• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.3
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• pp.195-202
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• 2012

Two nonlinear frame elements taking into account geometric nonlinearity is presented and compared based on the Lagrangian co-rotational formulation. The first frame element is believed to be geometrically-exact because not only tangent stiffness matrices is exactly evaluated including stiffness matrices due to initial deformation but also total member forces are directly determined from total deformations in the deformed state. Particularly two exact tangent stiffness matrices based on total Lagrangian and updated Lagrangian formulation, respectively, are verified to be identical. In the second frame element, the deformed curved shape is regarded as the polygon and current flexural deformations in iteration process are neglected in evaluating tangent stiffness matrices and total member forces. Two numerical examples are given to demonstrate the accuracy and the good performance of the first frame element compared with the second element. Furthermore it is shown that the first frame element can be used in tracing nonlinear behaviors of cable members.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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• pp.235-242
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• 2003

The solids and the fluids in porous media have a relative velocity to each other. Due to physically and chemically different material properties and their relative velocity, the behavior of saturated porous media is extremely complicated. Thus, in order to describe and clarify the deformation behavior of saturated porous media, constitutive models for deformation of porous media coupling several effects such as flow of the fluids or thermodynanical change need to be developed in frame of Arbitrary Lagrangian Eulerian (ALE) description. The aim of ALE formulations is to maximize the advantages of Lagrangian and Eulerian elements, and to minimize the disadvantages. Therefore, this method is appropriate for the analysis of porous media that are considered for the behavior of the solids and the fluids. In this work, governing equations of porous media based on ALE description are obtained from governing equations in frame of updated Lagrangian description. Then, weak forms of these equations are derived using arbitrary weighting functions.

• Coupled systems mechanics
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• v.7 no.5
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• pp.583-610
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• 2018

This paper discusses the issues associated with modeling frictional contact between solid bodies undergoing large deformations. The most common model for friction on contact interfaces in solid mechanics is the Coulomb friction model, in which two distinct responses are possible: stick and slip. Handling the transition between these two phases computationally has been a source of algorithmic instability, lack of convergence and non-unique solutions, particularly in the presence of large deformations. Most computational models for frictional contact have used penalty or updated Lagrangian approaches to enforce frictional contact conditions. These two approaches, however, present some computational challenges due to conditioning issues in penalty-type implementations and the iterative nature of the updated Lagrangian formulation, which, particularly in large simulations, may lead to relatively slow convergence. Alternatively, a plasticity-inspired implementation of frictional contact has been shown to handle the stick-slip conditions in a local, algorithmically efficient manner that substantially reduces computational cost and successfully avoids the issues of instability and lack of convergence often reported with other methods (Laursen and Simo 1993). The formulation of this approach, however, has been limited to the small deformations realm, a fact that severely limited its application to contact problems where large deformations are expected. In this paper, we present an algorithmically consistent formulation of this method that preserves its key advantages, while extending its application to the realm of large-deformation contact problems. We show that the method produces results similar to the augmented Lagrangian formulation at a reduced computational cost.

• Journal of the Korean Geotechnical Society
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• v.16 no.4
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• pp.191-199
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• 2000

In this research, the finite element analysis of piezocone penetration and dissipation tests has been conducted using the anisotropic elastoplastic-viscoplastic bounding surface model, virtual work equation, and theory of mixtures formulated in the Up[dated Lagrangian reference frame for the large deformation and finite strain nature of piezocone penetration. The formulated equations have been implemented into a finite element program. The cone resistance, excess pore water pressure, and dissipation of excess pore water pressure from the finite element analysis have been compared and investigated. An effective simulation could be performed with the use of the anisotropic and viscous soil model. The finite element formulations and the results are described in part 'I' and part 'II' respectively.

• Transactions of Materials Processing
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• v.14 no.1 s.73
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• pp.43-48
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• 2005

The production of metal strip with uniform thickness and flatness are two important problems associated thin strip rolling. The thickness and flatness of strip are affected by the flattening of contact surface between strip and roll, the elastic recovery and the bending of roll. Especially, the flatness of the strip is greatly affected by bending deflection of roll. The roll must be designed considered the elastic deformation of roll. This study describes the measurement of thickness and flatness of strip and shows the crown roll for producing flat strip. But it is difficult to produce the crown roller. The cross rolling that is a simple method which can produce the flat strip is introduced and it is found the optimal cross angle for improvement of flatness of plate. These problems are solved by the MARC code on the basis of elastic-plastic material and the updated Lagrangian formulation.

• Structural Engineering and Mechanics
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• v.12 no.1
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• pp.35-50
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• 2001

A numerical methodology is presented in this paper for the geometrically non-linear analysis of slender uni-dimensional structural elements under unilateral contact constraints. The finite element method together with an updated Lagrangian formulation is used to study the structural system. The unilateral constraints are imposed by tensionless supports or foundations. At each load step, in order to obtain the contact regions, the equilibrium equations are linearized and the contact problem is treated directly as a minimisation problem with inequality constraints, resulting in a linear complementarity problem (LCP). After the resulting LCP is solved by Lemke's pivoting algorithm, the contact regions are identified and the Newton-Raphson method is used together with path following methods to obtain the new contact forces and equilibrium configurations. The proposed methodology is illustrated by two examples and the results are compared with numerical and experimental results found in literature.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.9 no.3
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• pp.13-19
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• 1989

A system of coupled differential equations governing the lateral-torsional buckling of thin-walled arches subjected to pure bending moment is presented. The governing differential equations are derived using incremental form of principle of virtual displacement based on updated Lagrangian procedure. The differential equations are solved for the critical end moments of arches with I section, and then comparative studies are made with existing solutions.

• Structural Engineering and Mechanics
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• v.14 no.2
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• pp.135-150
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• 2002

Numerical analysis of ultimate behaviour of thin bionics shells is treated in present paper. Interactive conditions in resonance and stability ultimate response are considered. Numerical treatment of nonlinear problems appearing is made using the updated Lagrangian formulation of motion. Each step of the iteration approaches the solution of linear problem and the feasibility of parallel processing FETM-technique with adaptive mesh refinement and substructuring for the analysis of ultimate action of thin bionics shells is established. Some numerical results are submitted in order to demonstrate the efficiency of the procedures suggested.

• Computational Structural Engineering
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• v.10 no.2
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• pp.139-148
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• 1997

A finite element method is programmed to analyse the nonlinear behavior of axisymmetric structures. The lst order Mindlin shell theory which takes into account the transversal shear deformation is used to formulate a conical two node element with six degrees of freedom. To evade the shear locking phenomenon which arises in Mindlin type element when the effect of shear deformation tends to zero, the reduced integration of one point Gauss Quadrature at the center of element is employed. This method is the Updated Lagrangian formulation which refers the variables to the state of the most recent iteration. The solution is searched by Newton-Raphson iteration method. The tangent matrix of this method is obtained by a finite difference method by perturbating the degrees of freedom with small values. For the moment this program is limited to the analyses of non-linear elastic problems. For structures which could have elastic stability problem, the calculation is controled by displacement.

• 한국전산유체공학회:학술대회논문집
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• 2002.10a
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• pp.47-52
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• 2002

We present an improved Lagrangian vortex method in 2-D incompressible unsteady viscous flows, which is based on a mesh-free integral approach of the velocity-vorticity formulation. Vorticity fields are represented by discrete vortex blobs that are updated by the Lagrangian vorticity transport with the particle strength exchange scheme. Velocity fields are expressed in a form of the Helmholtz decomposition, which are calculated by a fast algorithm of the Biot-Savart integration with a smoothed kernel and by a well-established panel method. No-slip condition is enforced through viscous diffusion of vorticity from a solid body into field. The vorticity flux is determined in such a way that spurious slip velocity vanishes. Through the comparison with the existing finite volume scheme for the transient vortical flows around an impulsively started cylinder at Reynolds number Re=550, we would obtain a more accurate scheme for vortex methods in complicated flows.