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 (E11/E22), 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.
Taguchi based optimization of natural frequency of perforated stiffened hypars is performed to consider the role of fibre lamination, width/thickness ratio of shell and position of perforation centre along x- and y-direction. Natural frequency of stiffened shell is obtained for simply supported boundary condition using finite element procedure based on L27 orthogonal array (OA) considering three settings of each parameter. Main effect plot is analyzed to identify the significant parameters. Natural frequency becomes maximum for a combination of 450 fibre lamination, width/thickness value of 20 and perforation centre position (0.4, 0.4). Interaction graphs identify the interaction parameters. ANOVA study provides the significant contribution of the parameters considered here. Present analysis identifies width/thickness as the most significant factor and other parameters yield very little significance while no interaction is found to be significant. Width/thickness value of shell yields major (98.64%) contribution to natural frequency and other factors yield very little significance. Residual analysis for natural frequency and confirmatory test validate the present study. S/N ratio gets improved by 38.3% at optimal condition compared to the initial parameter setting.
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