Dynamic and static analysis of FGM skew plates with 3D elasticity based graded finite element modeling

摘要

The present article deals with static and dynamic behavior of functionally graded skew plates based on the three-dimensional theory of elasticity. On the basis of the principle of minimum potential energy and the Rayleigh Ritz method, the equations of motion are derived in conjunction with the graded finite element approach. Solution of the resulted system of equations in time domain is carried out via Newmark's time integration method. Calculations are applied for fully clamped boundary condition. In the present paper, two different sets of distributions for material properties are considered. For the static analysis, material properties are considered to vary through the thickness direction according to an exponential law. In the case of dynamic analysis, variations of the volume fractions through the thickness are assumed to obey a power law function. Thus, the effective material properties at each point are determined by the Mori-Tanaka scheme. In case of dynamic analysis, the results are obtained for uniform step loadings. The effects of material gradient index and skew angle on displacement components and stress response are studied. Results of present formulations are verified by available results of a functionally graded rectangular plate for different boundary conditions and also compared with result of a homogenous skew plate by commercial FEM software.