zbMATH — the first resource for mathematics

Semi-analytical buckling analysis of heterogeneous variable thickness viscoelastic circular plates on elastic foundations. (English) Zbl 1272.74183
Summary: Buckling analysis of the functionally graded viscoelastic circular plates has not been carried out so far. In the present paper, a series solution is developed for buckling analysis of radially graded FG viscoelastic circular plates with variable thickness resting on two-parameter elastic foundations, based on Mindlin’s plate theory. The complex modulus approach in combination with the elastic-viscoelastic correspondence principle is employed to obtain the solution for various edge conditions. A comprehensive sensitivity analysis is carried out to evaluate effects of various parameters on the buckling load. Results reveal that the viscoelastic behavior of the materials may postpone the buckling occurrence and the stiffness reduction due to the section variations may be compensated by the graded material properties.

74G60 Bifurcation and buckling
74K20 Plates
74D05 Linear constitutive equations for materials with memory
Full Text: DOI Link
[1] Alipour, M. M.; Shariyat, M.; Shaban, M.: A semi-analytical solution for free vibration and modal stress analyses of circular plates resting on two-parameter elastic foundations, J. solid mech. 2, No. 1, 63-78 (2010)
[2] Arikoglu, A.; Ozkol, I.: Solution of boundary value problems for integro-differential equations by using differential transform method, Appl. math. Comput. 168, 1145-1158 (2005) · Zbl 1090.65145 · doi:10.1016/j.amc.2004.10.009
[3] Chen, C. K.; Ho, S. H.: Application of differential transformation to eigenvalue problems, Appl. math. Comput. 79, 173-188 (1998) · Zbl 0879.34077 · doi:10.1016/0096-3003(95)00253-7
[4] Chen, L. W.; Hwang, J. R.: Vibrations of initially stressed thick circular and annular plates based on a high-order plate theory, J. sound. Vib. 122, 79-95 (1988)
[5] Hal, F.; Brinson, L.: Catherine brinson, polymer engineering science and viscoelasticity: an introduction, (2008)
[6] Raju, K. Kanaka; Rao, G. Venkateswara: Post-buckling analysis of moderately thick elastic circular plates, J. appl. Mech. 50, 468-470 (1983) · Zbl 0638.73010
[7] Katsikadelis, J. T.; Babouskos, N. G.: Post-buckling analysis of viscoelastic plates with fractional derivative models, Compos. struct. 59, 99-107 (2003) · Zbl 1244.74058
[8] Lakes, R. S.: Viscoelastic materials, (2009) · Zbl 1049.74012
[9] Ma, L. S.; Wang, T. J.: Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings, Int. J. Solids struct. 40, 3311-3330 (2003) · Zbl 1038.74547 · doi:10.1016/S0020-7683(03)00118-5
[10] Ma, L. S.; Wang, T. J.: Axisymmetric post-buckling of a functionally graded circular plate subjected to uniformly distributed radial compression, Mater. sci. Forum 423/425, 719-724 (2003)
[11] Malik, M.; Dang, H. H.: Vibration analysis of continuous systems by differential transformation, Appl. math. Comput. 96, 17-26 (1998) · Zbl 0969.74539 · doi:10.1016/S0096-3003(97)10076-5
[12] Najafizadeh, M. M.; Eslami, M. R.: Buckling analysis of circular plates of functionally graded materials under uniform radial compression, Int. J. Mech. sci. 44, 2479-2493 (2002) · Zbl 1031.74027 · doi:10.1016/S0020-7403(02)00186-8
[13] Najafizadeh, M. M.; Eslami, M. R.: First order theory based thermoelastic stability of functionally graded materials circular plates, Aiaa j 40, 1444-1450 (2002) · Zbl 1031.74027
[14] Najafizadeh, M. M.; Eslami, M. R.: Refined theory for thermoelastic stability of functionally graded circular plates, J. therm. Stresses 27, 857-880 (2004)
[15] Najafizadeh, M. M.; Heydari, H. R.: An exact solution for buckling of functionally graded circular plates based on higher order shear deformation plate theory under uniform radial compression, Int. J. Mech. sci. 50, 603-612 (2008) · Zbl 1264.74065
[16] Prakash, T.; Ganapathi, M.: Asymmetric flexural vibration and thermoelastic stability of FGM circular plates using finite element method, Compos. part B 37, 642-649 (2006)
[17] Reddy, J. N.: Mechanics of laminated composite plates and shells theory and analysis, (2004) · Zbl 1075.74001
[18] Reddy, J. N.: Theory and analysis of elastic plates and shells, (2007)
[19] Saidi, A. R.; Rasouli, A.; Sahraee, S.: Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained third-order shear deformation plate theory, Compos. struct. 89, No. 1, 110-119 (2009) · Zbl 1176.74110
[20] Shariyat, M.: A double-superposition global-local theory for vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates: a complex modulus approach, Arch. appl. Mech. 81, 1253-1268 (2011) · Zbl 1271.74184
[21] Shariyat, M.: A nonlinear double superposition global-local theory for dynamic buckling of imperfect viscoelastic composite/sandwich plates: A hierarchical constitutive model, Compos. struct. 93, 1890-1899 (2011)
[22] Shariyat, M.: Nonlinear thermomechanical dynamic buckling analysis of imperfect viscoelastic composite/sandwich shells by a double-superposition global-local theory and various constitutive models, Compos. struct. 93, 2833-2843 (2011)
[23] Shariyat, M.; Alipour, M. M.: Differential transform vibration and modal stress analyses of circular plates made of two-directional functionally graded materials, resting on elastic foundations, Arch. appl. Mech. 81, 1289-1306 (2011) · Zbl 1271.74185
[24] Uthgenant, E. B.; Brand, R. S.: Buckling of orthotropic annular plates, Aiaa j. 8, 2102-2104 (1970)
[25] Wang, H. -J.; Chen, L. -W.: Axisymmetric dynamic stability of sandwich circular plates, Compos. struct. 59, 99-107 (2003)
[26] Wang, C. M.; Xiang, Y.; Kitipornchai, S.; Liew, K. M.: Axisymmetric buckling of circular Mindlin plates with ring supports, J. struct. Eng. 119, 782-793 (1993) · Zbl 0775.73112
[27] Xu, R. Q.; Wang, Y.; Chen, W. Q.: Axisymmetric buckling of transversely isotropic circular and annular plates, Arch. appl. Mech. 74, 692-703 (2005) · Zbl 1097.74025 · doi:10.1007/s00419-005-0379-4
[28] Yalcin, H. S.; Arikoglu, A.; Ozkol, I.: Free vibration analysis of circular plates by differential transformation method, Appl. math. Comput. 212, 377-386 (2009) · Zbl 1182.74116 · doi:10.1016/j.amc.2009.02.032
[29] Yeh, Y. L.; Jang, M. J.; Wang, C. C.: Analyzing the free vibrations of a plate using finite difference and differential transformation method, Appl. math. Comput. 178, 493-501 (2006) · Zbl 1102.74024 · doi:10.1016/j.amc.2005.11.068
[30] Yeh, Y. -L.; Wang, C. C.; Jang, M. -J.: Using finite difference and differential transformation method to analyze of large deflections of orthotropic rectangular plate problem, Appl. math. Comput. 190, 1146-1156 (2007) · Zbl 1137.74036 · doi:10.1016/j.amc.2007.01.099
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.