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Seungeock Kim - One of the best experts on this subject based on the ideXlab platform.
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levy type solution for free vibration analysis of Orthotropic Plates based on two variable refined plate theory
Applied Mathematical Modelling, 2012Co-Authors: Huu-tai Thai, Seungeock KimAbstract:Abstract Closed-form solutions for free vibration analysis of Orthotropic Plates are obtained in this paper based on two variable refined plate theory. The theory, which has strong similarity with classical plate theory in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Equations of motion are derived from the Hamilton’s principle. The closed-form solutions of rectangular Plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions are obtained by applying the state space approach to the Levy-type solution. Comparison studies are performed to verify the validity of the present results. The effects of boundary condition, and variations of modulus ratio, aspect ratio, and thickness ratio on the natural frequency of Orthotropic Plates are investigated and discussed in detail.
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analytical solution of a two variable refined plate theory for bending analysis of Orthotropic levy type Plates
International Journal of Mechanical Sciences, 2012Co-Authors: Huu-tai Thai, Seungeock KimAbstract:Abstract This paper presents analytical solutions of deflection and stress for Orthotropic Plates using a two variable refined plate theory. The theory accounts for parabolic variation of transverse shear stress through the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factor. Additional features of the theory are that it has strong similarity with classical plate theory in many aspects, and the number of involved variables is only two as against three in case of other shear deformation theories. The Levy-type solution procedure in conjunction with the state space concept is used to determine the closed-form solutions for Orthotropic rectangular Plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions. Comparison studies are performed to verify the validity of the present results. Finally, the effects of thickness ratio, modulus ratio and aspect ratio on the deflection and stress of Orthotropic Plates are investigated and discussed.
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levy type solution for buckling analysis of Orthotropic Plates based on two variable refined plate theory
Composite Structures, 2011Co-Authors: Huu-tai Thai, Seungeock KimAbstract:Abstract This paper presents closed-form solution for buckling analysis of Orthotropic Plates using two variable refined plate theory. The theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Governing equations are derived from the principle of minimum total potential energy. The closed-form solutions of rectangular Plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions are obtained by applying the state space approach to the Levy-type solution. Comparison studies are performed to verify the validity of the present results. The effects of boundary condition, loading condition, and variations of modulus ratio, aspect ratio, and thickness ratio on the critical buckling load of Orthotropic Plates are investigated and discussed in detail.
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BUCKLING ANALYSIS OF Plates USING THE TWO VARIABLE REFINED PLATE THEORY
Thin-Walled Structures, 2009Co-Authors: Seungeock Kim, Huu-tai Thai, Jaehong LeeAbstract:Buckling analysis of isotropic and Orthotropic Plates using the two variable refined plate theory is presented in this paper. The theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to in-plane loading has been obtained by using the Navier method. Numerical results obtained by the present theory are compared with classical plate theory solutions, first-order shear deformable theory solutions, and available exact solutions in the literature. It can be concluded that the present theory, which does not require shear correction factor, is not only simple but also comparable to the first-order shear deformable theory.
Huu-tai Thai - One of the best experts on this subject based on the ideXlab platform.
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isogeometric simulation for buckling free and forced vibration of Orthotropic Plates
International Journal of Applied Mechanics, 2013Co-Authors: N Valizadeh, Huu-tai Thai, Tinh Quoc Bui, Minh NguyenAbstract:Buckling, free and forced vibration analyses of Orthotropic Plates are studied numerically using Isogeometric analysis. The present formulation is based on the classical plate theory (CPT) while the NURBS basis function is employed for both the parametrization of the geometry and the approximation of plate deflection. An efficient and easy-to-implement technique is used for imposing the essential boundary conditions. Numerical examples for free and forced vibration and buckling of Orthotropic Plates with different boundary conditions and configurations are considered. The numerical results are compared with other existing solutions to show the efficiency and accuracy of the proposed approach for such problems.
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levy type solution for free vibration analysis of Orthotropic Plates based on two variable refined plate theory
Applied Mathematical Modelling, 2012Co-Authors: Huu-tai Thai, Seungeock KimAbstract:Abstract Closed-form solutions for free vibration analysis of Orthotropic Plates are obtained in this paper based on two variable refined plate theory. The theory, which has strong similarity with classical plate theory in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Equations of motion are derived from the Hamilton’s principle. The closed-form solutions of rectangular Plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions are obtained by applying the state space approach to the Levy-type solution. Comparison studies are performed to verify the validity of the present results. The effects of boundary condition, and variations of modulus ratio, aspect ratio, and thickness ratio on the natural frequency of Orthotropic Plates are investigated and discussed in detail.
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analytical solution of a two variable refined plate theory for bending analysis of Orthotropic levy type Plates
International Journal of Mechanical Sciences, 2012Co-Authors: Huu-tai Thai, Seungeock KimAbstract:Abstract This paper presents analytical solutions of deflection and stress for Orthotropic Plates using a two variable refined plate theory. The theory accounts for parabolic variation of transverse shear stress through the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factor. Additional features of the theory are that it has strong similarity with classical plate theory in many aspects, and the number of involved variables is only two as against three in case of other shear deformation theories. The Levy-type solution procedure in conjunction with the state space concept is used to determine the closed-form solutions for Orthotropic rectangular Plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions. Comparison studies are performed to verify the validity of the present results. Finally, the effects of thickness ratio, modulus ratio and aspect ratio on the deflection and stress of Orthotropic Plates are investigated and discussed.
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levy type solution for buckling analysis of Orthotropic Plates based on two variable refined plate theory
Composite Structures, 2011Co-Authors: Huu-tai Thai, Seungeock KimAbstract:Abstract This paper presents closed-form solution for buckling analysis of Orthotropic Plates using two variable refined plate theory. The theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Governing equations are derived from the principle of minimum total potential energy. The closed-form solutions of rectangular Plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions are obtained by applying the state space approach to the Levy-type solution. Comparison studies are performed to verify the validity of the present results. The effects of boundary condition, loading condition, and variations of modulus ratio, aspect ratio, and thickness ratio on the critical buckling load of Orthotropic Plates are investigated and discussed in detail.
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BUCKLING ANALYSIS OF Plates USING THE TWO VARIABLE REFINED PLATE THEORY
Thin-Walled Structures, 2009Co-Authors: Seungeock Kim, Huu-tai Thai, Jaehong LeeAbstract:Buckling analysis of isotropic and Orthotropic Plates using the two variable refined plate theory is presented in this paper. The theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to in-plane loading has been obtained by using the Navier method. Numerical results obtained by the present theory are compared with classical plate theory solutions, first-order shear deformable theory solutions, and available exact solutions in the literature. It can be concluded that the present theory, which does not require shear correction factor, is not only simple but also comparable to the first-order shear deformable theory.
Tomas Nordstrand - One of the best experts on this subject based on the ideXlab platform.
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on buckling loads for edge loaded Orthotropic Plates including transverse shear
Composite Structures, 2004Co-Authors: Tomas NordstrandAbstract:Abstract Corrugated board usually exhibits low transverse shear stiffness, especially across the corrugations. In the present study the transverse shear is included in an analysis to predict the critical buckling load of an edge-loaded Orthotropic linear elastic sandwich plate with all edges simply supported. In the analysis, effective (homogenised) properties of the corrugated core are used. Classical elastic buckling theory of Orthotropic sandwich Plates predicts that such Plates have a finite buckling coefficient when the aspect ratio, i.e. the ratio between the height and width of the plate, becomes small. However, inclusion in the governing equilibrium equations of the additional moments, produced by the membrane stresses in the plate at large transverse shear deformations, gives a buckling coefficient which approaches infinity when the aspect ratio goes to zero. This improvement was first included in the buckling theory of helical springs by Harinx [Proc. Konjlike Nederland Akademie Wettenschappen, vol. 45, 1942, Amsterdam, Holland, pp. 533–539, 650–654] and later applied to Orthotropic Plates by Bert and Chang [J. Eng. Mech. Division, Proc. Am. Soc. Civil Engrs. 98 (EM6) (1972) 1499–1509]. Some inconsistencies in the latter analysis have been considered. The critical buckling load calculated with corrected analysis is compared with a predicted load obtained using finite element analysis of a corrugated board panel, and also with the critical buckling load obtained from panel compression tests.
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Analysis and testing of corrugated board panels into the post-buckling regime
Composite Structures, 2004Co-Authors: Tomas NordstrandAbstract:Abstract Testing of the load bearing capacity of corrugated board boxes is often associated with uncertainties, e.g. the creases along the edges of the side panels introduce eccentricities. An alternative to the testing of boxes is therefore attractive. One suggestion is testing of panels. However, panels are sensitive to the boundary conditions. A panel compression test (PCT-) rig, similar to a test frame for metal Plates designed by A.C. Walker, was therefore built to achieve accurately defined load and boundary conditions. The PCT-rig furnishes simply supported boundary conditions, i.e. the edges of the panel are prevented from moving out-of-plane without any rotational restraint. The edges are also free to move in-plane. In order to describe the buckling behaviour, a non-linear buckling analysis of Orthotropic Plates, derived by Rhodes and Harvey, was modified to include initial imperfections. The critical buckling load of the panels was evaluated by fitting the analytical expression by non-linear regression to experimentally measured load–displacement curves. The results show a difference in the order of 15–20% between experimentally estimated critical buckling load and the analytically predicted critical buckling load for Orthotropic Plates. This is mainly attributed to transverse shear deformations. A corresponding difference was observed between analytically predicted and experimentally measured load–displacement curves at large out-of-plane deformation, i.e. twice or three times the board thickness. This is probably caused by the non-linear response of paper at high stresses and local buckling of the panel facings, i.e. the liners. A predicted failure load of the corrugated board panel was determined when stresses in the facings reached the Tsai–Wu failure criterion. The predicted failure load and measured average experimental failure load were close, indicating that collapse of the panel is triggered by material failure of one of the liners.
Sigong Zhang - One of the best experts on this subject based on the ideXlab platform.
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new exact series solutions for transverse vibration of rotationally restrained Orthotropic Plates
Applied Mathematical Modelling, 2019Co-Authors: Sigong ZhangAbstract:Abstract The exact series solutions of Plates with general boundary conditions have been derived by using various methods such as Fourier series expansion, improved Fourier series method, improved superposition method and finite integral transform method. Although the procedures of the methods are different, they are all Fourier-series based analytical methods. In present study, the foregoing analytical methods are reviewed first. Then, an exact series solution of vibration of Orthotropic thin plate with rotationally restrained edges is obtained by applying the method of finite integral transform. Although the method of finite integral transform has been applied for vibration analysis of Orthotropic Plates, the existing formulation requires of solving a highly non-linear equation and the accuracy of the corresponding numerical results can be questionable. For that reason, an alternative formulation was proposed to resolve the issue. The accuracy and convergence of the proposed method were studied by comparing the results with other exact solutions as well as approximate solutions. Discussions were made for the application of the method of finite integral transform for vibration analysis of Orthotropic thin Plates.
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Free Transverse Vibration of Rectangular Orthotropic Plates with Two Opposite Edges Rotationally Restrained and Remaining Others Free
'MDPI AG', 2018Co-Authors: Yuan Zhang, Sigong ZhangAbstract:Many types of engineering structures can be effectively modelled as Orthotropic Plates with opposite free edges such as bridge decks. The other two edges, however, are usually treated as simply supported or fully clamped in current design practice, although the practical boundary conditions are intermediate between these two limiting cases. Frequent applications of Orthotropic Plates in structures have generated the need for a better understanding of the dynamic behaviour of Orthotropic Plates with non-classical boundary conditions. In the present study, the transverse vibration of rectangular Orthotropic Plates with two opposite edges rotationally restrained with the remaining others free was studied by applying the method of finite integral transforms. A new alternative formulation was developed for vibration analysis, which provides much easier solutions. Exact series solutions were derived, and the excellent accuracy and efficiency of the method are demonstrated through considerable numerical studies and comparisons with existing results. Some new results have been presented. In addition, the effect of different degrees of rotational restraints on the mode shapes was also demonstrated. The present analytical method is straightforward and systematic, and the derived characteristic equation for eigenvalues can be easily adapted for broad applications
Qinghui Liu - One of the best experts on this subject based on the ideXlab platform.
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buckling analysis of restrained Orthotropic Plates under combined in plane shear and axial loads and its application to web local buckling
Composite Structures, 2014Co-Authors: Qinghui Liu, Pizhong Qiao, Xingwen GuoAbstract:Abstract Buckling analysis of Orthotropic Plates with two opposite edges simply supported and the other two opposite edges rotationally-restrained (RR) and under combined uniform in-plane shear and linearly varying axial loads is presented, and its application to web local buckling of composite structural shapes is illustrated. A new plate buckled displacement shape function is proposed, and the approximate solution is obtained by the Rayleigh–Ritz method. The accuracy of analytical solution is validated with the numerical finite element analysis, and excellent agreements are achieved. A parametric study is conducted to evaluate the influence of loading ratio and rotational restraint stiffness. By introducing generic non-dimensional parameters, the buckling formulas of long Plates under uniform in-plane compression, pure in-plane bending and uniform in-plane shear are obtained using the curve fitting technique. Interaction curves between the uniform in-plane shear and pure in-plane bending for the simply supported (SS) and clamped-simply supported (CS) Plates are established, and it is found that the interaction curve is only related to the material Orthotropic parameter of β . Finally, the proposed discrete restrained plate solution is applied to predict the web local buckling of FRP shapes by adopting the proper rotational restraint stiffness.