Abstract
Abstract This article deals with finite element method for the analysis of antisymmetric angle-ply laminated composite hypar shells (hyperbolic paraboloid bounded by straight edges) that applies an eight-noded isoparametric shell element and a three-noded beam element to study the mode-frequency analysis of stiffened shell with cutout. Two-, 4-, and 10-layered antisymmetric angle-ply laminations with different lamination angles are considered. Among these, 10-layer antisymmetric angle-ply shells are considered for elaborate study. The shells have different boundary conditions along its four edges. The formulation is based on the first-order shear deformation theory. The reduced method of eigen value solution is chosen for the undamped free vibration analysis. The first five modes of natural frequency are presented. The numerical studies are conducted to determine the effects of width-to-thickness ratio (b/h), degree of orthotropy (E 11/E 22), and fiber orientation angle (θ) on the nondimensional natural frequency. The results reveal that free vibration behavior mainly depends on the number of boundary constraints rather than other parametric variations such as change in fiber orientation angle and increase in degree of orthotropy and width-to-thickness ratio.
Highlights
Received Nov 02, 2017; revised May 10, 2018; accepted Nov 20, 2018 AbstractThis article deals with finite element method for the analysis of antisymmetric angle-ply laminated composite hypar shells that applies an eight-noded isoparametric shell element and a three-noded beam element to study the mode-frequency analysis of stiffened shell with cutout
For CSSC shell, the maximum fundamental frequency occurs at the lamination angle of 45∘
It is observed that for all the boundary conditions considered here, 4- and 10-layered laminates exhibit the maximum value of frequency parameter for the same lamination angle., The maximum fundamental frequency occurs at the lamination angle, θ, of 75∘ and 45∘, respectively, for CSCS and CSSC shells; at θ = 0∘ for FCFC shells; and at θ = 30∘ for FCCF, FSFS and FSSF shells
Summary
A laminated composite hypar shell of uniform thickness h (Figure 1) and twist radius of curvature Rxy is considered. Three-noded isoparametric beam elements (Figure 2b) are used to model the stiffeners, which are taken to run only along the boundaries of the shell elements. The element mass matrix for shell is obtained from the following integral equation:. The element size is gradually decreased near the cutout margins Benchmark problems are used to check the suitability of the present approach and a number of authors’ own problems (7) are taken up to assess the mode–frequency behavior of antisymmetric angle-ply composite stiffened hypar shells with cutout. Antisymmetric angle-ply laminated composite stiffened hypar shells with cutout are analyzed to study the behavior of the shell under free vibration at higher mode for different parametric variation.
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