• Journal of the Korean Society of Safety
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• v.18 no.1
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• pp.19-27
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• 2003

This paper presented an experimental modal analysis of clamped perforated rectangular plates submerged in water. The penetration of holes in the plates had a triangular pattern with P/D (pitch to diameter) 1.750, 2.125, 2.500, 3.000 and 3.750. The natural frequencies of the perforated plates in air were obtained by the Rayleigh-Ritz method and compared with the experimental results. Good agreement was obtained between the analytical solution and experimental result. The experimental results in water showed that the mode shapes are not sensitive to the depth of submergence. The natural frequencies were shown to decrease drastically once the perforated plates come in contact with water. However, the natural frequencies decrease with the depth of submergence until a certain depth is reached, and become the asymptotic values beyond this depth of submergence. The depth of submergence did not affect the damping ratio greatly.

• Steel and Composite Structures
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• v.19 no.4
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• pp.897-916
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• 2015

A procedure for critical buckling moment of a tapered beam is proposed with the application of potential energy calculations using Ritz method. Respective solution allows to obtain critical moments initiating lateral buckling of the simply supported, modestly tapered steel I-beams. In particular, lateral-torsional buckling of beams with simultaneously tapered flanges and the web are considered. Detailed, numerical, parametric analyses are carried out. Typical engineering, uniformly distributed design loads are considered for three cases of the load, applied to the top flange, shear centre, as well as to the bottom flange. In addition simply supported beam under gradient moments is investigated. The parametric analysis of simultaneously tapered beam flanges and the web, demonstrates that tapering of flanges influences much more the critical moments than tapering of the web.

• Korean Journal of Computational Design and Engineering
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• v.1 no.2
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• pp.107-121
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• 1996

An optimization procedure is proposed to determine the optimal stacking sequence on the buckling of laminated composite plates with midplane symmetry under various loading conditions. Classical lamination theory is used for the determination of the critical buckling load of simply supported angle-ply laminates. Analysis is performed by the Galerkin method and Rayleigh-Ritz method. The approximate solution of buckling is replaced by the algorithms that produce generalized eigenvalue problem. Direct search technique is employed to solve the optimization problem effectively. A series of computations is carried out for plates having different aspect ratios, different load ratios and different number of lay-ups.

• Steel and Composite Structures
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• v.2 no.5
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• pp.315-330
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• 2002

This paper proposes a model for analysing the non-linear behaviour of steel concrete composite beams prestressed by external slipping cables, taking into account the deformability of the interface shear connection. By assuming a suitable admissible displacement field for the composite beam, the balance condition is obtained by the virtual work principle. The solution is numerically achieved by approximating the unknown displacement functions as series of shape functions according to the Ritz method. The model is applied to real cases by showing the consequences of different connection levels between the concrete slab and the steel beam. Particular attention is focused on the limited ductility of the shear connection that may be the cause of premature failure of the composite girder.

• Structural Engineering and Mechanics
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• v.51 no.2
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• pp.333-347
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• 2014

Nonlinear bending of super-elliptical plates of uniform thickness under uniform transverse pressure was investigated by the Ritz method. The material was assumed to be homogeneous and isotropic. The contribution of the boundary conditions at the point supports was introduced by the Lagrange multipliers. The solution was obtained by the Newton-Raphson method. The influence of the location of the point supports on the central deflection was highlighted by sensitivity analysis. An approximate relationship between the central deflection and the super-elliptical power was obtained using the method of least squares. The critical points where the maximum deflection may develop, and the influence of nonlinearity were highlighted. The nonlinearity was found to be sensitive to the aspect ratio. The accuracy of the algorithm was validated by comparing the central deflection with the solutions of elliptical and rectangular plates.

• Structural Engineering and Mechanics
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• v.74 no.5
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• pp.577-588
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• 2020

A unified solution is presented for the buckling analysis of rectangular laminated composite plates with elastically restrained edges. The plate is subjected to biaxial in-plane compression, and the boundary conditions are simulated by employing uniform distribution of linear and rotational springs at all edges. The critical values of buckling loads and corresponding modes are calculated based on classical lamination theory and using the Ritz method. The deflection function is defined based on simple polynomials without any auxiliary function. The verifications of the current study are carried out with available combinations of classic boundary conditions in the literature. Through parametric study with a wide range of spring factors with some classical as well as some not classical boundary conditions, competency of the present model of boundary conditions is proved.

• Journal of Korean Society of Steel Construction
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• v.8 no.3 s.28
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• pp.55-65
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• 1996

For stability analysis of stifened rectangular thin plates with various boundary conditions, Ritz method is presented. An energy method is especially useful in those cases where a rigorous solution of the diferential eqution is unknown or where we have a plate reinforced by stiffeners and it is required to find only an approximate value of the critical load. The strain energy due to the plate bending and the work done by the in-plane forces are taken into account in order to apply the principle of the minimum potential energy. The buckling mode shapes of flexural beams with various boundary conditions are derived, and shape functions consistent with the given boundary conditions in the two orthogonal directions are chosen from those displacement functions of beams. The matrix equations for stability of stiffened rectangular thin plates are determined from the stationary condition of the total potential energy. Numerical example for stability behaviors of horizontally and vertically stiffened plates subjected to uniform compression, bending and shear loadings are presented and the obtained results are compared with other researchers' results.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.401-408
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• 2001

The main objective of this study is to analyze the distortion of curved steel box girders. For the distortional analysis of steel box girders, two approaches are presented. One is the development of approximate formulas obtained by applying Ritz method. The other is the formulation of stiffness matrix which is derived from the exact solution of the differential equation for distortion. Distortional analysis is carried out by utilizing 3-dimensional elements of a structural analysis computer program (SAP2000). The present analysis focuses on the distortional stress and the effects of the diaphragm. The results of several example cases are compared with those by the Nakai, Sakai, Heins, and Oleinik's theory and get the effect of diaphragm spacing on the distortional warping stress of the curved steel box girder.

• Structural Engineering and Mechanics
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• v.40 no.5
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• pp.689-703
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• 2011

A new perturbation method is introduced to study the undamped free vibration of a non-prismatic Timoshenko beam for its natural frequencies and vibration modes. For simplicity, the natural modes of vibration of its corresponding prismatic Euler-Bernoulli beam with the same length and boundary conditions are used as Ritz base functions with necessary modifications to account for shear strain in the Timoshenko beam. The new method can transform two coupled partial differential equations governing the transverse vibration of the non-prismatic Timoshenko beam into a set of nonlinear algebraic equations. It significantly simplifies the solution process and is applicable to non-prismatic beams with various boundary conditions. Three examples indicated that the new method is more accurate than the previous perturbation methods. It successfully takes into account the effect of shear deformation of Timoshenko beams particularly at the free end of cantilever structures.

• Journal of the Korean Society of Safety
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• v.13 no.3
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• pp.163-170
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• 1998

The differential quadrature method (D.Q.M.) is applied to computation of eigenvalues of small-amplitude free vibration for horizontally curved beams including a warping contribution. Fundamental frequencies are calculated for a single-span, curved, wide-flange beam with both ends simply supported or clamped, or simply supported-clamped end conditions. The results are compared with existing exact solutions and numerical solutions by other methods for cases in which they are available. The differential quadrature method gives good accuracy even when only a limited number of grid points is used.