• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.10 s.181
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• pp.2469-2476
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• 2000

The meshing of the domain has long been the major bottleneck in performing the finite element analysis. Research efforts which are so-called meshfree methods have recently been directed towards eliminating or at least easing the requirement for meshing of the domain. In this paper, a new meshfree method for solving nonlinear boundary value problem, based on the bubble packing technique and Delaunay triangle is proposed. The method can be efficiently implemented to the problems with singularity by using formly distributed nodes.

• Computers and Concrete
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• v.18 no.6
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• pp.1097-1112
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• 2016

Fire loading causes a critical collapse of RC (Reinforced Concrete) Structures since the embedded steels inside are relative week against high elevated temperature. Several numerical frameworks for fire resistance have been proposed, however they have limitations such as unstable convergence and long calculation period. In the work, 2-D nonlinear FE technique is proposed using Galerkin method for RC structures under fire loading. Closed-form element stiffness with a triangular element is adopted and verified with fire test on three RC slabs with different fire loading conditions. Several simulations are also performed considering fire loading conditions, water contents, and cover depth. The proposed numerical technique can handle time-dependent fire loading, convection, radiation, and material properties. The proposed technique can be improved through early-aged concrete behavior like moisture transport which varies with external temperature.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.7 no.1
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• pp.33-45
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• 1995

This paper as a sequel to Kang et al. (1994) describes the development of a three-dimensional nonlinear Galerkin-FEM model. Nonlinear advective terms have been incorporated in a manner used by Lardner and Song (1992), that is, using velocities at given nodes computed with linear Galerkin FEM model. The Proposed model is computationally more efficient than previous nonlinear Galerkin models developed by Owen (1980) and Davies (1980) because the model uses a linear shape function as a basis and, furthermore, the similarity transform technique developed by Kang (1994). Two experiments have been carried out to examine effects of nonlinear terms. One is an experiment of wind-driven current in a rectangular basin (Heaps' basin) and the other is an experiment concerning eddy generation behind a jetty with specified downstream and upstream open boundary conditions. The computed Pattern was found to be in good agreement qualitatively with previous model experiments by Stelling (1984).

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.947-964
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• 2012

In this paper, the memory type boundary stabilization for an Euler-Bernoulli beam with one end fixed and control at the other end is considered. We prove the existence of solutions using the Galerkin method and then investigate the exponential stability of solutions by using multiplier technique.

• Wind and Structures
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• v.14 no.5
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• pp.465-480
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• 2011

In this paper, a stabilized large eddy simulation technique is developed to predict turbulent flow with high Reynolds number. Streamline Upwind Petrov-Galerkin (SUPG) stabilized method and three-step technique are both implemented for the finite element formulation of Smagorinsky sub-grid scale (SGS) model. Temporal discretization is performed using three-step technique with viscous term treated implicitly. And the pressure is computed from Poisson equation derived from the incompressible condition. Then two numerical examples of turbulent flow with high Reynolds number are discussed. One is lid driven flow at Re = $10^5$ in a triangular cavity, the other is turbulent flow past a square cylinder at Re = 22000. Results show that the present technique can effectively suppress the instabilities of turbulent flow caused by traditional FEM and well predict the unsteady flow even with coarse mesh.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.244-262
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• 2022

In this paper, we analyze the hybridizable discontinuous Galerkin (HDG) method for second-order elliptic equations with nonlinear coefficients, which are used in many fields. We present the HDG method that uses a mixed formulation based on numerical trace and flux. Under assumptions on the nonlinear coefficient and H²-regularity for a dual problem, we prove that the discrete systems are well-posed and the numerical solutions have the optimal order of convergence as a mesh parameter. Also, we provide a matrix formulation that can be calculated using an iterative technique for numerical experiments. Finally, we present representative numerical examples in 2D to verify the validity of the proof of Theorem 3.10.

• Journal of the Korean Mathematical Society
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• v.61 no.4
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• pp.621-657
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• 2024

In this study, the numerical solution of a space-fractional Burgers' equation with initial and boundary conditions is considered. This equation is the simplest nonlinear model for diffusive waves in fluid dynamics. It occurs in a variety of physical phenomena, including viscous sound waves, waves in fluid-filled viscous elastic pipes, magneto-hydrodynamic waves in a medium with finite electrical conductivity, and one-dimensional turbulence. The proposed QBS/CNG technique consists of the Galerkin method with a function basis of quadratic B-splines for the spatial discretization of the space-fractional Burgers' equation. This is then followed by the Crank-Nicolson approach for time-stepping. A linearized scheme is fully constructed to reduce computational costs. Stability analysis, error estimates, and convergence rates are studied. Finally, some test problems are used to confirm the theoretical results and the proposed method's effectiveness, with the results displayed in tables, 2D, and 3D graphs.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.35 no.3
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• pp.95-101
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• 1986

This paper describes two methods for analyzing distributed parameter systems (DPS) via Walsh series expansions. Firstly, a Walsh-Galerkin expansion approach technique (WGA) introduced by S.G. Tzafestas. is considered. The method which is based on Galerkin scheme, is well established by using Walsh series. But then, there are some difficulty in finding the proper basic functions at each systems. Secondly, a double Walsh series approach technique (DWA) is developed. The essential feature of DWA propoesed here is that it reduces the analysis problem of DPS to that of solving a set of linear algebraic equation which is extended in double Walsh series.

• Journal of computational fluids engineering
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• v.12 no.4
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• pp.14-19
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• 2007

We present a direct numerical simulation technique and some preliminary results of the capillary spreading of a droplet containing particles on the solid substrate. We used the level-set method with the continuous surface stress for description of droplet spreading with interfacial tension and employed the discontinuous Galerkin method for the stabilization of the interface advection equation. The distributed Lagrangian-multipliers method has been combined for the implicit treatment of rigid particles. We investigated the droplet spreading by the capillary force and discussed effects of the presence of particles on the spreading behavior. It has been observed that a particulate drop spreads less than the pure liquid drop. The amount of spread of a particulate drop has been found smaller than that of the liquid with effectively the same viscosity as the particulate drop.

• Structural Engineering and Mechanics
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• v.59 no.5
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• pp.901-920
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• 2016

MeshFree methods have become popular owing to the ease with which high stress gradients can be identified and node density distribution can be reformulated to accomplish faster convergence. This paper presents a strategy for nodal density refinement with strain energy as basis in Element-Free Galerkin MeshFree technique. Two popular flat plate problems are considered for the demonstration of the proposed strategies. Issue of integration errors introduced during nodal density refinement have been addressed by suggesting integration cell refinement. High stress effects around two symmetrical semi-circular notches under in-plane axial load have been addressed in the first problem. The second considers crack propagation under mode I and mode II fracture loading by the way of introducing high stress intensity through line crack. The computational efficacy of the adaptive refinement strategies proposed has been highlighted.