تحلیل خمشی ورق‌های دایره‌ای و حلقوی مدرج تابعی با تغییرات پله‌ای ضخامت با استفاده از یک حل دقیق فرم بسته جدید

[1] Hang L. T. T., Wang C. M. and Wu T. Y., Exact vibration results for stepped circular plates with free edges, Int. J. Mechanical Sciences, Vol. 47, pp. 1224-1248, 2005.

[2] Xiang Y. and Zhang L., Free vibration analysis of stepped circular Mindlin plates, J. Sound and Vibration,  Vol. 280, pp. 633–655, 2005.

[3] Hosseini-Hashemi S., Derakhshani M. and Fadaee M., An accurate mathematical study on the free vibration of stepped thickness circular/annular Mindlin functionally graded plates, Applied Mathematical Modelling Vol. 37, pp. 4147–4164, 2013

[4] Wu T. Y., Wang Y. Y. and Liu G. R., Free vibration analysis of circular plates using generalized differential quadrature rule, Computer Methods Applied Mechanic Engineering, Vol. 191, pp. 5365–5380, 2002.

[5] Duana W. H., Wang C. M. and Wang C. Y., Modification of fundamental vibration modes of circular plates with free edges, J. Sound and Vibration Vol. 317, pp. 709–715, 2008. 

[6] Mashat D. S. and Zenkour A. M., Hygrothermal bending analysis of a sector-shaped annular plate with variable radial thickness, Composite Structures Vol. 113, pp. 446–458, 2014.

[8] Alipour M. M. and Shariyat M., Semi-analytical buckling analysis of heterogeneous variable thickness viscoelastic circular plates on elastic foundations, Mechanics Research Communications, Vol. 38, pp. 594-601, 2011.

[9] Alipour M. M. and Shariyat M., A semi-analytical solution for buckling analysis of variable thickness two-directional functionally graded circular plates with non-uniform elastic foundations. Journal of Engineering Mechanics, Vol. 139, 664-676, 2013. 

[10] Alipour M. M., Shariyat M. and Shaban M., A semi-analytical solution for free vibration of variable thickness two-directional-functionally graded plates on elastic foundations, Int. J. Mechanics and Materials in Design, Vol. 6, nom. 4, pp. 293-304, 2010. 

[11] Alipour M. M. and Shariyat M., A power series solution for free vibration of variable thickness Mindlin circular plates with two-directional material heterogeneity and elastic foundations. J. Solid Mechanics. Vol. 3, nom. 2, 183-197, 2011.

[12] Alipour M. M. and Shariyat M., Stress analysis of two-directional FGM moderately thick constrained circular plates with non-uniform load and substrate stiffness distributions, Journal of Solid Mechanics, Vol. 2, nom. 4, 316-331, 2010.

[13] Shariyat M. and Alipour M. M., A power series solution for vibration and complex modal stress analyses of variable thickness viscoelastic two-directional FGM circular plates on elastic foundations. Applied Mathematical Modelling, Vol. 37, nom. 5, pp. 3063–3076, 2013.

[14] Shariyat M. and Alipour M. M., Differential transform vibration and modal stress analyses of circular plates made of two-directional functionally graded materials, resting on elastic foundations, Archive of Applied Mechanics, Vol. 81, pp. 1289-1306, 2011.

[15] Shariyat M. and Alipour M. M., A Differential Transform Approach for Modal Analysis of Variable Thickness Two-Directional FGM Circular Plates on Elastic Foundations, ISME, Vol. 11, nom. 2, pp. 15-38, 2010.

[16] Shariyat M., Jafari A. A., and Alipour M. M., Investigation of the thickness variability and material heterogeneity effects on free vibration of the viscoelastic circular plates, Acta Mechanica Solida Sinica, Vol. 26, nom. 1, pp. 83–98, 2013.

[17] Alipour M. M., Shariyat M. and Shaban M., A semi-analytical solution for free vibration and modal stress analyses of circular plates resting on two-parameter elastic foundations, J. Solid Mechanics, Vol. 2, nom. 1, pp. 63-78, 2010.

[18] Karttunen A. T., Hertzen R., Reddy J. N. and Romanoff J., Exact elasticity-based finite element for circular plates, Computers and Structures, Vol. 182, pp. 219–226, 2017. 

[19] Lamacchia E., Pirrera A., Chenchiah I. V. and Weaver P. M., Non-axisymmetric bending of thin annular plates due tocircumferentially distributed moments, Int. J. Solids and Structures, Vol. 51, pp. 622–632, 2014. 

[20] Mehrabian M. and Golmakani M. E., Nonlinear bending analysis of radial-stiffened annular laminated sector plates with dynamic relaxation method, Computers and Mathematics with Applications, Vol. 69, nom. 10, pp. 1272–1302, 2015. 

[21] Huang Y. and Li X. F., Effect of radial reaction force on the bending of circular plates resting on a ring support, Int. J. Mechanical Sciences, Vol. 119, pp. 197-207, 2016. 

[22] Reissner E., The Effect of Transverse Shear Deformation on the Bending of Elastic Plates, ASME Journal of Applied Mechanics, Vol. 12, pp. 69–76, 1945.

[23] Mindlin R. D., Influence of Rotatory Inertia and Shear in Flexural Motions of Isotropic Elastic Plates, ASME J. of Applied Mechanics, Vol. 18, pp. 1031–1036, 1951.