• 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.

• 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.

• Structural Engineering and Mechanics
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• v.75 no.6
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• pp.713-722
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• 2020

This article aims to illustrate the damped dynamic responses of layered functionally graded (FG) thick 2D beam under dynamic pulse sinusoidal load by using finite element method, for the first time. To investigate the response of thick beam accurately, two-dimensional plane stress problem is assumed to describe the constitutive behavior of thick beam structure. The material is distributed gradually through the thickness of each layer by generalized power law function. The Kelvin-Voigt viscoelastic constitutive model is exploited to include the material internal damping effect. The governing equations are obtained by using Lagrange's equations and solved by using finite element method with twelve -node 2D plane element. The dynamic equation of motion is solved numerically by Newmark implicit time integration procedure. Numerical studies are presented to illustrate stacking sequence and material gradation index on the displacement-time response of cantilever beam structure. It is found that, the number of waves increases by increasing the graduation distribution parameter. The presented mathematical model is useful in analysis and design of nuclear, marine, vehicle and aerospace structures those manufactured from functionally graded materials (FGM).

• 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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• 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.

• 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.

• Structural Engineering and Mechanics
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• v.67 no.3
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• pp.291-300
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• 2018

In this work, a new trigonometry theory of shear deformation is developed for the static analysis of thick isotropic beams. The number of variables used in this theory is identical to that required in the theory of Euler-Bernoulli, sine function is used in the displacement field in terms of the coordinates of the thickness to represent the effects of shear deformation. The advantage of this theory is that shear stresses can be obtained directly from the relationships constitute, while respecting the boundary conditions at the free surface level of the beam. Therefore, this theory avoids the use of shear correction coefficients. The differential equilibrium equations are obtained using the principle of virtual works. A thick isotropic beam is considered, whose numerical study to show the effectiveness of this theory.

• Journal of Electrical Engineering and Technology
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• v.2 no.3
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• pp.391-395
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• 2007

MgO enhanced $(Ba_{0.6}Sr_{0.4})$ $TiO_3$ thick films have been fabricated by a tape casting and firing method for tunable devices on the microwave frequency band. In order to improve ferroelectric properties, the composite thick films enhanced with MgO on BST have been asymmetrically annealed by a focused halogen beam method. Dielectric constants of composite thick films are changed from 1050 to 1300 at 100 kHz after 60 s and 150 s annealing by the focused halogen beam. Even though no prominent changes were previously observed from the thick films before and after annealing in terms of chemical composition and surface morphology, it is clear that the average particle size of the thick films calculated by Scherrer's formula were increased by annealing. Furthermore, a strong correlation between particle size and dielectric constant of the composite thick films has been observed; dielectric constant increases with increased particle size. This has been attributed to the increased volume of ferroelectric domain due to increased particle sizes. As a result, the tuning range was improved by halogen beam annealing.

• Structural Engineering and Mechanics
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• v.60 no.1
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• pp.111-130
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• 2016

Two new elements with six degrees of freedom are proposed by applying the equilibrium conditions and strain-displacement equations. The first element is formulated for the infinite ratio of beam radius to thickness. In the second one, theory of the thick beam is used. Advantage of these elements is that by utilizing only one element, the exact solution will be obtained. Due to incorporating equilibrium conditions in the presented formulations, both proposed elements gave the precise internal forces. By solving some numerical tests, the high performance of the recommended formulations and also, interaction effects of the bending and axial forces will be demonstrated. While the second element has less error than the first one in thick regimes, the first element can be used for all regimes due to simplicity and good convergence. Based on static responses, it can be deduced that the first element is efficient for all the range of structural characteristics. The free vibration analysis will be performed using the first element. The results of static and dynamic tests show no deficiency, such as, shear and membrane locking and excessive stiff structural behavior.

• Structural Engineering and Mechanics
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• v.75 no.3
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• pp.357-367
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• 2020

The objective of this article is investigation of dynamic response of thick multilayer functionally graded (FG) beam under generalized dynamic forces. The plane stress problem is exploited to describe the constitutive equation of thick FG beam to get realistic and accurate response. Applied dynamic forces are assumed to be sinusoidal harmonic, sinusoidal pulse or triangle in time domain and point load. Equations of motion of deep FG beam are derived based on the Hamilton principle from kinematic relations and constitutive equations of plane stress problem. The numerical finite element procedure is adopted to discretize the space domain of structure and transform partial differential equations of motion to ordinary differential equations in time domain. Numerical time integration method is used to solve the system of equations in time domain and find the time responses. Numerical parametric studies are performed to illustrate effects of force type, graduation parameter, geometrical and stacking sequence of layers on the time response of deep multilayer FG beams.