Effect of Exponential Stress Resultant on Buckling Response of Functionally Graded Rectangular Plates

Document Type: Original Article

Authors

Mechanical Engineering Department, Faculty of Engineering, Arak University, Arak, Iran.

Abstract

The effect of exponential stress resultant on buckling response of functionally graded rectangular plates based on exponential shear deformation theory is investigated in this paper. In exponential shear deformation theory, exponential functions are used in terms of thickness coordinate to include the effect of the transverse shear deformation and rotary inertia. The material properties of the functionally graded plate are assumed to vary according to a power low form according to the thickness direction. The equations of motions are derived based on Hamiltons principle. To validate the formulations, present results in specific cases are compared with available results in literature and good agreement could be seen. Finally, the influence of different parameters like power law indexes, aspect ratio, and the thickness ratio on the non-dimensional critical buckling load of rectangular FG plates are presented and discussed in detail.

Keywords


[1] E. Reissner, The effect of transverse shear deformation on the bending of elastic plates, J. Appl. Mech-T ASME., 12 (1945) 69-77.
[2] R.D. Mindlin, Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, J. Appl. Mech-T ASME., 18 (1951) 31-38.
[3] B. Mokhtar, T. Abedlouahed, A. Abbas, M. Abdelkader, Buckling analysis of functionally graded plates with simply supported edges, Leonardo J. Sci., 8 (2013) 21-32.
[4] M. S¸im¸sek, J.N. Reddy, Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory, Int. J. Eng. Sci., 64 (2013) 37-53.
[5] H. Matsunaga, Free vibration and stability of functionally graded plates according to a 2-D higherorder deformation theory, Compos. Struct., 82 (2008) 499-512.
[6] S. Yahia, H.A. Atmane, M.S.A. Houari, A. Tounsi, Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories, Struct. Eng. Mech., 53(6) (2015) 1143-1165.
[7] P. Malekzadeh, A.A. Beni, Free vibration of functionally graded arbitrary straight-sided quadrilateral plates in thermal environment, Compos. Struct., 92 (2010) 2758-2767.
[8] V. Ungbhakorn, N. Wattanasakulpong, Thermoelastic vibration analysis of third-order shear deformable functionally graded plates with distributed patch mass under thermal environment, Appl. Acousf., 74 (2013) 1045-1059.
[9] J. Reddy, Microstructure-dependent couple stress theories of functionally graded beams, J. Mech. Phys. Solid., 59(11) (2011) 2382-2399.
[10] A.S. Sayyad, Y.M. Ghugal, Bending and free vibration analysis of thick isotropic plates by using exponential shear deformation theory, Appl, Comput, Mech., 6(1) (2012) 65-82.
[11] K. Khorshidi, Effect of hydrostatic pressure on vibrating rectangular platescoupled with fluid, Sci. Iran: Trans A: Civ. Eng., 17(6) (2010) 41529.
[12] N.R. Senthilnathan, K.H. Lim, K.H. Lee, S.T. Chow, Buckling of shear deformable plates. AIAA J., 25(9) (1987) 1268-71.
[13] K. Khorshidi, M. Khodadadi, Precision closedform solution for out-of-plane vibration of rectangular plates via trigonometric shear deformation theory, Compos. Struct., 3(1) (2016) 31-43.
[14] K. Khorshidi, M. Pagoli, Analytical solution for sound radiation of vibrating circular plates coupled with piezo-electric layers, Compos. Struct., 3(2) (2016) 89-98.
[15] H.T. Thai, D.H. Choi, Size-dependent functionally graded Kirchhoff and Mindlin plate models based on a modified couple stress theory, Compos. Struct., 95 (2013) 142-153.
[16] K. Khorshidi, S. Farhadi, Free vibration analysis of a laminated composite rectangular plate in contact with a bounded fluid, Compos. Struct., 104 (2013) 176-186.