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.
Highlights
The variation of material property in the structural components may occur due to environmental effects [1,2,3] or it may be induced intentionally (FGMs) to achieve optimized characteristics of structures and overcome the limitation of conventional material [4]
All the panels are made of Graphite-Epoxy material [42] and the engineering material constants are given as [(Y1, Y2, Y3, G23, G13, G12), ]12, ]13, ]23] = [(181.0, 10.3, 10.3, 2.87, 7.17, 7.17) GPa, 0.28, 0.28, 0.33]
Through-thickness distribution of transverse stresses σz and τzx has been presented in Figure 14 for panel (d) in which material properties vary according to case and panel subjected to C-F boundary conditions
Summary
The variation of material property in the structural components may occur due to environmental effects [1,2,3] or it may be induced intentionally (FGMs) to achieve optimized characteristics of structures and overcome the limitation of conventional material [4]. [30] developed semianalytical elasticity solutions for static analysis of bidirectional FG beams using a hybrid state space-based method in conjunction with differential quadrature method They extend the same approach to develop 3D elasticity solutions for bidirectional functionally graded Levy-type rectangular plates [31]. Most of analytical studies related to in-plane FGM are based on two-dimensional approach, i.e., classical plate theory (CPT) [33,34,35], first order shear. Kumari et al [41] presented a three-dimensional analytical solution for Levy-type functionally graded plate using the extended Kantorovich method. The analytical solution for FGM laminated angleply flat panel under cylindrical bending by considering an inplane variation of material properties has not been reported yet in the literature. The effect of in-plane property variation on deformation and stress distribution is examined intensively by considering various cases
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