Accurate Critical Buckling Load/Temperature of Thick Annular Sector Plates
Publication: Journal of Engineering Mechanics
Volume 138, Issue 6
Abstract
In this paper, stability analysis of thick annular sector plates under mechanical and thermal loads based on third-order shear deformation theory (TSDT) is investigated. The equilibrium and stability equations based on TSDT are obtained and solved analytically by doing some mathematical manipulation. Then, for nine possible boundary conditions, the buckling load and temperature are calculated and compared with those obtained using different plate theories. As the results show, for boundary conditions that include simply supported and clamped edges, the minimum value for buckling load and temperature is predicted by first-order shear deformation theory (FSDT) and maximum value is predicted by classical plate theory (CPT). Also, for boundary conditions containing free edges, the value obtained by TSDT is larger than that obtained using CPT and FSDT for some values of thickness/length ratio. It is worthy to mention that the results obtained from CPT for boundary conditions containing free edges in a wide range of thickness/length ratio are acceptable.
Get full access to this article
View all available purchase options and get full access to this article.
References
Bodaghi, M., and Saidi, A. R. (2010). “Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory.” Appl. Math. Modell.AMMODL, 34(11), 3659–3673.
Brush, D. O., and Almroth, B. O. (1975). Chapter 3, Buckling of bars, plates and shells, McGraw-Hill, New York.
Javaheri, R., and Eslami, M. R. (2002). “Thermal of functionally graded plates based on higher order theory.” J. Therm. Stress.JTSTDA, 25(7), 603–625.
Levinson, M. (1980). “An accurate simple theory of the statics and dynamics of elastic plates.” Mech. Res. Commun.MRCOD2, 7(6), 343–350.
Liu, W. H., and Chen, W. C. (1989). “Note on the stability of annular sector plates with elastically restrained edges.” Int. J. Mech. Sci.IMSCAW, 31(8), 611–622.
Mindlin, R. D. (1951). “Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates.” J. Appl. Mech.JAMCAV, 18, 1, 31–38.
Naderi, A., and Saidi, A. R. (2011a). “An analytical solution for buckling of moderately thick functionally graded sector and annular sector plates.” Arch. Appl. Mech.AAMEEA, 81(6), 809–828.
Naderi, A., and Saidi, A R. (2011b). “Exact solution for stability analysis of moderately thick functionally graded sector plates on elastic foundation.” Compos. Struct.COMSE2, 93(2), 629–638.
Navaneethakrishnan, P. V. (1988). “Buckling of nonuniform plates: Spline method.” Eng. Mech.JENMDT, 114(5), 893–898.
Ni, Q. Q., Xie, J., and Iwamoto, M. (2005). “Buckling analysis of laminated composite plates with arbitrary edge supports.” Compos. Struct.COMSE2, 69(2), 209–217.
Nosier, A., and Reddy, J. N. (1992a). “On vibration and buckling of symmetric laminated plates to shear deformation theories according to shear deformation theories. Part I.” Acta Mech.AMHCAP, 94(3–4), 123–144.
Nosier, A., and Reddy, J. N. (1992b). “On vibration and buckling of symmetric laminated plates to shear deformation theories according to shear deformation theories. Part II.” Acta Mech.AMHCAP, 94(3–4), 145–169.
Reddy, J. N. (1984a). “A simple higher-order theory for laminated plates.” J. Appl. Mech.JAMCAV, 51(4), 745–752.
Reddy, J. N. (1984b) “A refined nonlinear theory of plates with transverse shear deformation.” Int. J. Solids Struct.IJSOAD, 20(9–10), 881–896.
Reddy, J. N., and Liu, C. F. (1985). “A higher-order shear deformation theory of laminated elastic shells.” Int. J. Eng. Sci.IJESAN, 23(3), 319–330.
Reddy, J. N., and Phan, N. D. (1985). “Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory.” J. Sound Vib.JSVIAG, 98(2), 157–170.
Reissner, E. (1945). “The effect of transverse shear deformation on the bending of elastic plates.” J. Appl. Mech.JAMCAV, 12(2), 69–77.
Rubin, C. (1978). “Stability of polar orthotropic sector plates.” J. Appl. Mech.JAMCAV, 45(2), 448–450.
Saidi, A. R., and Hasani Baferani, A. (2010). “Thermal buckling analysis of moderately thick functionally graded annular sector plates.” Compos. Struct.COMSE2, 92(7), 1744–1752.
Saidi, A. R., Rasouli, A., and Sahraee, S. (2009). “Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained third-order shear deformation plate theory.” Compos. Struct.COMSE2, 89(1), 110–119.
Samsam Shariat, B. A., and Eslami, M. R. (2007). “Buckling of thick functionally graded plates under mechanical and thermal loads.” Compos. Struct.COMSE2, 78(3), 433–439.
Sharma, A., Sharda, H. B., and Nath, Y. (2005a). “Stability and vibration of Mindlin sector plates: An analytical approach.” AIAA J.AIAJAH, 43(5), 1109–1116.
Sharma, A., Sharda, H. B., and Nath, Y. (2005b). “Stability and vibration of thick laminated composite sector plates.” J. Sound Vib.JSVIAG, 287(1–2), 1–23.
Srinivasan, R. S., and Thiruvenkatachari, V. (1984). “Stability of annular sector plates with variable thickness.” AIAA J.AIAJAH, 22(2), 315–317.
Wang, C. M., and Lee, K. H. (1998). “Buckling load relationship between Reddy and Kirchhoff circular plates.” J. Franklin Inst.JFINAB, 335(6), 989–995.
Wang, C. M., Reddy, J. N., and Lee, K. H. (2000). Shear deformable beams and plates: Relationships with classical solutions, Elsevier, Oxford, UK.
Wang, C. M., and Xiang, Y. (1999). “Deducing buckling loads of sectorial Mindlin plates from Kirchhoff plates.” Eng. Mech.GOLIEB, 125(5), 596–598.
Wang, C. M., Xiang, Y., Kitipornchai, S., and Liew, K. M. (1994). “Buckling solutions for Mindlin plates of various shapes.” Eng. Struct., 16(2), 119–127.
Watson, N. G. (1922). Theory of Bessel functions, Cambridge University Press, Cambridge.
Zhou, Y. H., Zheng, X., and Hariky, I. E. (1995). “A seminumerical method for buckling of sector plates.” Comput. Struct.CMSTCJ, 57(5), 847–854.
Information & Authors
Information
Published In
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Aug 9, 2010
Accepted: Dec 8, 2011
Published online: Dec 12, 2011
Published in print: Jun 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.