Bending and free vibration characteristics of various compositions of FG plates on elastic foundation via quasi 3D HSDT model

Bending and free vibration characteristics of various compositions of FG plates on elastic foundation via quasi 3D HSDT model

In this investigation, a novel analytical model based on combined (cubic, sinusoidal and exponential) higher order quasi-3D formulation is developed to examine flexural and free vibrational response on the various FG-plate resting on elastic foundation. The presented model is simple and contains a variable number less than others quasi-three dimensional theories. The effective properties of the structure are computed using linear, cubic, quadratic and inverse quadratic formulations which represent the volume fraction of the ceramic. The elastic foundation is structured by the constant parameter of Winkler which represents the reaction of the elastic springs and Pasternak one"s in the form of a shear layer of subgrade. The analytical solution of the problem is obtained on the basis of the both Hamilton’s principle and Navier’s technique. The exactness of the current combined quasi-3D HSDT which takes into account the thickness stretching effect are checked and compared with others existing analytical models. Parametric studies are performed to shows the effects of the material distribution, inhomogeneity index, elastic foundation parameters, geometry and dimension ratios on displacements, stresses and naturel frequencies of the simply supported FG-plates.

In this investigation, a novel analytical model based on combined (cubic, sinusoidal and exponential) higher order quasi-3D formulation is developed to examine flexural and free vibrational response on the various FG-plate resting on elastic foundation. The presented model is simple and contains a variable number less than others quasi-three dimensional theories. The effective properties of the structure are computed using linear, cubic, quadratic and inverse quadratic formulations which represent the volume fraction of the ceramic. The elastic foundation is structured by the constant parameter of Winkler which represents the reaction of the elastic springs and Pasternak one"s in the form of a shear layer of subgrade. The analytical solution of the problem is obtained on the basis of the both Hamilton’s principle and Navier’s technique. The exactness of the current combined quasi-3D HSDT which takes into account the thickness stretching effect are checked and compared with others existing analytical models. Parametric studies are performed to shows the effects of the material distribution, inhomogeneity index, elastic foundation parameters, geometry and dimension ratios on displacements, stresses and naturel frequencies of the simply supported FG-plates.