• Transactions of Materials Processing
• /
• v.8 no.1
• /
• pp.47-56
• /
• 1999

The governing functional in plastic deformation has to satisfy the incompressibility constraint. This incompressibility constraint imposed on velocity fields can be removed by introducing either Lagrange multiplier or the penalty constant into the functional. In this study, two-dimensional rigid plastic FEM programs using these schemes were developed. These two programs and DEFORM were applied in a cylinder upsetting and a closed die forging to compare the values of load, local mean stress and volume loss. As the results, the program using Lagrange multiplier obtained a more exact and stable solution, but it took more computational time than the program using the penalty constant. Therefore, according to user's need, one of these two programs can be chosen to simulate a metal forming processes.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.20 no.7
• /
• pp.2078-2086
• /
• 1996

This paper introduces two three-dimensional eight-node hexagonal elements obtained by using multivariable variational mehtod. Both of them are based on the modified hellinger-reissner principle to employ incompatible displacements and assumed stresses of assumed strains. The internal functions of element are introduced to as element formulation through two different methods : the first one uses the functions determined directly from the element boundary condition of the incompatible displacements ; while the second, being a kind of B-bar mehtod, employs the modification technique of strain-displacement matrix to pass the patch test. The elements are evaluated on the selective problems of bending and material incompressibility with regular and distorted meshes. The results show that the new elements perform with good accuracy in both of deformation and stress calculation and they are insensitive to distorted geometry of element.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.19 no.2
• /
• pp.486-494
• /
• 1995

This paper introduces two kinds of new four-node quadrilateral axisymmetric elements with independently-assumed strains. They are formulated by the modified Hellinger-Reissner principle so as to employ incompatible displacements and assumed strains. In one of the present elements, the strains from incompatible displacements are corrected to pass the constant strain patch test. The other contains incompatible functions that are obtained from the element boundary condition. The elements are evaluated on the several problems of bending and material incompressibility with regular and distorted meshes. The results show that the new element performs excellently in deformation and stress calculation.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.11
• /
• pp.2871-2882
• /
• 1994

Two kinds of 4-node plane stress/strain finite elements are presented in this work. They are derived from the modified Hellinger-Reissner variational principle so as to employ the internal incompatible displacement and independent stress fields, or the incompatible displacement and strain fields. The introduced incompatible functions are selected to satisfy the constant strain condition. The elements are evaluated on several problems of bending and material incompressibility with regular and distorted elements. The results show that the new elements perform excellently in the calculation of deformation and stresses.

• Structural Engineering and Mechanics
• /
• v.61 no.1
• /
• pp.31-47
• /
• 2017

As a relatively new type of multi-layered rubber-based seismic isolators, fiber-reinforced elastomeric isolators (FREIs) are composed of several thin rubber layers reinforced with flexible fiber sheets. Limited analytical studies in literature have pointed out that "warping" (distortion) of reinforcing sheets has significant influence on buckling behavior of FREIs. However, none of these studies, to the best knowledge of authors, has investigated their warping behavior, thoroughly. This study aims to investigate, in detail, the warping behavior of strip-shaped FREIs by deriving advanced analytical solutions without utilizing the commonly used "pressure", incompressibility, inextensibility and the "linear axial displacement variation through the thickness" assumptions. Studies show that the warping behavior of FREIs mainly depends on the (i) aspect ratio (shape factor) of the interior elastomer layers, (ii) Poisson's ratio of the elastomer and (iii) extensibility of the fiber sheets. The basic assumptions of the "pressure" method as well as the commonly used incompressibility assumption are valid only for isolators with relatively large shape factors, strictly incompressible elastomeric material and nearly inextensible fiber reinforcement.

• 한국전산유체공학회:학술대회논문집
• /
• 2009.11a
• /
• pp.1-1
• /
• 2009

In this presentation, I talk about various fluid simulation methods that have been developed for computer graphics special effects since 1996. They are all based on CFD but sacrifice physical reality for visual plausability and time. But as the speed of computer increases rapidly and the capability of GPU (graphics processing unit) improves, methods for more physical realism have been tried. In this talk, I will focus on four aspects of fluid simulation methods for computer graphics: (1) particle level-set methods, (2) particle-based simulation, (3) methods for exact satisfaction of incompressibility constraint, and (4) GPU-based simulation. (1) Particle level-set methods evolve the surface of fluid by means of the zero-level set and a band of massless marker particles on both sides of it. The evolution of the zero-level set captures the surface in an approximate manner and the evolution of marker particles captures the fine details of the surface, and the zero-level set is modified based on the particle positions in each step of evolution. (2) Recently the particle-based Lagrangian approach to fluid simulation gains some popularity, because it automatically respects mass conservation and the difficulty of tracking the surface geometry has been somewhat addressed. (3) Until recently fluid simulation algorithm was dominated by approximate fractional step methods. They split the Navier-Stoke equation into two, so that the first one solves the equation without considering the incompressibility constraint and the second finds the pressure which satisfies the constraint. In this approach, the first step introduces error inevitably, producing numerical diffusion in solution. But recently exact fractional step methods without error have been developed by fluid mechanics scholars), and another method was introduced which satisfies the incompressibility constraint by formulating fluid in terms of vorticity field rather than velocity field (by computer graphics scholars). (4) Finally, I want to mention GPU implementation of fluid simulation, which takes advantage of the fact that discrete fluid equations can be solved in parallel.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.6
• /
• pp.1655-1668
• /
• 2014

In this article, we propose and analyze a new nonconforming primal mixed finite element method for the stationary Stokes equations. The approximation is based on the pseudostress-velocity formulation. The incompressibility condition is used to eliminate the pressure variable in terms of trace-free pseudostress. The pressure is then computed from a simple post-processing technique. Unique solvability and optimal convergence are proved. Numerical examples are given to illustrate the performance of the method.

• 한국전산유체공학회:학술대회논문집
• /
• 2011.05a
• /
• pp.256-258
• /
• 2011

Using the axial Green's function method for Steady Stokes flows, we introduce a new pressure correction formula to satisfy the incompressibility condition, in which the pressure is related to the integral of the second order derivatives of the velocity. Based on this formula, we propose the iterative method for solving the Stokes flows in complicated domains. Even if the domain is complex, this method maintains the second order of convergence for the velocity.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 1997.10a
• /
• pp.40-44
• /
• 1997

The governing functional in plastic deformation has to satisfy the incompressible condition. This incompressible condition imposed on the velocity fields can be removed by introducing either the Langrange multiplier or the penalty function into the functional. In the study two-dimensional rigid plastic FEM programs using by Lagrange multiplier and penalty function are developed. A compression of cylinder and a spike forging are simulated to compare the data of loads, local mean stresses and reductions of volume.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 1997.10a
• /
• pp.57-61
• /
• 1997

The governing functional in plastic deformation has to satisfy the incompressible condition. This incompressible condition imposed on the velocity fields can be removed by introducing either the Langrange multiplier or the penalty function into the functional. In this study two-dimensional rigid plastic FEM programs using by Langrange multiplier and penalty function are developed. A compression of cylinder and a spike forging are simulated to compare the data of loads, local mean stresses and reductions of volume.