The prime aim of the present study is to present analytical formulations and solutions for the buckling analysis of simply supported functionally graded plates (FGPs) using higher order shear deformation theory (HSDT) without enforcing zero transverse shear stresses on the top and bottom surfaces of the plate. It does not require shear correction factors and transverse shear stresses vary parabolically across the thickness. Material properties of the plate are assumed to vary in the thickness direction according to a power law distribution in terms of the volume fractions of the constituents. The equations of motion and boundary conditions are derived using the principle of virtual work. Solutions are obtained for FGPs in closed-form using Navier’s technique. Comparison studies are performed to verify the validity of the present results from which it can be concluded that the proposed theory is accurate and efficient in predicting the buckling behavior of functionally graded plates. The effect of side-to-thickness ratio, aspect ratio, modulus ratio, the volume fraction exponent, and the loading conditions on the critical buckling load of FGPs is also investigated and discussed.
The analysis of functionally graded material (FGM) plates with material variation parameter (n), boundary conditions, aspect ratios and side to thickness ratios are investigated using higher order displacement model. The derivation of equations of motion for higher order displacement model is obtained using principle of virtual work. The nonlinear simultaneous equations are obtained by Navier's method considering certain parameters, loads and boundary conditions. The nonlinear algebraic equations are solved using Newton Raphson iterative method. The numerical results are obtained for various boundary conditions, material variation parameter, aspect ratio, side to thickness ratio and compared with the available solutions. The effect of shear deformation and nonlinearity response of functionally graded material plate is studied.
In the current paper, a theoretical study of the effect of the viscosity variation on the squeeze film performance of a short bearing operating with couple stress fluids is presented. The modified Reynolds equation accounting for the couple stresses and viscosity variation is mathematically derived. To obtain a closed form solution, the short bearing approximation under constant load is considered. The modified Reynolds equation is solved for the fluid film pressure and then the bearing characteristics, such as the load carrying capacity and the squeeze time for the fluid film are obtained. According to the results evaluated, the couple stress fluid as a lubricant improves the squeeze film characteristics and results in a longer bearing life. Whereas the viscosity variation factor decreases the load carrying capacity and squeeze film time. The results are compared with the Newtonian fluid.
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