• Structural Engineering and Mechanics
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• v.68 no.6
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• pp.639-646
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• 2018

The aim of the present paper deals with free vibration analysis of laminated composite skew plates with single and multiple cut-outs. For complete understanding of the dynamic behavior of laminated skew plates with cut-out a numerical analysis has been carried out by developing a computer code in FOTRAN. Special attention is drawn on the formulation of mass matrix by considering effect of rotary inertia. The results obtained by the finite element formulation using nine noded isoparametric plate bending element are validated by comparing the results from relevant published literature. Few new results on laminated skew plates with cut-out have been presented.

• Structural Engineering and Mechanics
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• v.17 no.6
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• pp.751-766
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• 2004

This paper extends the use of the hierarchic degenerated shell element to geometric non-linear analysis of composite laminated skew plates by the p-version of the finite element method. For the geometric non-linear analysis, the total Lagrangian formulation is adopted with moderately large displacement and small strain being accounted for in the sense of von Karman hypothesis. The present model is based on equivalent-single layer laminate theory with the first order shear deformation including a shear correction factor of 5/6. The integrals of Legendre polynomials are used for shape functions with p-level varying from 1 to 10. A wide variety of linear and non-linear results obtained by the p-version finite element model are presented for the laminated skew plates as well as laminated square plates. A numerical analysis is made to illustrate the influence of the geometric non-linear effect on the transverse deflections and the stresses with respect to width/depth ratio (a/h), skew angle (${\beta}$), and stacking sequence of layers. The present results are in good agreement with the results in literatures.

• Journal of the Korean Society for Advanced Composite Structures
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• v.1 no.4
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• pp.28-34
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• 2010

W e performed a geometrical nonlinear dynamic analysis 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 skew angles and layup 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 and skew plates, and the new results reported in this paper show the significant interactions between the skew angle and layup sequence in the skew laminate. Key observation points are discussed and a brief design guideline is given.

• 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.

• 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.25 no.2
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• pp.161-180
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• 2007

A first endeavor is made to exploit the differential quadrature method (DQM) as a simple, accurate, and computationally efficient numerical tool for the large deformation analysis of thin laminated composite skew plates, which has very strong singularity at the obtuse vertex. The geometrical nonlinearity is modeled by using Green's strain and von Karman assumption. A recently developed DQ methodology is used to exactly implement the multiple boundary conditions at the edges of skew plates, which is a major draw back of conventional DQM. Using oblique coordinate system and the DQ methodology, a mapping-DQ discretization rule is developed to simultaneously transform and discretize the equilibrium equations and the related boundary conditions. The effects of skew angle, aspect ratio and different types of boundary conditions on the convergence and accuracy of the presented method are studied. Comparing the results with the available results from other numerical or analytical methods, it is shown that accurate results are obtained even when using only small number of grid points. Finally, numerical results for large deflection behavior of antisymmetric cross ply skew plates with different geometrical parameters and boundary conditions are presented.

• Steel and Composite Structures
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• v.28 no.4
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• pp.509-516
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• 2018

The differential quadrature (DQ) and teaching-learning based optimization (TLBO) methods are coupled to introduce a hybrid numerical method for maximizing fundamental natural frequency of laminated composite skew plates. The fiber(s) orientations are selected as design variable(s). The first-order shear deformation theory (FSDT) is used to obtain the governing equations of the plate. The equations of motion and the related boundary conditions are discretized in space domain by employing the DQ method. The discretized equations are transferred from the time domain into the frequency domain to obtain the fundamental natural frequency. Then, the DQ solution is coupled with the TLBO method to find the maximum frequency of the plate and its related optimum stacking sequences of the laminate. Convergence and applicability of the proposed method are shown and the optimum fundamental frequency parameter of the plates with different skew angle, boundary conditions, number of layers and aspect ratio are obtained. The obtained results can be used as a benchmark for further studies.

• Journal of the Korea institute for structural maintenance and inspection
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• v.8 no.2
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• pp.147-158
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• 2004

For stiffened plates composed of composite materials, many researchers have used a finite element method which connected isoparametric plate elements and beam elements. However, the finite element method is difficult to reflect local behavior of stiffener because beam elements are transferred stiffness for nodal point of plate elements, especially the application is limited in case of laminated composite structures. In this paper, for analysis of laminated composite stiffened plates, 3D shell elements for stiffener and plate are employed. Reissner-Mindlin's first order shear deformation theory is considered in this study. But when thickness will be thin, isoparamatric plate bending element based on the theory of Reissner-Mindlin is generated by transverse shear locking. To eliminate the shear locking and virtual zero energy mode, the substitute shear strain field is used. A deflection distribution is investigated for simple supported rectangular and skew stiffened laminated composite plates with arbitrary orientation stiffener as not only variation of slenderness and aspect ratio of the plate but also variation of skew angle of skew stiffened plates.

• 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.

• Journal of Korean Society of Steel Construction
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• v.12 no.3 s.46
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• pp.291-302
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• 2000

In recent years the development of high modulus, high strength and low density boron and graphite fibers bonded together has brought renewed interestes in structural elements. When a plate with arbitrarily oriented layers and clamped boundary conditions is subjected to uniform loading, it is difficult to analyze and apply, compared with isotropic and orthotropic cases. Therefore the numerical methods, such as finite difference method or finite element method, should be emloyed to analyse such problems. In this study the finite difference technique is used to formulate the bending analysis of symmetric composite laminated skew plates. When this technique is used to solve the problem, it is desirable to reduce the order of the derivatives in order to minimize the number of the pivotal points involved in each equation. The 4th order partial differential equations of laminated skew plates are converted to an equivalent three of 2nd order partial differential equations with three dependant variables.