• Structural Engineering and Mechanics
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• v.31 no.5
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• pp.587-603
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• 2009

We performed a free vibration analysis of skew composite laminates with or without cutout based on the high-order shear deformation plate theory (HSDT). The effects of skew angles and ply orientations on the natural frequencies for various boundary conditions are studied using a nonlinear high-order finite element program developed for this study. The numerical results are in good agreement with those reported by other investigators for simple test cases, and the new results reported in this paper show the interactions between the skew angle, layup sequence and cutout size on the free vibration of the laminate. The findings highlight the importance of skew angles when analyzing laminated composite skew plates with cutout or without cutout.

• Composites Research
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• v.25 no.6
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• pp.217-223
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• 2012

This study investigates a geometrical nonlinear dynamic behaviors of laminated skew plates made of advanced composite materials (ACM). Based on the first-order shear deformation plate theory (FSDT), the Newmark method and Newton-Raphson iteration are used for the nonlinear dynamic solution. The effects of cutout sizes, skew angles and lay up sequences on the nonlinear dynamic response for various parameters are studied using a nonlinear dynamic finite element program developed for this study. The several numerical results were in good agreement with those reported by other investigators for square composite plates with or without central cutouts, and the new results reported in this paper show the significant interactions between the cutout, skew angles and layup sequence in the laminate. Key observation points are discussed and a brief design guideline of skew laminates is given.

• Structural Engineering and Mechanics
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• v.14 no.3
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• pp.245-262
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• 2002

The free vibration analysis of stiffened laminated composite plates has been performed using the layered (zigzag) finite element method based on the first order shear deformation theory. The layers of the laminated plate is modeled using nine-node isoparametric degenerated flat shell element. The stiffeners are modeled as three-node isoparametric beam elements based on Timoshenko beam theory. Bilinear in-plane displacement constraints are used to maintain the inter-layer continuity. A special lumping technique is used in deriving the lumped mass matrices. The natural frequencies are extracted using the subspace iteration method. Numerical results are presented for unstiffened laminated plates, stiffened isotropic plates, stiffened symmetric angle-ply laminates, stiffened skew-symmetric angle-ply laminates and stiffened skew-symmetric cross-ply laminates. The effects of fiber orientations (ply angles), number of layers, stiffener depths and degrees of orthotropy are examined.

• Structural Engineering and Mechanics
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• v.70 no.5
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• pp.551-562
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• 2019

In the present study, a suitable mathematical model considering parabolic transverse shear strains for dynamic analysis of laminated composite skew plates under different types of impulse and spatial loads was presented for the first time. The proposed mathematical model satisfies zero transverse shear strain at the top and bottom of the plate. On the basis of the cubic variation of thickness coordinate in in-plane displacement fields of the present mathematical model, a 2D finite element (FE) model was developed including skew transformations in the mathematical model. No shear correction factor is required in the present formulation and damping effect was also incorporated. This is the first FE implementation considering a cubic variation of thickness coordinate in in-plane displacement fields including skew transformations to solve the forced vibration problem of composite skew plates. The effect of transverse shear and rotary inertia was incorporated in the present model. The Newmark-${\beta}$ scheme was adapted to perform time integration from step to step. The $C^0$ FE formulation was implemented to overcome the problem of $C^1$ continuity associated with the cubic variation of thickness coordinate in in-plane displacement fields. The numerical studies showed that the present 2D FE model predicts the result close to the analytical results. Many new results varying different parameter such as skew angles, boundary conditions, etc. were presented.

• Structural Engineering and Mechanics
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• v.74 no.2
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• pp.227-241
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• 2020

The bi-axial and shear buckling behavior of laminated hypar shells having rhombic planforms are studied for various boundary conditions using the present mathematical model. In the present mathematical model, the variation of transverse shear stresses is represented by a second-order function across the thickness and the cross curvature effect in hypar shells is also included via strain relations. The transverse shear stresses free condition at the shell top and bottom surfaces are also satisfied. In this mathematical model having a realistic second-order distribution of transverse shear strains across the thickness of the shell requires unknown parameters only at the reference plane. For generality in the present analysis, nine nodes curved isoparametric element is used. So far, there exists no solution for the bi-axial and shear buckling problem of laminated composite rhombic (skew) hypar shells. As no result is available for the present problem, the present model is compared with suitable published results (experimental, FEM, analytical and 3D elasticity) and then it is extended to analyze bi-axial and shear buckling of laminated composite rhombic hypar shells. A C⁰ finite element (FE) coding in FORTRAN is developed to generate many new results for different boundary conditions, skew angles, lamination schemes, etc. It is seen that the dimensionless buckling load of rhombic hypar increases with an increase in c/a ratio (curvature). Between symmetric and anti-symmetric laminations, the symmetric laminates have a relatively higher value of dimensionless buckling load. The dimensionless buckling load of the hypar shell increases with an increase in skew angle.

• Structural Engineering and Mechanics
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• v.69 no.1
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• pp.21-31
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• 2019

Optimizing composite structures to exploit their maximum potential is a realistic application with promising returns. In this research, simultaneous maximization of the fundamental frequency and frequency separation between the first two modes by optimizing the fiber angles is considered. A high-fidelity design optimization methodology is developed by combining the high-accuracy of finite element method with iterative improvement capability of metaheuristic algorithms. Three powerful nature-inspired optimization algorithms viz. a genetic algorithm (GA), a particle swarm optimization (PSO) variant and a cuckoo search (CS) variant are used. Advanced memetic features are incorporated in the PSO and CS to form their respective variants-RPSOLC (repulsive particle swarm optimization with local search and chaotic perturbation) and CHP (co-evolutionary host-parasite). A comprehensive set of benchmark solutions on several new problems are reported. Statistical tests and comprehensive assessment of the predicted results show CHP comprehensively outperforms RPSOLC and GA, while RPSOLC has a little superiority over GA. Extensive simulations show that the on repeated trials of the same experiment, CHP has very low variability. About 50% fewer variations are seen in RPSOLC as compared to GA on repeated trials.