• Transactions of Materials Processing
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• v.22 no.7
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• pp.401-406
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• 2013

The use of roll-formed products increases every year due to its advantages, such as high production rates, reduced tooling cost and improved quality. However, till now, it is limited to part profiles with constant cross section. In recent years, the flexible roll forming process, which allows variable cross sections of profiles by adaptive roll stands, was developed. In this study, an attempt to optimize profile design for the flexible roll forming process was performed. An equation that predicts the longitudinal strain for part geometries with variable cross-sections was proposed. The relationship between geometrical parameters and the longitudinal strain was analyzed and investigations on the optimal profile design were performed. Experiments were conducted with a lab-scale roll forming machine to validate the proposed equation. The results show that the profile design method proposed in this study is feasible and parts with variable cross sections can be successfully fabricated with the flexible roll forming process.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2003.10a
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• pp.152-157
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• 2003

Natural frequencies of the transνerse vibration of beams with step change in cross-section are obtained by using the asymptotic closed form solution. This closed form solution is found by using WKB method under the assumption of slowly varying properties, such as mass, cross-section, tension etc., along the beam length. However, this solution is found to be still very accurate even in the case of large variation in cross-section and tension. Therefore, this result can be easily applied to many engineering problems.

• Journal of Aerospace System Engineering
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• v.8 no.1
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• pp.12-17
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• 2014

In this paper, optimal design of composite rotor blade cross-section to consider manufacturability was performed. Skin thickness, torsion box thickness and skin lay-up angle were adopted as discrete design variables and The position and width of a torsion box were considered as continuous variables. An object function of optimal design is to minimize the mass of a rotor blade, and various constraints such as failure index, center mass, shear center, natural frequency and blade minimum mass per unit length were adopted. Finally, design variables such as the thickness and lay-up angles of a skin, and the thickness, position and width of a torsion box were determined by using an in-house program developed for the optimal design of rotor blade cross-section.

• Steel and Composite Structures
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• v.45 no.1
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• pp.39-49
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• 2022

This research investigates a rotary disk with variable cross-section and incompressible hyperelastic material with functionally graded properties in large hyperelastic deformations. For this purpose, a power relation has been used to express the changes in cross-section and properties of hyperelastic material. So that (m) represents the changes in cross-section and (n) represents the manner of changes in material properties. The constants used for hyperelastic material have been obtained from experimental data. The obtained equations have been solved for different m, n, and (angular velocity) values, and the values of radial stresses, tangential stresses, and elongation have been compared. The results show that m and n have a significant impact on disk behavior, so the expected behavior of the disk can be obtained by an optimal selection of these two parameters.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.9 no.4
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• pp.1-8
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• 1989

The main purpose of the present paper is to present both the fundamental frequency and some higher free vibration frequencies for circular arches with variable section, in which rotatory inertia is included. The differential equations are derived for the in-plan free vibration of elastic circular arches with variable section. These equations were solved numerically for the linear variable circular cross-section with clamped-clamped end constraint. As the numerical results, the four lowest nondimensional natural frequencies presented as functions of the nondimensional system parameters : the end moment of inertia to crown moment of inertia ratio, the slenderness ratio, and the opening angle. The effect of rotatory inertia on the nondimensional natural frequency is also reported.

• International Journal of Aeronautical and Space Sciences
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• v.14 no.4
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• pp.310-323
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• 2013

In this paper, the aeroelastic static response of flexible wings with arbitrary cross-section geometry via a coupled CUF-XFLR5 approach is presented. Refined structural one-dimensional (1D) models, with a variable order of expansion for the displacement field, are developed on the basis of the Carrera Unified Formulation (CUF), taking into account cross-sectional deformability. A three-dimensional (3D) Panel Method is employed for the aerodynamic analysis, providing more accuracy with respect to the Vortex Lattice Method (VLM). A straight wing with an airfoil cross-section is modeled as a clamped beam, by means of the finite element method (FEM). Numerical results present the variation of wing aerodynamic parameters, and the equilibrium aeroelastic response is evaluated in terms of displacements and in-plane cross-section deformation. Aeroelastic coupled analyses are based on an iterative procedure, as well as a linear coupling approach for different free stream velocities. A convergent trend of displacements and aerodynamic coefficients is achieved as the structural model accuracy increases. Comparisons with 3D finite element solutions prove that an accurate description of the in-plane cross-section deformation is provided by the proposed 1D CUF model, through a significant reduction in computational cost.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.5
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• pp.1935-1946
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• 2013

In this study, the behavior characteristics of bent pile structures with varying cross-section was examined through the measured results of field load test. A framework for determining the bending stress is calculated based on the stresses in the circumference of the pile using 3D finite element analysis. It is found that the bending stress near the pile-column joint changes rapidly and fracture zones occurs easily at variable cross-sections in bent pile structures. Also, the optimized column-pile diameter ratio was analyzed through the relationship between the column-pile diameter ratio and lateral crack load ratio. Based on this study, the optimized column-pile diameter ratio can be obtained near the inflection point of the curve between the column-pile diameter ratio and lateral crack load ratio. Therefore, a present study by considering the optimized variable cross-section condition would be improved bent pile structures design.

• Transactions of Materials Processing
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• v.23 no.6
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• pp.369-375
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• 2014

Flexible roll forming allows profiles to have variable cross-sections. However, the profile may have some shape errors, such as, warping which is a major defect. The shape error is induced by geometrical deviations in both the concave zone and the convex zone. In the current study, flexible roll forming was modeled with FE simulations to analyze the shape error and the longitudinal strain distribution along the flange section over the profile. A distribution of analytically calculated longitudinal strains was used to develop relationships between the shape error and the longitudinal strain distribution as a function of the defined shape parameters for the profile. The FE simulations showed that the shape error is primarily affected by the deviations between the distribution of analytically calculated longitudinal strain and the longitudinal strain distribution of the profile. The results show that the shape error can be controlled by designing the shape parameters to control the geometrical deviations at the flange section in the transition zones.

• Structural Engineering and Mechanics
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• v.8 no.5
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• pp.465-476
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• 1999

A structural optimization process is presented for arches with varying cross-section. The optimality criteria method is used to develop a recursive relationship for the design variables considering displacement, stresses and minimum depth constraints. The depth at the crown and at the support are taken as design variables first. Then the approach is extended by taking the depth values of each joint as design variable. The curved beam element of constant cross section is used to model the parabolic and circular arches with varying cross section. A number of design examples are presented to demonstrate the application of the method.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2003.04a
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• pp.504-509
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• 2003

In this paper, a multi-step optimization using a G.A.(Genetic Algorithm) with variable penalty function is introduced to the structural design optimization of a high speed machining center. The design problem, in this case, is to find out the best cross-section shapes and dimensions of structural members which minimize the static compliance, the dynamic compliance, and the weight of the machine structure simultaneously. The first step is the cross-section shape optimization, in which only the section members are selected to survive whose cross-section area have above a critical value. The second step is a static design optimization, in which the static compliance and the weight of the machine structure are minimized under some dimensional constraints and deflection limits. The third step is a dynamic design optimization, where the dynamic compliance and the structure weight are minimized under the same constraints as those of the second step. The proposed design optimization method was successful applied to the machining center structural design optimization. As a result, static and dynamic compliances were reduced to 16% and 53% respectively from the initial design, while the weight of the structure are also reduced slightly.