• 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 Earthquake Engineering Society of Korea
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• v.23 no.1
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• pp.83-88
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• 2019

Structural analysis remains as an essential part of any integrated civil engineering system in today's rapidly changing computing environment. Even with enormous advancements in capabilities of computers and mobile tools, enhancing computational efficiency of algorithms is necessary to meet the changing demands for quick real time response systems. The finite element method is still the most widely used method of computational structural analysis; a robust, reliable and automated finite element structural analysis module is essential in a modern integrated structural engineering system. To be a part of an automated finite element structural analysis, an efficient adaptive mesh generation scheme based on R-H refinement for the mesh and error estimates from representative strain values at Gauss points is described. A coefficient that depends on the shape of element is used to correct overly distorted elements. Two simple case studies show the validity and computational efficiency. The scheme is appropriate for nonlinear and dynamic problems in earthquake engineering which generally require a huge number of iterative computations.

• Journal of Sensor Science and Technology
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• v.28 no.4
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• pp.216-220
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• 2019

In this paper, we propose a finite memory filter (estimator) for discrete-time stochastic linear systems with delays in state and measurement. A novel filtering algorithm is designed based on finite memory strategies, to achieve high estimation accuracy and stability under parametric uncertainties. The new finite memory filter uses a set of recent observations with appropriately chosen initial horizon conditions. The key contribution is the derivation of Lyapunov-like equations for finite memory mean and covariance of system state with an arbitrary number of time delays. A numerical example demonstrates that the proposed algorithm is more robust and accurate than the Kalman filter against dynamic model uncertainties.

• Journal of Korean Association for Spatial Structures
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• v.21 no.2
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• pp.57-66
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• 2021

This study develops finite element models for seismically-deficient reinforced concrete building frame retrofitted using fiber-reinforced polymer jacketing system and validates the finite element models with full-scale dynamic test for as-built and retrofitted conditions. The bond-slip effects measured from a past experimental study were modeled using one-dimensional slide line model, and the bond-slip models were implemented to the finite element models. The finite element model can predict story displacement and inter-story drift ratio with slight simulation variation compared to the measured responses from the full-scale dynamic tests.

• Structural Engineering and Mechanics
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• v.80 no.5
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• pp.553-562
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• 2021

In this paper, a hybrid scaled boundary finite element and finite volume method (SBFEM-FVM) is proposed for simulating hydraulic-fracture propagation in brittle concrete materials. As a semi-analytical method, the scaled boundary finite element method is introduced for modelling concrete crack propagation under both an external force and water pressure. The finite volume method is employed to model the water within the crack and consider the relationship between the water pressure and the crack opening distance. The cohesive crack model is used to analyse the non-linear fracture process zone. The numerical results are compared with experimental data, indicating that the F-CMOD curves and water pressure changes under different loading conditions are approximately the same. Different types of water pressure distributions are also studied with the proposed coupled model, and the results show that the internal water pressure distribution has an important influence on crack propagation.

• Advances in nano research
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• v.15 no.5
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• pp.411-422
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• 2023

In the present study, the axial vibration of the nanorods is investigated in the framework of the doublet mechanics theory. The equations of motion and boundary conditions of nanorods are derived by applying the Hamilton principle. A finite element method is developed to obtain the vibration frequencies of nanorods for different boundary conditions. A two-noded higher order rod finite element is used to solve the vibration problem. The natural frequencies of nanorods obtained with the present finite element analysis are validated by comparing the results of classical doublet mechanics and nonlocal strain gradient theories. The effects of rod length, mode number and boundary conditions on the axial vibration frequencies of nanorods are examined in detail. Mode shapes of the nanorods are presented for the different boundary conditions. It is shown that the doublet mechanics model can be used for the dynamic analysis of nanotubes, and the presented finite element formulation can be used for mechanical problems of rods with unavailable analytical solutions. These new results can also be used as references for the future studies.

• Journal for History of Mathematics
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• v.13 no.2
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• pp.151-160
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• 2000

In this paper we prove that for all irreducible complex characters of a finite group, there exist F-representations and a finite degree field extension F ⊇ Q, where Q is the rational number field.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.2
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• pp.53-61
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• 2001

We introduce sums and joins of fuzzy finite state machines and investigate their algebraic structures.

• Journal of the Korean Mathematical Society
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• v.59 no.4
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• pp.805-819
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• 2022

We describe the structure of finite p-groups in which all normal closures of non-normal subgroups have two orders for p > 2.

• 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.