Analytical Solution for Bending Analysis of Axially Functionally Graded Angle-Ply Flat Panels

Abstract

In this paper, the analytical solution is presented for axially functionally graded (AFG) angle-ply flat panels subjected to arbitrary boundary condition. Material properties of AFG panels are assumed to vary linearly along x-direction. Reissner-type variation principle is used to derive the governing equations in mixed form. By employing extended Kantorovich method (EKM), a set of nonhomogeneous ordinary differential equations (ODEs) are obtained along the in-plane (x) and thickness (z) direction. The system of ODEs along the z-direction has constant coefficients, solved analytically. However, the system of ODEs along x-direction has variable coefficients, solved using modified power series method. The influence of property variation on the deflection and stresses is studied and discussed comprehensively for different sets of boundary conditions. Numerical results are validated through comparison with 3D FE. The presented analytical solution can serve as a benchmark for assessing the accuracy of the two-dimensional solution or 3D numerical solutions.

Viscoelastic free vibration analysis of in-plane functionally graded orthotropic plates integrated with piezoelectric sensors: Time-dependent 3D analytical solutions

“…) and ζ (thickness coordinate) only. The solution along these two-directions (for x and z-direction) is obtained further by employing recently developed the multi-term extended Kantorovich method [34,38,40,44,74,92]. The solution of X l , lth variable X, is assumed as the summation of n terms series containing products of two separable unknown functions g i l (ζ) and f i l (ξ 1 ).…”

“…This analysis shows that the behaviour of rectangular plates is affected more by axial stiffness variation than throughthickness stiffness variation. Singh and Kumari developed a power series-based extended Kantorovich elasticity analytical approach for flexural analysis of in-plane functionally graded composite beams [34][35][36][37], panels [38,39], and rectangular plates [40]. Using a similar approach, Ravindran and Bhaskar [41] developed a 3D analytical approach for flexural analysis of IPFG simply-supported plates subjected to sinusoidal loading.…”

2‐D Analytical solutions for the multisegmented panel subjected to arbitrary boundary condition

“…Singh et al. [37] have presented an analytical solution for the bending analysis of axially functionally graded panels. This method has been applied to solve the problem of skew‐symmetric plates [38, 39], sector plates [40], stepped plates [41].…”

“…Further, a technique was applied to analyze the stress behavior of the piezoelectric plates [35] and functionally graded plates [36]. Singh et al [37] have presented an analytical solution for the bending analysis of axially functionally graded panels. This method has been applied to solve the problem of skew-symmetric plates [38,39], sector plates [40], stepped plates [41].…”