• Structural Engineering and Mechanics
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• v.32 no.4
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• pp.501-516
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• 2009

This paper aims to study the large deflections of variable-arc-length elastica subjected to the terminal forces (e.g., axial force and torque). Based on Kirchhoff's rod theory and with help of Euler parameters, the set of nonlinear governing differential equations which free from the effect of singularity are established together with boundary conditions. The system of nonlinear differential equations is solved by using the shooting method with high accuracy integrator, seventh-eighth order Runge-Kutta with adaptive step-size scheme. The error norm of end conditions is minimized within the prescribed tolerance ($10^{-5}$). The behavior of VAL elastica is studied by two processes. One is obtained by applying slackening first. After that keeping the slackening as a constant and then the twist angle is varied in subsequent order. The other process is performed by reversing the sequence of loading in the first process. The results are interpreted by observing the load-deflection diagram and the stability properties are predicted via fold rule. From the results, there are many interesting aspects such as snap-through phenomenon, secondary bifurcation point, loop formation, equilibrium configurations and effect of variable-arc-length to behavior of elastica.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.59-64
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• 2006

A new method to obtain explicit re-parameterization that preserves the curve degree and parametric domain is presented in this paper. The re-parameterization brings a curve very close to the arc length parameterization under $L_2$ norm but with less segmentation. The re-parameterization functions we used are $C^1$ continuous piecewise rational linear functions, which provide more flexibility and can be easily identified by solving a quadratic equation. Based on the outstanding performance of Mobius transformation on modifying pieces with monotonic parametric speed, we first create a partition of the original curve, in which the parametric speed of each segment is of monotonic variation. The values of new parameters corresponding to the subdivision points are specified a priori as the ratio of its cumulative arc length and its total arc length. $C^1$ continuity conditions are imposed to each segment, thus, with respect to the new parameters, the objective function is linear and admits a closed-form optimization. Illustrative examples are also given to assess the performance of our new method.

• Journal of Korean Society of Steel Construction
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• v.23 no.5
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• pp.535-546
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• 2011

In this paper, semi-rigid elasto-plastic post-buckling analysis of a space frame was performed using various explicit arc-length methods. Various explicit arc-length methodsand a large-deformation and small-strain elasto-plastic 3D space frame element with semi-rigid connections and plastic hinges were developed. This element can be appliedto both explicit and implicit numerical algorithms. In this study, the Dynamic Relaxation method was adopted in the predictor and corrector processesto formulate an explicit arc-length algorithm. The developed "explicit-predictor" or "explicit-corrector" were used in the elasto-plastic post-buckling analysis. The Eulerian equations for a beam-column with finite rotation, which considers the bowing effects, were adopted for the elastic system and extended to theinelastic system with a plastic hinge concept. The derived tangent stiffness matrix was asymmetrical due to the finite rotation. The joint connection elements were introduced for semi-rigidity using a static condensation technique. Semi-rigid elasto-plastic post-buckling analyses were carried out to demonstrate the potential of the developed explicit arc-length method and advanced space frame element in terms of accuracy and efficiency.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1993.10a
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• pp.47-54
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• 1993

This paper is concerned with the geometrically nonlinear behavior of elastic systems under conservative loading conditions. In particular, the topic are snap through problems and the arc-length method to pass limit points of space trusses is used. And numerical examples are presented to trace nonlinear equilibrium paths.

• Structural Engineering and Mechanics
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• v.4 no.1
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• pp.49-59
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• 1996

This paper considers large deflection problem of a simply supported beam with variable are length subjected to a point load. The beam has one of its ends hinged and at a fixed distance from this end propped by a frictionless support over which the beam can slide freely. This highly nonlinear flexural problem is solved by elliptic-integral method and shooting-optimization technique, thereby providing independent checks on the new solutions. Because the beam can slide freely over the frictionless support, there is a maximum or critical load which the beam can carry and it is dependent on the position of the load. Interestingly, two possible equilibrium configurations can be obtained for a given load magnitude which is less than the critical value. The maximum arc-length was found to be equal to about 2.19 times the fixed distance between the supports and this value is independent of the load position.

• Journal of the Ergonomics Society of Korea
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• v.33 no.4
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• pp.299-311
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• 2014

Objective: The aim of this study was to develop a method for measuring breast size from three-dimensional (3D) body scan image data. Background: Previous bra studies established reference points by directly contacting the subject's naked skin to determine the boundary of the breast. But some subjects were uncomfortable with these types of measurements. This study examined noncontact methods of extracting breast reference points from 3D body scan data that were collected while subjects were wearing standardized soft bras. Method: 3D body scan data of 32 Korean women were analyzed. The subjects were selected from the Size Korea 2010 study. The breast landmarks were identified by graphic analyses of slicing contour lines on 3D body scan data. Results: Three methods determining bra cup size were compared. The M1 and M2 methods determined cup size by calculating the difference between bust girth and under-bust girth. The M3 method determined bra cup size by measuring breast arc length. Conclusion: The researchers proposed an anthropometric bra cup sizing system with the breast arc length (M3 method). It was measured from the geometrically defined landmarks on the 3D body scan slicing contour lines. The new bra cup size was highly correlated with breast depth. Application: The noncontact measuring method used in this study can be applied to the ergonomic studies measuring sensitive body parts.

• Computational Structural Engineering
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• v.10 no.4
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• pp.177-184
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• 1997

In this paper, numerical methods are developed for solving the elastica of simple beams with variable-arc-length subjected to a point loading. The beam model is based on Bernoulli-Euler beam theory. The Runge-Kutta and Regula-Falsi methods, respectively, are used to solve the governing differential equations and to compute the beam's rotation at the left end of the beams. Extensive numerical results of the elastica responses, including deflected shapes, rotations of cross-section and bending moments, are presented in non-dimensional forms. The possible maximum values of the end rotation, deflection and bending moment are determined by analyzing the numerical data obtained in this study.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2003.05a
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• pp.27-31
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• 2003

Recently, buckling is easy to happen as that High tensile steel that is the thin plate absence is used comprehensively for the structure. Specially, buckling is getting into important design standard in hull construction which use High tensile steel. Therefore, that grasp conduct exactly after buckling is important in stability of hull structure. In this study, examined closely about conduct and secondary buckling after initial buckling of thin plate structure which receive compressive load according to various kinds yield strength under simply supported condition that make by buckling strength formula standard in each payment in advance rule to place that is representative construction of hull in this research. Analysis method is F.E.M by ANSYS and complicated nonlinear behaviour to analyze such as secondary buckling in used arc-length method.

• Journal of the Korean Society of Safety
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• v.14 no.4
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• pp.28-36
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• 1999

In this paper, A circular arc crackered plate in biaxially stretched sheets was investigated in the boundary element method. The applications of fracture mechanics have traditionally concentrated on crack problems under an mode I, straight crack. However, many service failures occur from growth of cracks subjected to mixed mode loadings. A rectangular plate with arc crack or slanted central crack, under biaxial tensile loading, was treated analytically and also solved numerically. The Results from BEM applying different loading conditions, crack length (a/W), arc angle($\alpha$) are presented and discussed. The stress intensity factors are evaluated by the techniques of the J-integral. The decomposition method, used to decouple the stress intensity factors in mixed mode problems, is implemented by a considering a small circular contour path around each crack tip. The BIE method was successfully applied to a circular arc crackerd plate problem, also slanted centre cracked plate under mixed mode.

• 전기의세계
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• v.29 no.6
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• pp.401-409
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• 1980

This paper deals with the implementation of forced reclosing the transmission line. Because the ground circuit breaker method decrease the secondary arc current sufficiently, the reclosing time can be reduced. As the secondary arc current is large and its residual time is long in UHV transmission line, this method is more effective in that system. The resistance of ground circuit breaker which minimize the secondary arc current is determined according to the system voltage and the length of transmission line.