• Journal of the Korea Academia-Industrial cooperation Society
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• v.8 no.1
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• pp.116-120
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• 2007

In this study, it is presented analytic results of bending problems in the anisotropic curved thick beam and the anisotropic curved thin beam. The anisotropy is that the material properties are different in each directions and it is difficult to solve the analytical solutions because the behavior is complex. In applying numerical method to solve differential equations of anisotropic curved beams, this study uses the finite element method. Both thin beam theory and thick beam theory are used as the basic governing equations of bending problems in the anisotropic beams. The analytic results are compared between the anisotropic curved thick beams and the anisotropic curved thin beams.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2005.04a
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• pp.167-171
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• 2005

The thick open section composite beams are used extensively as load carrying members and stiffeners of structural elements. However, most of studies on thick composite beams are limited only to closed section beams. In this study, an open cross-section thick-walled composite beam model which includes coupled stiffness, transverse shear, and warping effects is suggested and the deflections associated with the thick-walled composite beams and thin-walled composite beams are obtained and compared with the finite element analysis results. The correlation between thin and thick walled composite beam was achieved for two different layup configurations which are the circumferentially asymmetric stiffness (CAS) and circumferentially uniform stiffness (CUS) beams.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2005.11a
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• pp.202-206
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• 2005

Most of studies on the open section composite beams are confined to the thin composite beams. There are some works focused on the thick composite beams but they are limited only to closed section beams. Therefore, it is required to develop an appropriate model to analyze the thick open section composite beams. In this study, the cantilever beams of two specific lay-up configurations are considered which are the circumferentially asymmetric stiffness (CAS) and circumferentially uniform stiffness (CUS) beams. Under the torsional loading, loading induced deformations are obtained for the thick beams using the suggested model. The model includes coupled stiffness and secondary warping effects. The results are compared with those obtained using thin beam model to observe the thickness effects. Those results are also compared with the finite element analysis results.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.480-485
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• 2004

The applications of composite materials have increased over the past few decades in a variety of structures that require high ratio of stiffness and strength to weight ratios. Recently the thick open section composite beams are used extensively as load carrying members and stiffeners of structural elements. However, most of studies on thick composite beams are limited only to closed section beams. In this study, an open cross-section thick-walled composite beam model which includes coupled stiffness, transverse shear, and warping effects is suggested and the deflections associated with the thick-walled composite beams and thin-walled composite beams are obtained and compared with the finite element analysis results.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.04a
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• pp.69-73
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• 2003

A open section thick composite beam model is suggested in this study. In the model, the primary and secondary warping and transverse shear effects are incorporated. The rigidities associated with thick channel composite beam and thin channel composite beam are obtained and compared. The results show that the difference among rigidities of the thick and thin composite beams increase as the wall thickness increases.

• Steel and Composite Structures
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• v.31 no.5
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• pp.489-502
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• 2019

This article presents a unified mathematical model to investigate free and forced vibration responses of perforated thin and thick beams. Analytical models of the equivalent geometrical and material characteristics for regularly squared perforated beam are developed. Because of the shear deformation regime increasing in perforated structures, the investigation of dynamical behaviors of these structures becomes more complicated and effects of rotary inertia and shear deformation should be considered. So, both Euler-Bernoulli and Timoshenko beam theories are proposed for thin and short (thick) beams, respectively. Mathematical closed forms for the eigenvalues and the corresponding eigenvectors as well as the forced vibration time response are derived. The validity of the developed analytical procedure is verified by comparing the obtained results with both analytical and numerical analyses and good agreement is detected. Numerical studies are presented to illustrate effects of beam slenderness ratio, filling ratio, as well as the number of holes on the dynamic behavior of perforated beams. The obtained results and concluding remarks are helpful in mechanical design and industrial applications of large devices and small systems (MEMS) based on perforated structure.

• Steel and Composite Structures
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• v.35 no.4
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• pp.555-566
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• 2020

This paper aims to present an analytical methodology to investigate influences of nanoscale and surface energy on buckling stability behavior of perforated nanobeam structural element, for the first time. The surface energy effect is exploited to consider the free energy on the surface of nanobeam by using Gurtin-Murdoch surface elasticity theory. Thin and thick beams are considered by using both classical beam of Euler and first order shear deformation of Timoshenko theories, respectively. Equivalent geometrical constant of regularly squared perforated beam are presented in simplified form. Problem formulation of nanostructure beam including surface energies is derived in detail. Explicit analytical solution for nanoscale beams are developed for both beam theories to evaluate the surface stress effects and size-dependent nanoscale on the critical buckling loads. The closed form solution is confirmed and proven by comparing the obtained results with previous works. Parametric studies are achieved to demonstrate impacts of beam filling ratio, the number of hole rows, surface material characteristics, beam slenderness ratio, boundary conditions as well as loading conditions on the non-classical buckling of perforated nanobeams in incidence of surface effects. It is found that, the surface residual stress has more significant effect on the critical buckling loads with the corresponding effect of the surface elasticity. The proposed model can be used as benchmarks in designing, analysis and manufacturing of perforated nanobeams.

• Structural Engineering and Mechanics
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• v.13 no.3
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• pp.261-276
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• 2002

A novel, 6-node, two-dimensional mixed finite element (FE) model has been developed to analyze laminated composite beams by using the minimum potential energy principle. The model has been formulated by considering four degrees of freedom (two displacement components u, w and two transverse stress components ${\sigma}_z$, $\tau_{xz}$) per node. The transverse stress components have been invoked as nodal degrees of freedom by using the fundamental elasticity equations. Thus, the present mixed finite element model not only ensures the continuity of transverse stress and displacement fields through the thickness of the laminated beams but also maintains the fundamental elasticity relationship between the components of stress, strain and displacement fields throughout the elastic continuum. This is an important feature of the present formulation, which has not been observed in various mixed formulations available in the literature. Results obtained from the model have been shown to be in excellent agreement with the elasticity solutions for thin as well as thick laminated composite beams. A few results for a cross-ply beam under fixed support conditions are also presented.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.12 no.5
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• pp.73-79
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• 2003

In this paper, RKPM is extended for solving moderately thick and thin beams. General Timoshenko beam theory is used for formulation. Shear locking is the main difficulty in analysis of these kinds of structures. Shear relaxation factor, which is formulated using the difference between bending and shear strain energy, and corrected shear rigidity are introduced to overcome shear locking. Analysis results obtained reveal that RKPM using introduced methods is free of locking and very effectively applicable to deep beams as well as shallow beams.

• Structural Engineering and Mechanics
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• v.69 no.4
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• pp.427-437
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• 2019

In this study, an alternative solution procedure presented by using variational methods for analysis of shear deformable functionally graded material (FGM) beams with mixed formulation. By using the advantages of $G{\hat{a}}teaux$ differential approaches, a refined complex general functional and boundary conditions which comprises seven independent variables such as displacement, rotation, bending moment and higher-order bending moment, shear force and higher-order shear force, is derived for general thick-thin FGM beams via shear deformation beam theories. The mixed-finite element method (FEM) is employed to obtain a beam element which have a 2-nodes and total fourteen degrees-of-freedoms. A computer program is written to execute the analyses for the present study. The numerical results of analyses obtained for different boundary conditions are presented and compared with results available in the literature.