• Steel and Composite Structures
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• 제24권6호
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• pp.697-709
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• 2017

The current study addresses the local buckling analysis of an infinite thin rectangular symmetrically laminated composite plate restrained by a tensionless Winkler foundation and subjected to uniform in-plane shear loading. An analytic method (i.e., one-dimensional mathematical method) is used to achieve the analytical solution estimate of the contact buckling coefficient. In addition, to study the effect of ply angle and foundation stiffness on the critical buckling coefficients for the laminated composite plates, the parametric studies are implemented. Moreover, the convergence for finite element (FE) mesh is analysed, and then the examples in the parametric study are validated by the FE analysis. The results show that the FE analysis has a good agreement with the analytical solutions. Finally, an example with the analytical solution and FE analysis is presented to demonstrate the availability and feasibility of the presented analytical method.

• 한국강구조학회 논문집
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• 제15권2호
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• pp.97-107
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• 2003

복합재료 적층판의 보다 정확한 해석결과를 얻기 위해서는 종방향 전단변형, 종방향 수직 변형률/응력에 의한 효과와 두께방향좌표에 관한 면내변위의 비선형 변화등이 고려되어야 한다. 본 연구에서는 3차원 고차이론을 이용하여 복합적층판의 좌굴하중 및 고유진동수를 구하였다. 단순지지된 적층판과 샌드위치의 해는 이중삼각함수형태의 Fourier 급수로 변환한 Navier 해법을 사용하였고, 일차전단변형, 고차전단변형이론에 의한 결과와 비교 분석하였다. 본 연구는 매개변수 즉, 보강각도, 적층수와 배열조건, 폭-두께비, 형상비의 변화에 따른 수치 해석 결과를 제시하였다.

• Structural Engineering and Mechanics
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• 제3권2호
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• pp.121-133
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• 1995

It is well known that two-dimensional simplified third-order theories satisfy the layer interface continuity of transverse shear strains, thus these theories violate the continuity of transverse shear stresses when two consecutive layers differ either in fibre orientation or material. The third-order theories considered herein involve four/or five dependent unknowns in the displacement field and satisfy the condition of vanishing of transverse shear stresses at the bounding planes of the plate. The objective of this investigation is to examine (i) the flexural response prediction accuracy of these third-order theories compared to exact elasticity solution (ii) the effect of layer interface continuity conditions on the flexural response. To investigate the effect of layer interface continuity conditions, three-dimensional elasticity solutions are developed by enforcing the continuity of different combinations of transverse stresses and/or strains at the layer interfaces. Three dimensional twenty node solid finite element (having three translational displacements as degrees of freedom) without the imposition of any of the conditions on the transverse stresses and strains is also employed for the flexural analysis of the laminated plates for the purposes of comparison with the above theories. These shear deformation theories and elasticity approaches in terms of accuracy, adequacy and applicability are examined through extensive numerical examples.

• Steel and Composite Structures
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• 제21권4호
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• pp.883-919
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• 2016

In this research, buckling analysis of an embedded laminated composite plate is investigated. The elastic medium is simulated with spring constant of Winkler medium and shear layer. With considering higher order shear deformation theory (Reddy), the total potential energy of structure is calculated. Using Principle of Virtual Work, the constitutive equations are obtained. The analytical solution is performed in order to obtain the buckling loads. A detailed parametric study is conducted to elucidate the influences of the layer numbers, orientation angle of layers, geometrical parameters, elastic medium and type of load on the buckling load of the system. Results depict that the highest buckling load is related to the structure with angle-ply orientation type and with increasing the angle up to 45 degrees, the buckling load increases.

• 대한기계학회논문집
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• 제17권7호
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• pp.1686-1699
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• 1993

In this paper, the thermal buckling of thick composite angle-ply laminates subject to uniform temperature distribution is studied. For the plates of 4-edges simply supported condition and those of 4-edges clamped condition, the critical buckling temperatue is derived, using tile finite element method based on the shear deformation theory. The effects of lamination angle, layer number, laminate thickness, plate aspect ratio and boundary constraints upon the critical buckling temperature are presented.

• Structural Engineering and Mechanics
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• 제40권2호
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• pp.257-277
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• 2011

In this paper the geometrically nonlinear continuum plate finite element model, hitherto not reported in the literature, is developed using the total Lagrange formulation. With the layerwise displacement field of Reddy, nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. By performing the linearization on nonlinear integral form and then the discretization on linearized integral form, tangent stiffness matrix is obtained with less manipulation and in more consistent form, compared to the one obtained using laminated element approach. Symmetric tangent stiffness matrixes, together with internal force vector are then utilized in Newton Raphson's method for the numerical solution of nonlinear incremental finite element equilibrium equations. Despite of its complex layer dependent numerical nature, the present model has no shear locking problems, compared to ESL (Equivalent Single Layer) models, or aspect ratio problems, as the 3D finite element may have when analyzing thin plate behavior. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the author's previous papers.

• Structural Engineering and Mechanics
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• 제67권6호
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• pp.617-628
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• 2018

This paper deals with the maximization of the critical buckling load of simply supported antisymmetric angle-ply plates resting on Pasternak foundation subjected to compressive loads using teaching learning based optimization method (TLBO). The first order shear deformation theory is used to obtain governing equations of the laminated plate. In the present optimization problem, the objective function is to maximize the buckling load factor and the design variables are the fibre orientation angles in the layers. Computer programming is developed in the MATLAB environment to estimate optimum stacking sequences of laminated plates. A comparison also has been performed between the TLBO, genetic algorithm (GA) and differential evolution algorithm (DE). Some examples are solved to show the applicability and usefulness of the TLBO for maximizing the buckling load of the plate via finding optimum stacking sequences of the plate. Additionally, the influences of different number of layers, plate aspect ratios, foundation parameters and load ratios on the optimal solutions are investigated.

• 한국강구조학회 논문집
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• 제18권2호
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• pp.161-171
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• 2006

본 논문은 고정과 자유 경계의 다양한 조합을 갖는 직사각형 복합적층판의 고유진동에하고 있다. 본 연구에서는 수학적으로 완전한 특성직교다항식으로 표현되는 근사변위와 Ritz법을 이용하여 Lagrange 범함수의 정상값을 구하였다. 3차원 모델의 정확성이 무차원 진동수의 수렴도를 검토하여 이루어졌으며, 또한 기존 문헌상의 해석결과와의 비교를 통하여 진동수의 정확성을 검토하였다. 본 논문에서 제시된 3차원 진동수의 결과를 이용하여 복합적층판의 기하 및 재료에 관한 매개변수 즉, 형상비(${\mathcal{a/b}}$), 폭두께비(${\mathcal{a/h}}$), 재료의 직교이방성, 플라이 수(${\mathcal{N}}$), 섬유배향각(${\theta}$) 및 적층순서가 미치는 효과를 설명하였다.

• Steel and Composite Structures
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• 제17권1호
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• pp.1-19
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• 2014

Buckling and vibration characteristics of circular laminated plates under in-plane edge loads and resting on Winkler-type foundation are solved by the Ritz method. Inclusive numerical data are presented for the first three eigen-frequencies as a function of in-plane load for different classical edge conditions. Moreover, the effects of fiber orientation on the natural frequencies and critical buckling loads of laminated angle-ply plates with stacking sequence of $[({\beta}/-{\beta}/{\beta}/-{\beta})]_s$, are studied. Also, selected deformation mode shapes are illustrated. The correctness of results is established using finite element software as well as by comparison with the existing results in the literature.

• Steel and Composite Structures
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• 제22권6호
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• pp.1261-1280
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• 2016

We study chaotic motion in a nonlinear laminated composite plate under subsonic fluid flow and a simultaneous external load in this paper. We derive equations of motion of the plate using the von-$K{\acute{a}}rm{\acute{a}}n^{\prime}s$ hypothesis and the Hamilton's principle. Galerkin's approach is adopted as the solution method. We then conduct a divergence analysis to obtain critical velocities of the transient flow. Melnikov's integral approach is used to find the critical parameters in which chaos takes place. Effects of different parameters including the aspect ratio, plate material and the ply angle in laminates on the critical flow speed are investigated. In a parametric study, we show that how the linear and nonlinear stiffness of the plate and the load frequency and amplitude would influence the chaotic behavior of the plate.