Effect of Non-ideal Boundary Conditions on Buckling of Rectangular Functionally Graded Plates

Document Type: Research Paper

Authors

1 Department of Mechanical Engineering, Islamic Azad University, Arak Branch

2 Faculty of Engineering, Islamic Azad University, Khomein Branch

Abstract

We have solved the governing equations for the buckling of rectangular functionally graded plates which one of its edges has small non-zero deflection and moment. For the case that the material properties obey a power law in the thickness direction, an analytical solution is obtained using the perturbation series. The applied in-plane load is assumed to be perpendicular to the edge which has non-ideal boundary conditions. Making use of the Linshtead-Poincare perturbation technique, the critical buckling loads are obtained. The results were then verified with the known data in the literature.

Keywords

[1] Reddy J.N., 2000, Analysis of functionally graded plates, International Journal for Numerical Methods in Engineering 47: 663-684.

[2] Najafizadeh M.M., Eslami M.R., 2002, Buckling analysis of circular plates of functionally graded materials based on first order theory, AIAA Journal 40(7): 1444-1450.

[3] Javaheri R., Eslami M.R., 2002, Thermal buckling of functionally graded plates, AIAA Journal 40(1): 162-169.

[4] Gorman D.J., 2000, Free vibration and buckling of in-plane loaded plates with rotational elastic edge support, Journal of Sound and Vibration 229(4): 755-773.

[5] Pakdemirli M., Boyaci H., 2002, Effect of non-ideal boundary conditions on the vibrations of continuous systems, Journal of Sound and Vibration 249: 815-823.

[6] Pakdemirli M., Boyaci H., 2003, Non-linear vibrations of a simple-simple beam with a non-ideal support in between, Journal of Sound and Vibration 268: 331-341.

[7] Aydogdu M., Ece M.C., 2006, Buckling and vibration of non-ideal simply supported rectangular isotropic plates, Mechanics Research Communications 33: 532-540.

[8] Nayfeh A.H., 1981, Introduction to Perturbation Techniques, Wiley, New York.