• 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.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.1
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• pp.1-8
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• 2023

Let C be a smooth projective curve and W a symplectic bundle over C of degree w. Let π : 𝕃𝔾(W) → C be the relative Lagrangian Grassmannian over C and S_d(W) be the space of Lagrangian subbundles of degree w -d. Then Kontsevich's space ${\bar{\mathcal{M}}}_g$(𝕃𝔾(W), β_d) of stable maps to 𝕃𝔾(W) is a compactification of S_d(W). In this article, we give an upper bound on the dimension of ${\bar{\mathcal{M}}}_g$(𝕃𝔾(W), β_d), which is an analogue of a result in [8] for the relative Lagrangian Grassmannian.

• Journal of Soil and Groundwater Environment
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• v.11 no.1
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• pp.37-44
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• 2006

This study summarizes advantages and disadvantages of numerical methods and compares ELLAM and LEZOOMPC to develop an efficient numerical modeling technique on contaminant transport. Eulerian-Lagrangian method and Eulerian method are commonly used numerical techniques. However Eulerian-Lagrangian method does not conserve mass globally and fails to treat boundary in a straightforward manner. Also, Eulerian method has restrictions on the size of Courant number and mesh Peclet number because of time truncation error. ELLAM (Eulerian Lagrangian Localized Adjoint Method) which has been popularly used for past 10 years in numerical modeling, is known for overcoming these numerical problems of Eulerian-Lagrangian method and Eulerian method. However, this study investigates advantages and disadvantages of ELLAM and suggests a change for the better. To figure out the disadvantages of ELLAM, the results of ELLAM, LEZOOMPC (Lagrangian-Eulerian ZOOMing Peak and valley Capturing), and visual MODFLOW are compared for four examples having different mesh Peclet numbers. The result of ELLAM generates numerical oscillation at infinite of mesh Peclet number, but that of LEZOOMPC yields accurate simulations. The simulation results suggest that the numerical error of ELLAM could be alleviated by adopting some schemes in LEZOOMPC. In other words, the numerical model which combines ELLAM with backward particle tracking, forward particle tracking, adaptively local zooming, and peak/valley capturing of LEZOOMPC can be developed for not only overcoming the numerical error of ELLAM, but also keeping the numerical advantage of ELLAM.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.33 no.1
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• pp.17-23
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• 2020

In this study, the behaviors of a vessel and the ground during the vessel impacting an underwater slope that is part of an artificial protective island are analyzed using the coupled Eulerian-Lagrangian scheme. To consider the large deformation including the shear failure of soil, the Eulerian domain is used to model the ground and water, while the impacting objects are modeled as the Lagrangian domain. For efficiency, the mass scaling scheme is applied to the modeling of the impacting objects, and the ground is modeled by setting the Eulerian volume fraction values. To verify the applicability of the constructed model, a dynamic penetration anchor problem is analyzed. The impacting vessel is modeled using solid elements following the external shape of a container ship, and an analysis of a collision on the slope is performed. As a result, collision behaviors such as displacement, velocity, and dissipation energy are estimated, and the necessity of a parametric study as further research is established.

• Proceedings of the Korea Water Resources Association Conference
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• 1993.07a
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• pp.151-157
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• 1993

• Bulletin of the Society of Naval Architects of Korea
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• v.27 no.2
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• pp.21-30
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• 1990

Theoretical and experimental techniques to analyze the two-dimensional liquid motion in a tank are discussed. A Lagrangian FEM with a velocity correction procedure is introduced to describe incompressible free surface fluid flow. A mesh rezoning technique is used to prevent strong distortion of finite elements in the Lagrangian description. Model test technique for sloshing tank is developed using a hydraulic type bench tester. The influence of the variation in the exciting frequency and amplitude are observed for various fill depths. The results of theoretical calculations are compared with those of experiments.

• Journal of the Korean Society for Advanced Composite Structures
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• v.3 no.2
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• pp.1-10
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• 2012

In the present study, an Element-Based Lagrangian Formulation for the nonlinear analysis of shell structures is presented. The strains, stresses and constitutive equations based on the natural co-ordinate have been used throughout the Element-Based Lagrangian Formulation of the present shell element which offers an advantage of easy implementation compared with the traditional Lagrangian Formulation. The Element-Based Lagrangian Formulation of a 9-node resultant-stress shell element is presented for the anisotropic composite material. The element is free of both membrane and shear locking behavior by using the assumed natural strain method such that the element performs very well in thin shell problems. The arc-length control method is used to trace complex equilibrium paths in thin shell applications. Numerical examples for laminated composite curved shells presented herein clearly show the validity of the present approach and the accuracy of the developed shell element.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.8
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• pp.47-54
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• 2006

In this paper, numerical algorithms applied in two-step eulerian scheme are investigated and implemented. Element quantities are advected with donor or van Leer algorithm. Nodal quantities are advected with Simplifed ALE [SALE] algorithm. Material interfaces are determined with Simple Line Interface Calculation [SLIC] algorithm. Practical aspects considered for code development are addressed in detail. The results of developed two-step Eulerian code are verified by comparing with those from pure lagrangian scheme and commercial code.

• Magazine of the Korean Society of Agricultural Engineers
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• v.36 no.1
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• pp.128-140
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• 1994

Coastal areas, especially embayments are apt to be polluted easily and many embayments in Korea are already suffering from pollution problems. To manage such pollution, it is strongly needed to develop technique to trace movements of pollution. Such technique cove- ring the embayment affected by the tidal influence, should take account both of the convection and the diffusion motions which cause lots of problems in numerical calculation. In this study, a Eulerian-Lagrangian Analysis(ELA) model was applied to Young Il bay and tested for its applicablity, which was developed by using the Eulerian-Lagrangian Method that reduce the numerical disperison and oscillation by way of solving convection and diffusion terrns separately. Concentration of Chemical Oxygen Demand(COD) and Suspend Solid(SS) of the embay- ment area were estimated by the model and compared with the observed values and the sound results were obtained. At the same time the diffsion coefficient and decay coefficient for Chemical Oxygen Demand in the Young II Bay were found as Dx = Dy = 20m$^2$/sec, kd=2.5 ${\times}$ 10-5/sec respectively, and for Suspend Solid, Dx =Dy = 30m$^2$/sec, kd=5.0${\times}$ 10-5/sec

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.8 no.2
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• pp.185-192
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• 1996

In order to simulate the coastal dispersion effectively, hybrid concept of operator split Eulerian-lagrangian concentration model and random-walk particle tracking model are developed. Especially the random-walk model is adequate for region with steep slope of concentration. According to model tests, it agrees perfectly with analytical solution on around the source point for therefore. ▽C $\geq$ 0.005, meanwhile it shows poor results for ▽C$\leq$0.002. trial modeling for real situation therefore, random-walk model is applied for near field henceforth Eulerian-Lagrangian concentration model is adoped for whole domain so that overall performance and accuracy can be achieved by using developed hybrid model.