• Structural Engineering and Mechanics
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• 제43권2호
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• pp.253-271
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• 2012

To analyze the bending and transverse shear effects of laminated composite plates, a thirteen nodes triangular element will be presented. The suggested formulations consider a parabolic variation of the transverse shear strains through the thickness. As a result, there is no need to use shear correction coefficients in computing the shear stresses. The proposed element can model both thin and thick plates without any problems, such as shear locking and spurious modes. Moreover, the effectiveness of $w_{,n}$, as an independent degree of freedom, is concluded by the present study. To perform the accuracy tests, several examples will be solved. Numerical results for the orthotropic materials with different boundary conditions, shapes, number of layers, thickness ratios and fiber orientations will be presented. The suggested element calculates the deflections and stresses more accurate than those available in the literature.

• Wind and Structures
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• 제27권4호
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• pp.235-245
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• 2018

In this study the stress analysis of orthotropic thin plate with arbitrary shapes for different boundary conditionsis investigated. Meshfreemethod is applied to static analysis of thin plates with various geometries based on the Kirchhoff classical plate theory. According to the meshfree method the domain of the plates are expressed through a set of nodes without using mesh. In this method, a set of nodes are defined in a standard rectangular domain, then via a third order map, these nodes are transferred to the main domain of the original geometry; therefore the analysis of the plates can be done. Herein, Meshless local Petrov-Galerkin (MLPG) as a meshfree numerical method is utilized. The MLS function in MLPG does not satisfy essential boundary conditions using Delta Kronecker. In the MLPG method, direct interpolation of the boundary conditions can be applied due to constructing node by node of the system equations. The detailed parametric study is conducted, focusing on the arbitrary geometries of the thin plates. Results show that the meshfree method provides better accuracy rather than finite element method. Also, it is found that trend of the figures have good agreement with relevant published papers.

• 대한기계학회논문집
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• 제18권6호
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• pp.1520-1534
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• 1994

A new analytical method for the prediction of the buckling behavior of laminated plates consisting of layers having different properties in tension and compression, so called bimodulus, is proposed in this paper. Buckling analysis of bimodular composite laminated paltes are performed with the results reduced from plate bending analysis. The governing equations of bimodular plates are based on the first shear deformation theory. As a case study, bending and buckling of simply supported, multilayered, symmetric, antisymmtric, and specially orthotropic laminates under uniformly distributed lateral load for bending analysis and in-plane load for buckling are considered. The results of the bending analysis are compared with the previous papers. Then, the fundamental critical buckling loads and buckling modes are calculated for the various bimodular composite rectangular thin plates.

• 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.

• 복합신소재구조학회 논문집
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• 제3권1호
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• pp.21-28
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• 2012

이 연구에서는 직교이방성 판의 좌굴 및 직교이방성 판요소로 구성된 구조용 압축재의 국부좌굴에 대한 해석적 연구를 수행하였다. 섬유보강 폴리머 플라스틱 재료는 높은 비강도 및 비강성, 높은 부식저항성, 경량성 등 강재나 콘크리트와 비교해서 많은 장점을 가지고 있다. 특히, 펄트루젼 생산 방식은 섬유보강 폴리머 플라스틱 재료의 여러가지 생산방법 중 구조용 플라스틱 부재를 대량으로 생산하기에 가장 적합한 방법이다. 펄트루젼 생산방식은 부재의 축을 따라 주요 보강섬유가 배치되기 때문에 이 재료는 직교이방성으로 간주된다. 그러나, 펄트루젼 섬유보강 플라스틱 부재는 낮은 탄성을 갖고 있고 얇은 판요소로 구성되어 있기 때문에 압축하중이 재하될 경우 좌굴이 발생할 수 있다. 따라서, 이 부재를 설계하는데 안정성은 매우 중요한 문제가 된다. 이 연구에서는 기존의 연구를 따라서 직교이방성 판 및 직교이방성 판요소로 구성된 압축재의 국부좌굴에 대하여 검토하였으며, 국내에서 생산된 직교이방성 판요소로 구성된 압축재의 국부좌굴강도를 계산하였다.

• Computers and Concrete
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• 제25권6호
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• pp.537-549
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• 2020

Geometrically nonlinear axisymmetric bending analysis of shear deformable circular plates on a nonlinear three-parameter elastic foundation was made. Plates ranging from "thin" to "moderately thick" were investigated for three types of material: isotropic, transversely isotropic, and orthotropic. The differential equations were discretized by means of the finite difference method (FDM) and the differential quadrature method (DQM). The Newton-Raphson method was applied to find the solution. A parametric investigation using seven unknowns per node was presented. The novelty of the paper is that detailed numerical simulations were made to highlight the combined effects of the material properties and the boundary conditions on (i) the deflection, (ii) the stress resultants, and (iii) the external load. The formulation was verified through comparison studies. It was observed that the results are highly influenced from the boundary conditions, and from the material properties.

• Steel and Composite Structures
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• 제29권3호
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• pp.333-348
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• 2018

An analytical method is developed for analysing the contact buckling response of infinitely long, thin corrugated plates and flat plates restrained by a Winkler tensionless foundation and subjected to linearly varying in-plane loadings, where the corrugated plates are modelled as orthotropic plates and the flat plates are modelled as isotropic plates. The critical step in the presented method is the explicit expression for the lateral buckling mode function, which is derived through using the energy method. Simply supported and clamped edges conditions on the unloaded edges are considered in this study. The acquired lateral deflection function is applied to the governing buckling equations to eliminate the lateral variable. Considering the boundary conditions and continuity conditions at the border line between the contact and non-contact zones, the buckling coefficients and the corresponding buckling modes are found. The analytical solution to the buckling coefficients is also expressed through a fitted approximate formula in terms of foundation stiffness, which is verified through previous studies and finite element (FE) method.

• Structural Engineering and Mechanics
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• 제70권4호
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• pp.445-455
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• 2019

Since the days of yore, plate's flexural analysis and formulation were dependent on the assumed coordinate system. In uncovering the coordinates-independent flexural interpretation, in this study, the plate bending analysis has been interpreted in terms of the tensor's components of curvatures and bending moments, in accordance with the continuum mechanics. The paper herein presents the theoretical formulations and conceptual perspectives of the Hydrostatic Method of Analysis (HM) that combines the continuum mechanics with the elasticity theory; the graphical statics and analysis; the theory of thin isotropic and orthotropic plates.

• Structural Engineering and Mechanics
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• 제77권6호
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• pp.765-777
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• 2021

Recently, the plate bending analysis has been interpreted in terms of the tensor's components of curvatures and bending moments by presenting the conceptual perspectives of the Hydrostatic Method of Analysis (HM) and theoretical formulations that combine the continuum mechanics with the graphical statics analysis, the theory of thin orthotropic and isotropic plates, and the elasticity theory. In pursuance of uncovering a genuine formulation of the plate's flexural differential equations, that possess the general-covariance and coordinates-independency. This study had then, tackled various natural and structural problems in both solid and fluid branches of the continuum mechanics in a description of such theoretical and conceptual attainment in uncovering the dimensional independent diffeomorphism covariant partial differential laws.

• 한국강구조학회 논문집
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• 제18권3호
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• pp.289-299
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• 2006

강바닥판 교량은 비교적 얇은 강판을 서로 용접에 의해 연결한 구조물로서 많은 양의 용접을 피할 수 없다. 강바닥판의 횡리브복부판에서는 전단력과 비틀림 모멘트가 작용하는 동시에 종리브의 비틀림으로 인한 면내 면외 변형이 작용하기 때문에 종리브-횡리브 복부판-데크플레이트 교차부 및 횡리브복부판 컷아웃(슬릿)부에서 응력집중 현상이 두드러지게 발생하게 된다. 본 논문에서는 교차부 및 컷아웃(슬릿)부에서의 응력집중 현상 완화 및 피로성능 개선에 유리한 구조상세를 도출하고자 교차부에 스캘럽 유무 및 횡리브 복부판면과 일치되도록 종리브 내부에 설치하는 다이아프램의 설치 유무를 매개변수로 구조해석을 수행하였다. 다이아프램을 설치하는 동시에 교차부에 스캘럽을 두지 않을 경우 교차부 및 컷아웃(슬릿)부에서 최대응력 감소효과가 있음을 알 수 있었다. 따라서 교차부 및 컷아웃부에서의 응력집중 현상을 완화시켜 피로성능 개선에 기대효과가 있음을 알 수 있었다.