Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Elastic analysis of pressurized thick truncated conical shells made of functionally graded materials

  • Ghannad, M. (Mechanical Engineering Faculty, Shahrood University of Technology) ;
  • Nejad, M. Zamani (Mechanical Engineering Department, Yasouj University) ;
  • Rahimi, G.H. (Mechanical Engineering Department, Tarbiat Modares University) ;
  • Sabouri, H. (Mechanical Engineering Department, Tarbiat Modares University)
  • Received : 2011.12.21
  • Accepted : 2012.05.31
  • Published : 2012.07.10
⟨ Previous Next ⟩

Abstract

Based on the first-order shear deformation theory (FSDT), and the virtual work principle, an elastic analysis for axisymmetric clamped-clamped Pressurized thick truncated conical shells made of functionally graded materials have been performed. The governing equations are a system of nonhomogeneous ordinary differential equations with variable coefficients. Using the matched asymptotic method (MAM) of the perturbation theory, these equations could be converted into a system of algebraic equations with variable coefficients and two systems of differential equations with constant coefficients. For different FGM conical angles, displacements and stresses along the radius and length have been calculated and plotted.

Keywords

References

  1. Asemi, K., Akhlaghi, M., Salehi, M. and Zad, S.K.H. (2010), "Analysis of functionally graded thick truncated cone with finite length under hydrostatic internal pressure", Arch. Appl. Mech., 81, 1063-1074.
  2. Asemi, K., Salehi, M. and Akhlaghi, M. (2010), "Dynamic analysis of a functionally graded thick truncated cone with finite length", Int. J. Mech. Mater. Des., 6, 367-378. https://doi.org/10.1007/s10999-010-9144-0
  3. Asemi, K., Salehi, M. and Akhlaghi, M. (2011), "Elastic solution of a two-dimensional functionally graded thick truncated cone with finite length under hydrostatic combined loads", Acta. Mech., 217, 119-134. https://doi.org/10.1007/s00707-010-0380-z
  4. Chaudhry, H.R., Bukiet, B. and Davis, A.M. (1996), "Stresses and strains in the left ventricular wall approximated as a thick conical shell using large deformation theory", J. Biol. Syst., 4, 353-372. https://doi.org/10.1142/S0218339096000247
  5. Eipakchi, H.R. (2010), "Third-order shear deformation theory for stress analysis of a thick conical shell under pressure", J. Mech. Mater. Struct., 5, 1-17. https://doi.org/10.2140/jomms.2010.5.1
  6. Eipakchi, H.R., Khadem, S.E. and Rahimi, G.H. (2008), "Axisymmetric stress analysis of a thick conical shell with varying thickness under nonuniform internal pressure", J. Eng. Mech., 134, 601-610. https://doi.org/10.1061/(ASCE)0733-9399(2008)134:8(601)
  7. Eipakchi, H.R., Rahimi, G.H. and Khadem, S.E. (2003), "Closed form solution for displacements of thick cylinders with varying thickness subjected to nonuniform internal pressure", Struct. Eng. Mech., 16, 731-748. https://doi.org/10.12989/sem.2003.16.6.731
  8. Ghannad, M., Nejad, M.Z. and Rahimi, G.H. (2009), "Elastic solution of axisymmetric thick truncated conical shells based on first-order shear deformation theory", Mechanika, 79, 13-20.
  9. Ghannad, M. and Nejad, M.Z. (2010), "Elastic analysis of pressurized thick hollow cylindrical shells with clamped-clamped ends", Mechanika, 85, 11-18.
  10. Ghannad, M., Rahimi, G.H. and Nejad, M.Z. (2012), "Determination of displacements and stresses in pressurized thick cylindrical shells with variable thickness using perturbation technique", Mechanika, 18, 14-21.
  11. Hausenbauer, G.F. and Lee, G.C. (1966), "Stresses in thick-walled conical shells", Nucl. Eng. Des., 3, 394-401. https://doi.org/10.1016/0029-5493(66)90130-0
  12. McDonald, C.K. and Chang, C.H. (1973), "A second order solution of the nonlinear equations of conical shells", Int. J. Nonlin. Mech., 8, 49-58. https://doi.org/10.1016/0020-7462(73)90014-0
  13. Mirsky, I. and Hermann, G. (1958), "Axially motions of thick cylindrical shells", J. Appl. Mech-T. ASME., 25, 97-102.
  14. Naghdi, P.M. and Cooper, R.M. (1956), "Propagation of elastic waves in cylindrical shells, including the effects of transverse shear and rotary inertia", J. Acoust. Soc. Am., 29, 56-63.
  15. Nayfeh, A.H. (1993), Introduction to Perturbation Techniques, John Wiley, New York.
  16. Nejad, M.Z., Rahimi, G.H. and Ghannad, M. (2009), "Set of field equations for thick shell of revolution made of functionally graded materials in curvilinear coordinate system", Mechanika, 77, 18-26.
  17. Ozturk, B. and Coskun, S.B. (2011), "The Homotopy Perturbation Method for free vibration analysis of beam on elastic foundation", Struct. Eng. Mech., 37, 415-425. https://doi.org/10.12989/sem.2011.37.4.415
  18. Pan, D., Chen, G. and Lou, M. (2011), "A modified modal perturbation method for vibration characteristics of non-prismatic Timoshenko beams", Struct. Eng. Mech., 40, 689-703. https://doi.org/10.12989/sem.2011.40.5.689
  19. Sundarasivaraoa, B.S.K. and Ganesan, N. (1991), "Deformation of varying thickness of conical shells subjected to axisymmetric loading with various end conditions", Eng. Fract. Mech., 39, 1003-1010. https://doi.org/10.1016/0013-7944(91)90106-B
  20. Takahashi, S., Suzuki, K. and Kosawada, T. (1986), "Vibrations of conical shells with variable thickness", B. JSME., 29, 4306-4311. https://doi.org/10.1299/jsme1958.29.4306
  21. Vlachoutsis, S. (1992), "Shear correction factors for plates and shells", Int. J. Numer. Method. Eng., 33, 1537-1552. https://doi.org/10.1002/nme.1620330712

Cited by

  1. Application the mechanism-based strain gradient plasticity theory to model the hot deformation behavior of functionally graded steels vol.51, pp.4, 2014, https://doi.org/10.12989/sem.2014.51.4.627
  2. Magneto-thermo-elastic response of a rotating functionally graded cylinder vol.56, pp.1, 2015, https://doi.org/10.12989/sem.2015.56.1.137
  3. Time-Dependent Creep Analysis for Life Assessment of Cylindrical Vessels Using First Order Shear Deformation Theory vol.33, pp.04, 2017, https://doi.org/10.1017/jmech.2017.6
  4. Stress intensity factor calculation for semi-elliptical cracks on functionally graded material coated cylinders vol.55, pp.6, 2015, https://doi.org/10.12989/sem.2015.55.6.1087
  5. Thermomechanical Creep Analysis of FGM Thick Cylindrical Pressure Vessels with Variable Thickness 2018, https://doi.org/10.1142/S1758825118500084
  6. Three dimensional static and dynamic analysis of two dimensional functionally graded annular sector plates vol.51, pp.6, 2014, https://doi.org/10.12989/sem.2014.51.6.1067
  7. Thermo-elastic analysis of axially functionally graded rotating thick truncated conical shells with varying thickness vol.96, 2016, https://doi.org/10.1016/j.compositesb.2016.04.026
  8. Elastic analysis of FGM rotating thick truncated conical shells with axially-varying properties under non-uniform pressure loading vol.122, 2015, https://doi.org/10.1016/j.compstruct.2014.12.028
  9. Eringen's non-local elasticity theory for bending analysis of bi-directional functionally graded Euler–Bernoulli nano-beams vol.106, 2016, https://doi.org/10.1016/j.ijengsci.2016.05.005
  10. Magneto-thermo-elastic analysis of a functionally graded conical shell vol.16, pp.1, 2014, https://doi.org/10.12989/scs.2014.16.1.077
  11. New enhanced higher order free vibration analysis of thick truncated conical sandwich shells with flexible cores vol.55, pp.4, 2015, https://doi.org/10.12989/sem.2015.55.4.719
  12. Elastic analysis of pressurized thick cylindrical shells with variable thickness made of functionally graded materials vol.45, pp.1, 2013, https://doi.org/10.1016/j.compositesb.2012.09.043
  13. Mechanical and thermal stresses in radially functionally graded hollow cylinders with variable thickness due to symmetric loads pp.2204-2253, 2018, https://doi.org/10.1080/14484846.2018.1481562
  14. Consistent couple-stress theory for free vibration analysis of Euler-Bernoulli nano-beams made of arbitrary bi-directional functionally graded materials vol.63, pp.2, 2012, https://doi.org/10.12989/sem.2017.63.2.161
  15. Buckling analysis of FGM Euler-Bernoulli nano-beams with 3D-varying properties based on consistent couple-stress theory vol.26, pp.6, 2012, https://doi.org/10.12989/scs.2018.26.6.663
  16. Time-dependent creep analysis and life assessment of 304 L austenitic stainless steel thick pressurized truncated conical shells vol.28, pp.3, 2012, https://doi.org/10.12989/scs.2018.28.3.349
  17. Bending analysis of bi-directional functionally graded Euler-Bernoulli nano-beams using integral form of Eringen's non-local elasticity theory vol.67, pp.4, 2012, https://doi.org/10.12989/sem.2018.67.4.417
  18. Dynamic analysis of non-symmetric FG cylindrical shell under shock loading by using MLPG method vol.67, pp.6, 2012, https://doi.org/10.12989/sem.2018.67.6.659
  19. Thermo-Elastic Creep Analysis and Life Assessment of Thick Truncated Conical Shells with Variable Thickness vol.11, pp.9, 2012, https://doi.org/10.1142/s1758825119500868
  20. Free vibrations analysis of arbitrary three-dimensionally FGM nanoplates vol.8, pp.2, 2012, https://doi.org/10.12989/anr.2020.8.2.115
  21. Mechanical analysis of functionally graded spherical panel resting on elastic foundation under external pressure vol.74, pp.2, 2012, https://doi.org/10.12989/sem.2020.74.2.297
  22. Meshless Local Petrov-Galerkin (MLPG) method for dynamic analysis of non-symmetric nanocomposite cylindrical shell vol.74, pp.5, 2020, https://doi.org/10.12989/sem.2020.74.5.679
  23. Thermoelastoplastic response of FGM linearly hardening rotating thick cylindrical pressure vessels vol.38, pp.2, 2021, https://doi.org/10.12989/scs.2021.38.2.189