• Structural Engineering and Mechanics
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• v.33 no.6
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• pp.675-696
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• 2009

In this paper, a unified solution method is presented for the classical beam theory. In Strength of Materials approach, the geometry, material properties and load system are known and related with the unknowns of forces, moments, slopes and deformations by applying a classical differential analysis in addition to equilibrium, constitutive, and kinematic laws. All these relations are expressed in a unified formulation for the classical beam theory. In the special case of simple beams, a system of four linear ordinary differential equations of first order represents the general mechanical behaviour of a straight beam. These equations are solved using the numerical differential quadrature method (DQM). The application of DQM has the advantages of mathematical consistency and conceptual simplicity. The numerical procedure is simple and gives clear understanding. This systematic way of obtaining influence line, bending moment, shear force diagrams and deformed shape for the beams with geometric and load discontinuities has been discussed in this paper. Buckling loads and natural frequencies of any beam prismatic or non-prismatic with any type of support conditions can be evaluated with ease.

• Structural Engineering and Mechanics
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• v.7 no.3
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• pp.241-257
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• 1999

This paper presents a procedure to minimize the cost of materials of cable-stayed bridges with composite box girder and concrete tower. Two sets of iterations are included in the proposed procedure. The first set of iteration performs the structural analysis for a cable-stayed bridge. The second set of iteration performs the optimization process. The design is formulated as a general mathematical problem with the cost of the bridge as the objective function and bending forces, shear forces, fatigue stresses, buckling and deflection as constraints. The constraints are developed based on the Canadian National Standard CAN/CSA-S6-88. The finite element method is employed to perform the complicated nonlinear structural analysis of the cable-stayed bridges. The internal penalty function method is used in the optimization process. The limit states design method is used to determine the load capacity of the bridge. A computer program written in FORTRAN 77 is developed and its validity is verified by several practical-sized designs.

• Advances in aircraft and spacecraft science
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• v.8 no.4
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• pp.345-372
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• 2021

The analysis of nonlinear vibrations, buckling, post-buckling, flutter boundary determination and post-flutter behavior of a homogeneous curved plate assuming cylindrical bending is conducted in this article. Other assumptions include simply-supported boundary conditions, supersonic aerodynamic flow at the top of the plate, constant pressure conditions below the plate, non-viscous flow model (using first- and third-order piston theory), nonlinear structural model with large deformations, and application of mechanical and thermal loads on the curved plate. The analysis is performed with constant environmental indicators (flow density, heat, Reynolds number and Mach number). The material properties (i.e., coefficient of thermal expansion and modulus of elasticity) are temperature-dependent. The equations are derived using the principle of virtual displacement. Furthermore, based on the definitions of virtual work, the potential and kinetic energy of the final relations in the integral form, and the governing nonlinear differential equations are obtained after fractional integration. This problem is solved using two approaches. The frequency analysis and flutter are studied in the first approach by transferring the handle of ordinary differential equations to the state space, calculating the system Jacobin matrix and analyzing the eigenvalue to determine the instability conditions. The second approach discusses the nonlinear frequency analysis and nonlinear flutter using the semi-analytical solution of governing differential equations based on the weighted residual method. The partial differential equations are converted to ordinary differential equations, after which they are solved based on the Runge-Kutta fourth- and fifth-order methods. The comparison between the results of frequency and flutter analysis of curved plate is linearly and nonlinearly performed for the first time. The results show that the plate curvature has a profound impact on the instability boundary of the plate under supersonic aerodynamic loading. The flutter boundary decreases with growing thermal load and increases with growing curvature.

• Structural Engineering and Mechanics
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• v.30 no.6
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• pp.763-785
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• 2008

In this study, a flexibility-based finite element method considering geometric and material nonlinearities is developed for analyzing steel-concrete frame structures. The stability functions obtained from the exact buckling solution of the beam-column subjected to end moments are used to accurately capture the second-order effects. The proposed method uses the force interpolation functions, including a moment magnification due to the axial force and lateral displacement. Thus, only one element per a physical member can account for the interaction between the bending moment and the axial force in a rational way. The proposed method applies the Newton method based on the load control and uses the secant stiffness method, which is computationally both efficient and stable. According to the evaluation result of this study, the proposed method consistently well predicts the nonlinear inelastic behavior of steel-concrete composite frames and gives good efficiency.

• Journal of Navigation and Port Research
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• v.31 no.3 s.119
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• pp.271-279
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• 2007

Ship structures are basically an assembly of plate elements and estimation load-carrying capacity or the ultimate strength is one of the most important criterion for estimated safety assessment and rational design on the ship structure. Also, Structural elements making up ship plated structures do not work separately against external load. One of the critical collapse events of a ship structure is the occurrence of overall buckling and plastic collapse of deck or bottom structure subjected to longitudinal bending. So, the deck and the bottom plates are reinforced by a number af longitudinal stiffeners to increase their strength and load-carrying capacity. For a rational design avoiding such a sudden collapse, it is very important to know the buckling and plastic behaviour or collapse pattern of the stiffened plate under axial compression. In this present study, to investigate effect af modeling range, the finite element method are used and their results are compared varying the analysis ranges. When making the FEA model, six types of structural modeling are adopted varying the cross section of stiffener. In the present paper, a series of FEM elastoplastic large deflection analyses is performed on a stiffened plate with fiat-bar, angle-bar and tee-bar stiffeners. When the applied axial loading, the influences of cross-sectional geometries on collapse behaviour are discussed. The purpose of the present study is examined to numerically calculate the characteristics of buckling and ultimate strength behavior according to the analysis method of ship's stiffened plate subject to axial loading.

• Proceedings of the KSR Conference
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• 2000.11a
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• pp.358-365
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• 2000

For the general case of loading conditions and boundary conditions, it is very difficult to obtain closed form solutions for buckling loads and natural frequencies of thin-walled structures because its behaviour is very complex due to the coupling effect of bending and torsional behaviour. In consequence, most of previous finite element formulations are introduce approximate displacement fields to use shape functions as Hermitian polynomials, and so on. The Purpose of this study is to presents a consistent derivation of exact dynamic stiffness matrices of thin-walled straight beams, to be used ill tile free vibration analysis, in which almost types of boundary conditions are exist An exact dynamic element stiffness matrix is established from governing equations for a uniform beam element of nonsymmetric thin-walled cross section. This numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. The natural frequency is evaluated for the thin-walled straight beam structure, and the results are compared with analytic solutions in order to verify the accuracy of this study.

• Journal of Navigation and Port Research
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• v.30 no.6 s.112
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• pp.439-446
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• 2006

In ship structures many of the structural plates have cutouts, for example, at inner bottom structure, girder, upper deck hatch, floor and dia-frame etc. In the case where a plate has a cutout it experiences reduced buckling and ultimate strength and at the same time the in-plane stress under compressive load produced by hull girder bending will be redistributed In general, actual ship structure adopted reinforcement of stiffener around the cutout in order to preventing from buckling so it need to examine a buckling and ultimate strength behaviour considering a cutout because In many ship yards used class rule for calculating buckling strength but it is difficult to evaluate perforate stiffened plate with random size. In the present paper, we investigated several kinds of perforated stiffened model from actual ship and then was performed finite element series analysis varying the cutout ratio, web height, thickness and type of cross-section using commercial FEA program(ANSYS) under compressive load.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.689-694
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• 2000

This paper presents a modeling method for the vibration analysis of cantilever beams with an elastically restrained root. Mass and stiffness matrices are derived explicitly by considering the elastically restrained root coupling effect between stretching and bending motion. Numerical results show that the two effects influence the vibration characteristics of rotating beams significantly. The results also present the magnitude of the elastic stiffness of the root to avoid the dynamic buckling. The method presented in this paper can be used to provide accurate predictions of the variations of natural frequencies of rotating beams with an elastically restrained root.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.21 no.2
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• pp.142-150
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• 1985

In this paper, stress distribution were given in consideration of bending effects in hemi-spherical shell and a modified equation of buckling load was represented with implicating the effects of plastic deformations and shape parameters. Especially, the distributions of shell near it's vertex were analyzed numerically, according to several cases of loading. For the sake of more good estimation of plastic dissipating energy, we used the yield-line method from plate theory. The modified criterion of bucking, P super(*) sub(cr), that was suggested in this study, was applied to SUS 302 stain-less steel hemi-spherical shell which had it's Poisson's ratio and Young's modulus with 0.33 and 19700 kg/mm$^2$. From some experiments and comparisons with other results, 재 suggested the critical buckling-load-equation with P super(*) sub(cr)=2E super(*).(t super(2)/a super(2)).{3(1-ν super(*2)} and computed the buckling initiation load with this equation. Because these result from modified criterion have more coincidence than previous one, we prospect this equation can be magnified it's utilities to the other materials.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.10
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• pp.6504-6510
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• 2015

Horizontally curved I-girders are subjected to not only bending moments but also torsional moments. The torsional moment of the plate girder is addition of St. Venant torsion and non-uniform torsion. In the flange of I-shaped plate girder, a kind of open-section, the normal stresses is not distributed uniformly due to the non-uniform torsion. Because of that, one of compression flange tip can be yielded faster than the flange of general straight girder. In other words, the flange local buckling strength is decreased when the girder has initial curvature. In this paper, the numerical analysis is conducted to investigate the average stresses in flange for curved girders. The subtended angle and slenderness ratio are taken as parameters.