential quadrature method", Int. J. Mech. Sci., 61(1), 71-87. https://doi.org/10.1016/j.ijmecsci.2012.05.007
  37. Tornabene, F., Fantuzzi, N., Ubertini, F. and Viola, E. (2015), "Strong formulation finite element method based on differential quadrature: A survey", Appl. Mech. Rev., 67(2), 020801-020801-55. https://doi.org/10.1115/1.4028859
  38. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2017), "Foam core composite sandwich plates and shells with variable stiffness: Effect of the curvilinear fiber path on the modal response", J. Sandw. Struct. Mater. DOI: 10.1177/1099636217693623
  39. Vinson, J.R. (2001), "Sandwich structures", Appl. Mech. Rev., 54(3), 201-214. https://doi.org/10.1115/1.3097295
  40. Washizu, K. (1975), Variational Methods in Elasticity and Plasticity, Pergamon Press, Oxford, UK.
  41. Zhong, H. and Yu, T. (2009), "A weak form quadrature element method for plane elasticity problems", Appl. Math. Model., 33(10), 3801-3814. https://doi.org/10.1016/j.apm.2008.12.007
  42. Zhao, X., Ng, T.Y. and Liew, K.M. (2004), "Free vibration of twoside simply supported laminated panels via the mesh-free Kp-Ritz method", Int. J. Mech. Sci., 46(1), 123-142. https://doi.org/10.1016/j.ijmecsci.2004.02.010
  43. Zenkert, D. (1995), An Introduction to Sandwich Construction, Chameleon Press, London, UK.