Abstract
Bifurcation behavior of heated conical shell made of a through-the-thickness functionally graded material is investigated in the present research. Properties of the shell are obtained based on a power law form across the thickness. Temperature dependency of the constituents is also taken into account. The heat conduction equation of the shell is solved based on an iterative generalized differential quadrature method (GDQM). General nonlinear equilibrium equations and the associated boundary conditions are obtained using the virtual displacement principle in the Donnell sense. The prebuckling solution of the shell is obtained under the assumption of linear membrane deformations. The stability equations are extracted via the concept of the adjacent equilibrium criterion. A semi-analytical solution employing the GDQM and trigonometric expansion is implemented to solve the stability equations. Numerical results of the present research are compared and validated with the known available data through the open literature. Some parametric studies are conducted to investigate the influences of various involved parameters, such as the cone semi-vertex angle, boundary conditions, power law index of composition rule, length to thickness ratio, and the radius to thickness ratio.
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References
Seide P.: Axisymmetrical buckling of circular cones under axial compression. J. Appl. Mech. 23(4), 625–628 (1956)
Singer J.: Buckling of circular conical shells under uniform axial compression. AIAA J. 3(5), 985–987 (1965)
Singer J.: The effect of axial constraint on the instability of thin conical shells under external pressure. J. Appl. Mech. 29(1), 212–214 (1962)
Baruch M., Harari O., Singer J.: Low buckling loads of axially compressed conical shells. J. Appl. Mech. 37(2), 384–392 (1970)
Lu S.Y., Chang L.K.: Thermal buckling of conical shells. AIAA J. 5(10), 1877–1882 (1967)
Chang L.K., Lu S.Y.: Nonlinear thermal elastic buckling of conical shells. Nucl. Eng. Des. 7(2), 159–169 (1968)
Tani J.: Influence of axisymmetric initial deflections on the thermal buckling of truncated conical shells. Nucl. Eng. Des. 48(2–3), 393–403 (1978)
Tani J.: Buckling of truncated conical shells under combined pressure and heating. J. Therm. Stresses 7(3–4), 307–316 (1984)
Tani J.: Buckling of truncated conical shells under combined axial load, pressure, and heating. J. Appl. Mech. 52(2), 402–408 (1985)
Wu C.P., Chiu S.J.: Thermoelastic buckling of laminated composite conical shells. J. Therm. Stresses 24(9), 881–901 (2001)
Patel B.P., Shukla K.K., Nath Y.: Thermal postbuckling analysis of laminated cross-ply truncated circular conical shells. Compos. Struct. 71(1), 101–114 (2005)
Patel B.P., Shukla K.K., Nath Y.: Nonlinear thermoelastic stability characteristics of cross-ply laminated oval cylindrical/conical shells. Finite Elem. Anal. Des. 42(12), 1061–1070 (2006)
Roh J.H., Woo J.H., Lee I.: Thermal post-buckling and vibration analysis of composite conical shell structures using layerwise theory. J. Therm. Stresses 32(1–2), 41–64 (2008)
Singh B.N., Babu J.B.: Thermal buckling of laminated composite conical shell panel with and without piezoelectric layer with random material properties. Int. J. Crashworthiness 14(1), 73–81 (2009)
Singh B.N., Babu J.B.: Thermal buckling of laminated conical shells embedded with and without piezoelectric layer. J. Reinf. Plast. Compos. 28(7), 791–812 (2009)
Bhangale R., Ganesan N., Padmanabhan Ch.: Linear thermoelastic buckling and free vibration behavior of functionally graded truncated conical shells. J. Sound Vib. 292(1–2), 341–371 (2006)
Naj R., Sabzikar M., Eslami m.R.: Thermal and mechanical instability of functionally graded truncated conical shells. Thin-Walled Struct. 46(1), 65–78 (2008)
Sofiyev A.H.: Thermoelastic stability of functionally graded truncated conical shells. Compos. Struct. 77(1), 56–65 (2007)
Sofiyev A.H.: Thermal buckling of FGM shells resting on a two-parameter elastic foundation. Thin-Walled Struct. 49(10), 1304–1311 (2011)
Torabi J., Kiani Y., Eslami M.R.: Linear thermal buckling analysis of truncated hybrid FGM conical shells. Compos. B Eng. 50(1), 265–272 (2013)
Reddy J.N., Chin C. D.: Thermomechanical analysis of functionally graded cylinders and plates. J. Therm. Stresses 21(6), 593–626 (1998)
Jabareen M., Sheinman I.: Postbuckling analysis of geometrically imperfect conical shells. J. Eng. Mech. 132(12), 1326–1334 (2006)
Jabareen M., Sheinman I.: Stability of imperfect stiffened conical shells. Int. J. Solids Struct. 46(10), 2111–2125 (2009)
Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells, Theory and Application, 2nd edn. CRC Press, Boca Raton (2003)
Hetnarski R.B., Eslami M.R.: Thermal Stresses—Advanced Theory and Applications. Springer, Berlin (2009)
Shu, C.: Differential Quadrature and Its Application in Engineering. Springer, London (2000)
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Akbari, M., Kiani, Y. & Eslami, M.R. Thermal buckling of temperature-dependent FGM conical shells with arbitrary edge supports. Acta Mech 226, 897–915 (2015). https://doi.org/10.1007/s00707-014-1168-3
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DOI: https://doi.org/10.1007/s00707-014-1168-3