• 유체기계공업학회:학술대회논문집
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• 2006.08a
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• pp.349-352
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• 2006

The conventional segregated finite element formulation produces a small and simple matrix at each step than in an integrated formulation. And the memory and cost requirements of computations are significantly reduced because the pressure equation for the mass conservation of the Navier-Stokes equations is constructed only once if the mesh is fixed. However, segregated finite element formulation solves Poisson equation of elliptic type so that it always needs a pressure boundary condition along a boundary even when physical information on pressure is not provided. On the other hand, the conventional integrated finite element formulation in which the governing equations are simultaneously treated has an advantage over a segregated formulation in the sense that it can give a more robust convergence behavior because all variables are implicitly combined. Further it needs a very small number of iterations to achieve convergence. However, the saddle-paint-type matrix (SPTM) in the integrated formulation is assembled and preconditioned every time step, so that it needs a large memory and computing time. Therefore, we newly proposed the P2PI semi-segregation formulation. In order to utilize the fact that the pressure equation is assembled and preconditioned only once in the segregated finite element formulation, a fixed symmetric SPTM has been obtained for the continuity constraint of the present semi-segregation finite element formulation. The momentum equation in the semi-segregation finite element formulation will be separated from the continuity equation so that the saddle-point-type matrix is assembled and preconditioned only once during the whole computation as long as the mesh does not change. For a comparison of the CPU time, accuracy and condition number between the two methods, they have been applied to the well-known benchmark problem. It is shown that the newly proposed semi-segregation finite element formulation performs better than the conventional integrated finite element formulation in terms of the computation time.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.33 no.4
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• pp.242-247
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• 2009

AILU type preconditioners for a two-dimensional combined P2P1 finite element formulation of the interaction of rigid cylinder with incompressible fluid flow have been devised and tested by solving fluid-structure interaction (FSI) problems. The FSI code simulating the interaction of a rigid cylinder with an unsteady flow is based on P2P1 mixed finite element formulation coupled with combined formulation. Four different preconditioners were devised for the two-dimensional combined P2P1 finite element formulation extending the idea of Nam et al., which was proposed for the preconditioning of a P2P1 mixed finite element formulation of the incompressible Navier-Stokes equations. It was found that PC-III or PC-IV among them perform well with respect to computational memory and convergence rate for some bench-mark problems.

• Structural Engineering and Mechanics
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• v.51 no.4
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• pp.601-625
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• 2014

Based on continuum mechanics and the principle of virtual displacements, incremental total Lagrangian formulation (T.L.) and incremental updated Lagrangian formulation (U.L.) were presented. Both T.L. and U.L. considered the large displacement stiffness matrix, which was modified to be symmetrical matrix. According to the incremental updated Lagrangian formulation, small strain, large displacement, finite rotation of three dimensional Timoshenko fiber beam element tangent stiffness matrix was developed. Considering large displacement and finite rotation, a new type of tangent stiffness matrix of the beam element was developed. According to the basic assumption of plane section, the displacement field of an arbitrary fiber was presented in terms of nodal displacement of centroid of cross-area. In addition, shear deformation effect was taken account. Furthermore, a nonlinear finite element method program has been developed and several examples were tested to demonstrate the accuracy and generality of the three dimensional beam element.

• Structural Engineering and Mechanics
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• v.83 no.2
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• pp.273-282
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• 2022

In this paper, we propose a new concept for error estimation in finite element solutions, which we call mode-based error estimation. The proposed error estimation predicts a posteriori error calculated by the difference between the direct finite element (FE) approximation and the recovered FE approximation. The mode-based FE formulation for the recently developed self-updated finite element is employed to calculate the recovered solution. The formulation is constructed by searching for optimal bending directions for each element, and deep learning is adopted to help find the optimal bending directions. Through various numerical examples using four-node quadrilateral finite elements, we demonstrate the improved predictive capability of the proposed error estimator compared with other competitive methods.

• Journal of Mechanical Science and Technology
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• v.15 no.11
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• pp.1499-1506
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• 2001

Various transition elements are used in general for the effective finite element analysis of complicated mechanical structures. In this paper, a solid-to-beam transition finite element, which can b e used for connecting a C1-continuity beam element to a continuum solid element, is proposed. The shape functions of the transition finite element are derived to meet the compatibility condition, and a transition element equation is formulated by the conventional finite element procedure. In order to show the effectiveness and convergence characteristics of the proposed transition element, numerical tests are performed for various examples. As a result of this study, following conclusions are obtained. (1) The proposed transition element, which meets the compatibility of the primary variables, exhibits excellent accuracy. (2) In case of using the proposed transition element, the number of nodes in the finite element model may be considerably reduced and the model construction becomes more convenient. (3) This formulation method can be applied to the usage of higher order elements.

• Journal of the Korean Geotechnical Society
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• v.16 no.4
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• pp.183-190
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• 2000

In this research, the finite element analysis of piezocone penetration and dissipation tests have been conducted using the anisotropic elastoplastic-viscoplastic bounding surface model in the Updated Lagrangian reference frame for the large deformation and finite strain nu\ature of piezocone penetration. Accordingly, virtual work equation and corresponding finite element equations have been reformulated. Theory of mixtures has been incorporated to explain the behavior of the sol. It has been observed that the viscoplastic part of the soil model affected the whole formulation. The results of the finite element analysis have been compared and investigated with the experimental results. The formulations and the results are described in part 'I' and part 'II', respectively.

• Structural Engineering and Mechanics
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• v.26 no.1
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• pp.31-42
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• 2007

The unsymmetric finite element formulation has been proposed recently to improve predictions from distorted finite elements. Studies have also shown that this special formulation using parametric functions for the test functions and metric functions for the trial functions works surprisingly well because the former satisfy the continuity conditions while the latter ensure that the stress representation during finite element computation can retrieve in a best-fit manner, the actual variation of stress in the metric space. However, a question that remained was whether the unsymmetric formulation was variationally correct. Here we determine that it is not, using the simplest possible element to amplify the principles.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.351-356
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• 2000

Various transition elements are generally used for the effective analysis of a complicated mechanical structure. In this paper, a solid-to-beam transition finite element which connects a continuum element and a $c^1-continuity$ beam element each other is proposed. The shape functions of the transition finite elements, which a 8-noded hexahedral solid element fur 3D analysis and a 4-noded quadrilateral plane element fur 2D analysis are connected to a Euler's beam element, are explicitely formulated. In order to show the effectiveness and convergence characteristics of the proposed transition elements. numerical tests are performed for various examples and their results are compared with those obtained by other methods. As the result of this study. following conclusions are obtained: (1)The proposed transition finite elements show the monotonic convergence characteristics because of having used the compatible displacement folds. (2)As being used the transition element in the finite element analysis, the finite element modelings are more convenient and the analysis results are more accurate because of the formulation characteristies of the Euler's beam element.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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• pp.2492-2502
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• 2002

A rubber-like material model is generally characterized by hyperelasticity and formulated by a total stress-total strain relationship because the material shows nonlinear elastic behaviour under large deformation. In this study, a pressure potential obtained by a separately interpolated pressure is introduced to the non-linear finite element formulation incorporating with incompressible or almost incompressible condition of the material. The present formulation is somewhat different from the general formulation using the pressure computed in the displacement field. A non-linear finite element analysis program is developed for the plane strain and the axisymmetric contact problems of a rubber-like material. Various examples with rubber material are analyzed for its verification. The results about deformed shapes and stress distributions thought to be meaningful in comparison with a commercial program, MARC.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.4
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• pp.574-581
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• 2001

Transient linear elastodynamic problems are numerically analyzed in a time-domain by the Finite Element Method, for which the variational formulation based upon the equations of motion in convolution integral is newly derived. This formulation is implicit and does not include the time derivative terms so that the computation procedure is simple and less assumptions are required comparing to the conventional time-domain dynamic numerical algorithms, being able to get the improved numerical accuracy and stability. That formulation is expanded using the semi-discrete approximation to obtain the finite element equations. In the temporal approximation, the time axis is divided equally and constant and linear time variations are assumed in those intervals. It is found that unconditionally stable numerical results are obtained in case of the constant time variation. Some numerical examples are given to show the versatility of the presented formulation.