• The Korean Journal of Rheology
• /
• v.11 no.1
• /
• pp.18-27
• /
• 1999

Predicting the deformation behaviors of sheets in thermoforming processes has been a daunting challenge due to the strong nonlinearities arising from very large deformations, mold-polymer contact condition and hyperelasticity constitutive equations. Nonlinear numerical analysis is always required to face this challenge especially for realistic processing conditions. In this study a 3-D algorithm and the membrane approximation are developed for thermoforming processes. The constitutive equation is expressed in terms of the 2nd Piola-Kirchhoff stress tensor and the Cauchy-Green deformation tensor. The 2-term Mooney-Rivlin model is used for the material model equation. The algorithm is established by the finite element formulation employing the total Lagrangian coordinate. The deformation behavior and the stress distribution results of 3-D algorithm with various point boundary conditions are compared to those of the membrane approximation algorithm. Also, the slip boundary condition and the no-slip boundary condition are applied for the systems that have molds. Finally, the effect of sheet temperatures on the final thickness distribution is investigated for the ABS material.

• Bulletin of the Korean Mathematical Society
• /
• v.35 no.3
• /
• pp.473-484
• /
• 1998

We consider a finite difference approximation to a singular boundary value problem arising in the study of a nonlinear circular membrane under normal pressure. It is proved that the rate of convergence is $O(h^2)$. To obtain the solution of the finite difference equation, an iterative scheme converging monotonically to the solution of the finite difference equation is introduced. And the numerical experiment of this method is given.

• Transactions of the Korean hydrogen and new energy society
• /
• v.22 no.6
• /
• pp.835-841
• /
• 2011

The humidification is essential for performance enhancement of the electrolysis of PEMFC because proton conductivity depends on hydration of the proton exchange membrane. In this study, the humidification experiment did about On/Off control the humidification and dew condensation for PEMFC by using of the membrane humidifiers. As the results, it was possible to approximation control of the humidity by using of the solenoid valve On/Off control on the membrane humidifier. Also the problem on the dew condensation was resolved by approximation humidity control through solenoid valve On/Off control and the removal of the dew condensation in the flow channel was verified through visualization experiment.

• Structural Engineering and Mechanics
• /
• v.55 no.2
• /
• pp.349-364
• /
• 2015

Analytical solutions for modeling geotextile tubes during the filling process and approximation method to determine the densified tube shape are reviewed. The geotextile tube filling analysis is based on Plaut & Suherman's two-dimensional solution for geotextile tubes having a weightless and frictionless inextensible membrane resting on a rigid horizontal foundation subjected to internal and external hydrostatic pressures. The approximation for the densified tube shape developed by Leshchinsky et al. was adopted. A modified method for approximating the densified tube shape based on an areal-strain deformation analysis is introduced. Design diagrams useful for approximating geotextile tube measurements in the design process are provided.

• Proceeding of KASS Symposium
• /
• 2005.05a
• /
• pp.125-132
• /
• 2005

Membrane structures, a kind of lightweight soft structural system, are used for spatial structures. The material property of the membrane has strong axial stiffness, but little bending stiffness. The design procedure of membrane structures are needed to do shape finding, stress-deformation analysis and cutting pattern generation. In shape finding, membrane structures are unstable structures initially. These soft structures need to be introduced initial stresses because of its initial unstable state, and it happens large deformation phenomenon. And also there are highly varied in their size, curvature and material stiffness. So, the approximation inherent in cutting pattern generation methods is quite different. Therefore, in this study, to find the structural shape after large deformation caused by Initial stress, we need the shape analysis considering geometric nonlinear ten And the geodesic line on surface of initial equilibrium shape and the cutting pattern generation using the geodesic line is introduced.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2006.04a
• /
• pp.325-332
• /
• 2006

Membrane structures, a kind of lightweight soft structural system, are used for spatial structures. The design procedure of membrane structures are needed to do shape finding, stress-deformation analysis and cutting pattern generation, because the material property has strong axial stiffness, but little bending stiffness. The problem of cutting pattern is highly varied in their size, curvature and material stiffness. So, the approximation inherent in cutting pattern generation methods is quite different. Therefore the ordinary computer software of structural analysis & design is not suitable for membrane structures. In this study, we develop the program for cutting pattern generation using geodesic line, and investigate the result of example's cutting pattern in detail.

• Proceeding of KASS Symposium
• /
• 2006.05a
• /
• pp.205-213
• /
• 2006

Membrane structures, a kind of lightweight soft structural system, are used for spatial structures. The design procedure of membrane structures are needed to do shape finding, stress-deformation analysis and cutting pattern generation, because the material property has strong axial stiffness, but little bending stiffness. The problem of cutting pattern is highly varied in their size, curvature and material stiffness. So, the approximation inherent in cooing pattern generation methods is quite different. Therefore the ordinary computer software of structural analysis & design is not suitable for membrane structures. In this study, we develop the program for cutting pattern generation using geodesic line, and investigate the result of example's cutting pattern in detail.

• Journal of Korean Association for Spatial Structures
• /
• v.12 no.1
• /
• pp.109-119
• /
• 2012

For membrane structure, there are three main steps in design and construction, which are form finding, statistical load analysis, and cutting patterning. Unlike the first two stages, the step of cutting pattern involves the translation of a double-curved surface in 3D space into a 2D plane with minimal error. For economic reasons, the seam lines of generated cutting patterns rely greatly on the geodesic line. Generally, as searching regions of the seam line are plane elements in the step of shape analysis, the seam line is not a smooth curve, but an irregularly divided straight line. So, it is how we make an irregularly divided straight line a smooth curve that defines the quality of the pattern. Accordingly, in this paper, we analyzed interpolation schemes using spline, and apply these methods to cutting pattern generation on the curved surface. To generate the pattern, three types of spline functions were used, i.e., cubic spline function, B-spline, and least-square spline approximation, and simple model and the catenary-shaped membrane was adopted to examine the result of generation. The result of comparing the approximation curves by the number of elements and the number of extracted nodes of simple model revealed that the seam line for less number of extracted nodes with large number of elements were more efficient, and the least-square spline approximation provided smoother seam line than other methods.

• Membrane Journal
• /
• v.7 no.3
• /
• pp.142-149
• /
• 1997

The extended analysis on the diverging flow through asymmetric membrane pores has been performed in this study. Afore rigorous equations of velocity profile relevant to the divergent slit and cone shaped channels, which are widely used as a general pore model, have been obtained by employing a creeping flow approach of Newtonian fluids. As a degree of asymmetry (i.e., diverging angle) is increased, the predicted flow function shifts Toward the center region due to the incorporated wall effect, so that the overall velocity profile becomes decreased. It is true, as expected, that when the divergent channel is in the low diverging angle limit, the channel flow results in the Poiseuillean fashion by utilizing a lubrication approximation. The flow rate equation of each type of channel has been developed from the combined solution of velocity profile and pressure fields. The effect of diverging flow on the flow rate enhancement has been remarkably predicted, in which the flow rate increases with the increase of pore asymmetry. The advantage of our theoretical results lies in the analytical expression for the diverging flow behavior through pore channels as well as its ability to play a fundamental role on the related membrane filtrations such as microfiltration and ultrafiltration.

• Coupled systems mechanics
• /
• v.1 no.4
• /
• pp.325-343
• /
• 2012

We present different numerical methods for solving the shallow shelf equations with basal drag (SSAB). An alternative approach of splitting the SSAB equation into a Laplacian and diagonal shift operator is discussed with respect to the underlying eigenvalue problem. First, we solve the equations using standard methods. Then, the coupled equations are decomposed into operators for membranes stresses, basal shear stress and driving stress. Applying reasonable parameter values, we demonstrate that the operator of the membrane stresses is much stiffer than the operator of the basal shear stress. Here, we could apply a new splitting method, which alternates between the iteration on the membrane-stress operator and the basal-shear operator, with a more frequent iteration on the operator of the membrane stresses. We show that this splitting accelerates and stabilize the computational performance of the numerical method, although an appropriate choice of the standard method used to solve for all operators in one step speeds up the scheme as well.