• Journal of Ocean Engineering and Technology
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• v.25 no.2
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• pp.67-72
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• 2011

This study had the goal of investigating the effect of the curvature along the heating line on the transverse angular distortion of plates having an initial curvature from line heating. A thermo-elasto-plastic analysis was carried out using 54 models with various radii of curvature, plate thicknesses, and heating speeds. The results show the effect of the curvature along the heating line on the angular distortion in relation to changes in the magnitudes of the curvature, heating speed, and plate thickness. The present numerical results show that the time history of the angular distortion after cooling and reaching the final deformed shape for a plate having an initial curvature is quite different from that of a flat plate. This emphasized the importance of considering the curvature effect on the transverse angular distortion. From the viewpoint of the curvature effect on the deformation, it has been seen that the curvature does not affect the transverse shrinkage. In this study the predicting formula for the transverse angular distortion was derived through a regression analysis. It showed that as the curvature increased, the angular distortion was reduced because of the higher bending rigidity at the same heat input parameter, and the peak points moved toward the origin as the curvature increased.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.806-809
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• 2003

In this paper, extracting design information from arbitrary aspherical lens shape in reverse engineering is introduced. Deformation terms and sphere data equation with various variables compose asphere equation. Aspherical lens shape is expressed with complicated polynomial expression that includes deformation terms and sphere data. Deformation term and vertex curvature have direct influence on a geometric shape and an optical characteristics of aspherical lens. Hence, extracting these information mean that design information could be derived and analyzed from shape data of arbitrary aspherical lens. Furthermore, sharing designer's experience and knowledge for aspherical lens design could be expected.

• Steel and Composite Structures
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• v.21 no.6
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• pp.1347-1368
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• 2016

In this article, an exact analytical solution for mechanical buckling analysis of symmetrically cross-ply laminated plates including curvature effects is presented. The equilibrium equations are derived according to the refined nth-order shear deformation theory. The present refined nth-order shear deformation theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components, in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments The most interesting feature of this theory is that it accounts for a parabolic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Buckling of orthotropic laminates subjected to biaxial inplane is investigated. Using the Navier solution method, the differential equations have been solved analytically and the critical buckling loads presented in closed-form solutions. The sensitivity of critical buckling loads to the effects of curvature terms and other factors has been examined. The analysis is validated by comparing results with those in the literature.

• Journal of Ocean Engineering and Technology
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• v.24 no.2
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• pp.67-73
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• 2010

A simplified finite element analysis has been used to predict the weld-induced deformation to bead-on-plate welding of steel plates having curvatures in the welding direction. In this study, the equivalent loading method based on inherent strain was used to investigate the effect of longitudinal curvature on the weld-induced deformation of curved plates. Equivalent loads were derived from the inherent strain distribution around the weld line, and the loads were used for linear finite element analyses. These kinds of numerical simulations can, of course, be performed by using the rigorous thermalelastic-plastic analysis method. This approach is not, however, practical for use in weld-induced deformation analysis of large and complex structures, such as ship structures, in view of computing time and cost. The present equivalent load approach has been applied to several plate models having curvatures in the welding direction, and the results are compared with those obtained by thermal-elastic-plastic analysis and also with those obtained by the other simplified method found in reference. As far as the present results are concerned, the weld-induced deformation of curved plates can be accurately predicted by the method presented in this paper.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.11-16
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• 2007

The existence of grooves on the surface of bond coat has significant effect on the instability of thermal barrier system. In this work, the thermal-mechanical fatigue experiments were performed under various thermal and mechanical loads for FeCralloy specimens with and without yttrium dopant to observe the deformation of surface grooves. The effect of temperature, fatigue load and the ratio of curvature on the deformation of grooves were investigated. As the results, it has been found that the higher load level and the higher curvature ratio induces the larger deformation near the grooves. However, the addition of yittrium dopant induces the adverse results.

• Transactions of Materials Processing
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• v.6 no.2
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• pp.118-135
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• 1997

In order to analyze the deformation and residual curvature of steel sheets in the strip processing lines, a program for calculating curvature and work hardening of sheet was developed. Strip deformation caused by repeated bending under tension in the process lines was analyzed on the basis of the incremental-plasticity theory with the mixed hardenting model for the purpose of predicting the strip shape and the yield stress change. The developed calculation program was applied to predict curl and gutter of sheets within a 10% difference. The yield stress increment was also predicted with the similar accuracy. Application of the model to tension legvelling process showed that gutter could be controlled by intermesh and elongation. The yield stress increment in the electro-galvanizing line calculated by the developed program was found to be dependent on the yield strength, the applied tension and the diameter of the smallest roll.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1459-1468
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• 2018

We show that an umbilic-free minimal surface in ${\mathbb{R}}^3$ belongs to the associate family of the catenoid if and only if the geodesic curvatures of its lines of curvature have a constant ratio. As a corollary, the helicoid is shown to be the unique umbilic-free minimal surface whose lines of curvature have the same geodesic curvature. A similar characterization of the deformation family of minimal surfaces with planar lines of curvature is also given.

• Computers and Concrete
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• v.8 no.1
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• pp.43-57
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• 2011

Force-deformation modelling of cracked reinforced concrete is essential for a displacement-based seismic assessment of structures and can be achieved by fibre-element analysis of the cross-section of the major lateral resisting elements. The non-linear moment curvature relationship obtained from fibre-element analysis takes into account the significant effects of axial pre-compression and contributions by the longitudinal reinforcement. Whilst some specialised analysis packages possess the capability of incorporating fibre-elements into the modelling (e.g., RESPONSE 2000), implementation of the analysis on EXCEL is illustrated in this paper. The outcome of the analysis is the moment-curvature relationship of the wall cross-section, curvature at yield and at damage control limit states specified by the user. Few software platforms can compete with EXCEL in terms of its transparencies, versatility and familiarity to the computer users. The program has the capability of handling arbitrary cross-sections that are without an axis of symmetry. Application of the program is illustrated with examples of typical cross-sections of structural walls. The calculated limiting curvature for the considered cross-sections were used to construct displacement profiles up the height of the wall for comparison with the seismically induced displacement demand.

• Journal of Mechanical Science and Technology
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• v.18 no.1
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• pp.12-19
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• 2004

Using LSM (laser scanning method) , the radius of curvature due to thermal deformation in polyimide film coated on Si substrate is measured. Since the polyimide film shows viscoelastic behavior, i.e., the modulus and deformation of the film vary with time and temperature, we estimate the relaxation modulus and the residual stresses of the polyimide film by measuring the radius of curvature and subsequently by performing viscoelastic analysis. The residual stresses relax by an amount of 10％ at 100$^{\circ}C$ and 20% at 150$^{\circ}C$ for two hours.

• Transactions of Materials Processing
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• v.13 no.2
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• pp.122-128
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• 2004

In order to make a doubly-curved sheet metal effectively, a sheet metal forming process has been developed by adopting the flexibility of the incremental forming process and the principle of bending deformation which causes slight deformation in thickness. The developed process is an unconstrained forming process with no holder. For this study, the experimental equipment is set up with the roll set which consists of two pairs of support rolls and one center roll. In the experiments using aluminum sheets, it is found that the curvature of the formed sheet metal is determined by controlling the distance between supporting rolls in pairs and the forming depth of the center roll and it also depends on the thickness of the sheet metal. In order to check the effect of process parameters on the generation of sheet metal curvatures in this process, the orthogonal array is adopted. From the experimental results, among the process parameters, the distance between supporting rolls in pairs along the direction of one principal radius of curvature as well as the forming depth and the thickness of the material is shown to influence the generation of curvature in the same direction significantly. That is, the other distance between supporting rolls in pairs which are not located in the same direction of one principal radius of curvature, does not have an significant effect on the generation of the curvature in that direction. It mainly affects the generation of curvature in its own direction with the forming depth and the thickness of the material.