Free vibration analysis of functionally graded plates using higher order shear deformation theory (HSDT)

Abstract

A Functionally graded plate is made up of composite materials, microscopically inhomogeneous, in which the mechanical properties vary smoothly and continuously from one surface to another. It is a type of advanced materials in the field of composites, which can resist high temperatures and are proficient in reducing the thermal stresses. Functionally graded plates are becoming very popular in modern structural design as it allows excellent mechanical performance at minimal weight resulting higher payloads, increased range and decreased fuel consumption. FGMs are widely used to benefit a wide range of industries and have applications in industries like aerospace, transportation and nuclear industry. In this paper the free vibration behaviour of FGM pates is being provided. A programme has been developed using MATLAB. The material properties at any particular depth have been modelled following the power law. Third order transverse shear deformation is accounted along with eight noded serendipity plate finite elements. To implement the theory a suitable C0 continuous serendipity iso-parametric finite element with 7 degrees of freedom (DOFs) per node is proposed in order to reduce the computational efforts required in the formation of element matrices without affecting the solution accuracy. Numerical results have been presented for ceramic–metal graded plates with different boundary conditions. The convergence and validation studies manifest the accuracy and precision of the present proposed method. Parametric studies have been conducted by incorporating variation in support conditions, side to thickness ratio and different materials. Some results are presented in the form of tables and figures, which can suit as a benchmark for the future research.