• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2001.10a
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• pp.198-201
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• 2001

This paper deals with the Automatic Analysis of Continuous Beams with Variable Cross-Section. Based on the principle of superpositon and the method of consistent deformations, the governing differential equation is derived for the deflection and stress resultants of such continuous beam. The effects of variable load conditions, the end constraints on the deflection and the stress resultants are analyzed. It is expected that the results obtained herein can be used practically in the structural engineering.

• Steel and Composite Structures
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• v.33 no.1
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• pp.133-142
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• 2019

In the present study, microstructure-dependent static stability analysis of inhomogeneous tapered micro-columns is performed. It is considered that the micro column is made of functionally graded materials and has a variable cross-section. The material and geometrical properties of micro column vary continuously throughout the axial direction. Euler-Bernoulli beam and modified couple stress theories are used to model the nonhomogeneous micro column with variable cross section. Rayleigh-Ritz solution method is implemented to obtain the critical buckling loads for various parameters. A detailed parametric study is performed to examine the influences of taper ratio, material gradation, length scale parameter, and boundary conditions. The validity of the present results is demonstrated by comparing them with some related results available in the literature. It can be emphasized that the size-dependency on the critical buckling loads is more prominent for bigger length scale parameter-to-thickness ratio and changes in the material gradation and taper ratio affect significantly the values of critical buckling loads.

• Journal of the Korean Professional Engineers Association
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• v.16 no.4
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• pp.4-14
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• 1983

when one is designing a continuous bridge with variable cross sections, it is very troublesome to integrate explicitly load terms and various factor under consideration so that it has different moment of inertia at each cross section. In this paper to obtain the influence line of a arbitary-span continuous beam with variable cross sections, the value of some particular function due to a load at any point can be carried out by numerical integration instead of definite integral. The ordinate of the influence line equals the product of the magnitude of the final moment at each support due to unit moment at any support and the load terms due to unit load, measured at the point of application of the load. It is concluded that this method can be easily used to design continuous bridges with arbitary cross sections.

• Smart Structures and Systems
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• v.13 no.4
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• pp.659-683
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• 2014

The static analysis of structures with arbitrary cross-section geometry and material lamination via a refined one-dimensional (1D) approach is presented in this paper. Higher-order 1D models with a variable order of expansion for the displacement field are developed on the basis of Carrera Unified Formulation (CUF). Classical Euler-Bernoulli and Timoshenko beam theories are obtained as particular cases of the first-order model. Numerical results of displacement, strain and stress are provided by using the finite element method (FEM) along the longitudinal direction for different configurations in excellent agreement with three-dimensional (3D) finite element solutions. In particular, a layered thin-walled cylinder is considered as first assessment with a laminated conventional cross-section. An atherosclerotic plaque is introduced as a typical structure with arbitrary cross-section geometry and studied for both the homogeneous and nonhomogeneous material cases through the 1D variable kinematic models. The analyses highlight limitations of classical beam theories and the importance of higher-order terms in accurately detecting in-plane cross-section deformation without introducing additional numerical problems. Comparisons with 3D finite element solutions prove that 1D CUF provides remarkable three-dimensional accuracy in the analysis of even short and nonhomogeneous structures with arbitrary geometry through a significant reduction in computational cost.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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• v.17 no.2
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• pp.131-139
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• 1988

The thermoacoustic oscillation induced in an air column with variable cross section area is investigated theoretically and experimentally. The onset condition of the oscillation is derived by equating the acoustic power production to the power dissipation. The power production at the heater is predicted by using the efficiency factor obtained by heat transfer analysis for a single wire in a uniform cross flow and considering the interference between heater wires. The power dissipation is estimated by measuring the attenuating coefficient from the pressure decay curve. The theoretical prediction to the onset condition of the oscillation is confirmed experimentally. The effect of the variation of the column cross section area on the onset condition is presented.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.15 no.4
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• pp.73-82
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• 2016

Recently, automobile industries have been developing many structural automotive parts made of thin, high-strength steel strips to produce safer and more environmentally friendly cars. The roll forming process has been considered one of the most efficient processes in manufacturing high-strength steel parts because it is a high-speed process that forms sheets in increments. However, most automotive parts vary longitudinally in their cross-sections. Therefore, it is difficult to apply the roll forming process to automotive parts made of high-strength steel. A variable section roll forming process has been proposed in recent studies. The rotational axes of the forming rolls are fixed, and the forming rolls have three-dimensional shape. As such, the cross-section of the part varies linearly along its length, and the angle between the bend line and longitudinal axis is less than 1 degree. Thus, the rate of cross-sectional variation along the length is relatively small. In this study, the rate of cross-sectional change along the length of a forming roll has been increased. Moreover, the angle between the bend line and longitudinal axis has been increased up to 15 degrees. The variable sections of the forming rolls have been designed for high strength steel parts with a symmetric u-type cross-section that varies linearly and symmetrically along the longitudinal axis.

• Structural Engineering and Mechanics
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• v.70 no.2
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• pp.199-207
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• 2019

In this paper, a semi-analytical method will be discussed for free vibration analysis of rotating beams with variable cross sectional area. For this purpose, the rotating beam is discretized through applying the transfer matrix method and assumed the axial force is constant for each element. Then, the transfer matrix is derived based on Euler-Bernoulli's beam differential equation and applying boundary conditions. In the following, the frequencies of the rotating beam with constant and variable cross sections are determined using the transfer matrix method in several case studies. In order to eliminate numerical difficulties in the transfer matrix method, the Riccati transfer matrix is employed for high rotation speed and high modes. The results are compared with the results of the finite elements method and Rayleigh-Ritz method which show good agreement in spite of low computational cost.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2011.06a
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• pp.883-884
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• 2011

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.5
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• pp.623-631
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• 2000

Hot-wire measurements were carried out on the developing turbulent flows subject to plane rate of strain in a rotating curved duct. The cross-section of the curved duct varies from 100mm${\times}$50mm rectangular shape at the bend inlet gradually to the 50mm${\times}$100mm rectangular shape at the bend outlet. Experimental setup consists of the test section of $90^{\circ}$ curved duct, rotating disc of 1.95m diameter, Ag-Ni precision slip ring, automatic traversing mechanism, variable speed motor, centrifugal blower, orifice flowmeter and hot-wire anemometer. Data signals from the rotating curved duct are transmitted through the slip ring to the computer which is located at the outside of the rotating disc. 3-dimensional velocity and 6 Reynold stresses components were obtained from the fluctuating and mean voltage measured by the slant type hot-wire probe rotating into 6 orientations. We investigate the effects of Coriolis and centrifugal forces on the turbulence structure.

• Journal of the Korean Society for Advanced Composite Structures
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• v.6 no.3
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• pp.77-85
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• 2015

In this paper, we present the result of investigations pertaining to the elastic buckling of simply supported columns with various cross-sectional dimensions but the same length and volume. In the investigations the accuracy of the analysis methods is studied and it was found that the result obtained by the successive approximations technique is the most accurate. In addition, the elastic buckling loads of columns with variable cross-section dimensions are obtained by the theoretical and numerical methods. From the results, it was found that the buckling loads obtained by the numerical methods are close to the buckling loads obtained by the successive approximations technique for the practical standpoints. Moreover, the buckling load of column with convexity in its middle is the highest while the buckling load of the tapered column is the lowest as expected.