• Magazine of the Korean Society of Agricultural Engineers
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• v.45 no.2
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• pp.68-77
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• 2003

Shell structure are widely used in a variety of engineering application and mathematical solution of shell structures are available only for a few special cases. The solution of shell structure is more complicated when it has such condition as winker foundation, variable thickness and other problem. In this paper, a simple finite element method is presented for the analysis of axisymmetric several types of shell structure subjected to axisymmetric loads and having uniform and varying wall thickness on elastic foundation. The method is based on the analogy with a beam on elastic foundation (BEF), foundation stiffness matrix where the foundation modulus and beam flexural rigidity are replaced by appropriate parameters pertaining to the shell under considerations. The technique is attractive for implementation on a numerical solution by means of a computer program coded in FORTRAN language with a few elements. To demonstrate this fact, it gives good results which compare well with SAP2000.

• Structural Engineering and Mechanics
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• v.37 no.4
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• pp.415-425
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• 2011

In this study, the homotopy perturbation method (HPM) is applied to free vibration analysis of beam on elastic foundation. This numerical method is applied on three different axially loaded cases, namely: 1) one end fixed, the other end simply supported; 2) both ends fixed and 3) both ends simply supported cases. Analytical solutions and frequency factors are evaluated for different ratios of axial load N acting on the beam to Euler buckling load, $N_r$. The application of HPM for the particular problem in this study gives results which are in excellent agreement with both analytical solutions and the variational iteration method (VIM) solutions for all the cases considered in this study and the differential transform method (DTM) results available in the literature for the fixed-pinned case.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.6
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• pp.709-717
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• 2007

This paper discussed on the effect of an intermediate support on the stability of a beam resting on elastic foundation subjected to follower force. The stability and dynamic responses of a beam resting on elastic foundation subjected to follower force are analyzed based on the finite element method. The dynamic responses of the system are studied by the mode superposition method to observe the damping rate of the motion. The beam resting on elastic foundation subjected to follower force loses its stability by flutter type or divergence type, depending on the location of the intermediate support.

• Steel and Composite Structures
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• v.34 no.1
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• pp.75-89
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• 2020

The current paper illustrates the effect of in-plane varying compressive force on critical buckling loads and buckling modes of sandwich composite laminated beam rested on elastic foundation. To generalize a proposed model, unified higher order shear deformation beam theories are exploited through analysis; those satisfy the parabolic variation of shear across the thickness. Therefore, there is no need for shear correction factor. Winkler and Pasternak elastic foundations are presented to consider the effect of any elastic medium surrounding beam structure. The Hamilton's principle is proposed to derive the equilibrium equations of unified sandwich composite laminated beams. Differential quadrature numerical method (DQNM) is used to discretize the differential equilibrium equations in spatial direction. After that, eigenvalue problem is solved to obtain the buckling loads and associated mode shapes. The proposed model is validated with previous published works and good matching is observed. The numerical results are carried out to show effects of axial load functions, lamination thicknesses, orthotropy and elastic foundation constants on the buckling loads and mode shapes of sandwich composite beam. This model is important in designing of aircrafts and ships when non-uniform compressive load and shear loading is dominated.

• Journal of KSNVE
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• v.10 no.6
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• pp.1022-1028
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• 2000

This paper presents a modeling method for the vibration analysis of rotating cantilever beams considering the elastic foundation effect. Mass and stiffness matrices are derided explicitly by considering coupling effect between stretching and bonding motion. Numerical results show that the bending direction elastic foundation stiffness influences the vibration characteristics significantly in practical range of beam configuration. The ranges of elastic foundation stiffness to avoid the dynamic buckling are also presented. The method presented in this paper can be used to predict the variations of natural frequencies of rotating cantilever beams with elastically restrained root.

• Structural Engineering and Mechanics
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• v.24 no.1
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• pp.51-62
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• 2006

Differential transform method (DTM) for free vibration analysis of both ends simply supported beam resting on elastic foundation is suggested. The fourth order partial differential equation for free vibration of the beam resting on elastic foundation subjected to bending moment, shear and axial compressive load is obtained by using Winkler hypothesis and small displacement theory. It is assumed that the material is linear-elastic, and that axial load and modulus of subgrade reaction to be constant. In the analysis, shear and axial load effects are considered. The frequency factors of the beam are calculated by using DTM due to the values of relative stiffness; the results are presented in graphs and tables.

• Structural Engineering and Mechanics
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• v.33 no.4
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• pp.447-484
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• 2009

The spatially coupled buckling, in-plane, and lateral bucking analyses of thin-walled Timoshenko curved beam with non-symmetric, double-, and mono-symmetric cross-sections resting on elastic foundation are performed based on series solutions. The stiffness matrices are derived rigorously using the homogeneous form of the simultaneous ordinary differential equations. The present beam formulation includes the mechanical characteristics such as the non-symmetric cross-section, the thickness-curvature effect, the shear effects due to bending and restrained warping, the second-order terms of semitangential rotation, the Wagner effect, and the foundation effects. The equilibrium equations and force-deformation relationships are derived from the energy principle and expressions for displacement parameters are derived based on power series expansions of displacement components. Finally the element stiffness matrix is determined using force-deformation relationships. In order to verify the accuracy and validity of this study, the numerical solutions by the proposed method are presented and compared with the finite element solutions using the classical isoparametric curved beam elements and other researchers' analytical solutions.

• Computers and Concrete
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• v.27 no.2
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• pp.85-97
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• 2021

In this study, the effect of steel fiber utilization, boundary conditions, different beam cross-section, and length parameter are investigated on the free vibration behavior of fiber reinforced self-compacting concrete beam on elastic foundation. In the analysis of the beam model recommended by Euler-Bernoulli, a method utilizing Stokes transformations and Fourier Sine series were used. For this purpose, in addition to the control beam containing no fiber, three SCC beam elements were prepared by utilization of steel fiber as 0.6% by volume. The time-dependent fresh properties and some mechanical properties of self-compacting concrete mixtures were investigated. In the modelled beam, four different beam specimens produced with 0.6% by volume of steel fiber reinforced and pure (containing no fiber) SCC were analyzed depending on different boundary conditions, different beam cross-sections, and lengths. For this aim, the effect of elasticity of the foundation, cross-sectional dimensions, beam length, boundary conditions, and steel fiber on natural frequency and frequency parameters were investigated. As a result, it was observed that there is a noticeable effect of fiber reinforcement on the dynamic behavior of the modelled beam.

• Structural Engineering and Mechanics
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• v.52 no.5
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• pp.1033-1049
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• 2014

The free vibration of functionally graded material (FGM) beams on an elastic foundation and spring supports is investigated. Young's modulus, mass density and width of the beam are assumed to vary in thickness and axial directions respectively following the exponential law. The spring supports are also taken into account at both ends of the beam. An analytical formulation is suggested to obtain eigen solutions of the FGM beams. Numerical analyses, based on finite element method by using a beam finite element developed in this study, are performed in order to show the legitimacy of the analytical solutions. Some results for the natural frequencies of the FGM beams are given considering the effect of various structural parameters. It is also shown that the spring supports show the greatest effect on the natural frequencies of FGM beams.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.12
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• pp.947-955
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• 2003

This research analyzes the dynamic stability of stiffened plates on elastic foundations using the finite element method. For analyzing the stiffened plates, both the Mindlin plate theory and Timoshenko beam-column theory were applied. In application of the finite element method, 8-nodes serendipity element system and 3-nodes finite element system were used for plate and beam elements, respectively Elastic foundations were modeled as the Pasternak foundations in which the continuity effect of foundation is considered. In order to verify the theory of this study, solutions obtained by this analysis were compared with the classical solutions in open literature and experimental solutions. The dynamic stability legions of stiffened plates on Pasternak foundations were determined according to changes of in-plane stresses, foundation parameters and dimensions of stiffener.