• 한국전산유체공학회:학술대회논문집
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• 1999.05a
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• pp.90-97
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• 1999

An implicit turbulent flow solver is developed for 2-D unstructured hybrid meshes. Spatial discretization is accomplished by a cell-centered finite volume formulation using an upwind flux differencing. Time is advanced by an implicit backward Euler time stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one equation model, which is coupled with wall function. The numerical method is applied for flows on a flat plate, the NACA 0012 airfoil, and the Douglas 3 element airfoil. The results are compared with experimental data.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1996.06a
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• pp.97-109
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• 1996

In the present work computations are carried out for analysis of complicated sheet metal forming process such as forming of a rear hinge. Finite element formulation using dynamic explicit time integration scheme and step-wise combined Implicit/Explicit scheme are introduced for numerical analysis of sheet metal forming process. The rigid-plastic finite element method based on membrane elements has long been employed as a useful numerical technique for the analysis of sheet metal forming because of its time effectiveness. The explicit scheme in general use is based on the elastic-plastic modelling of material requiring large computation time. In finite element simulation of sheet metal forming processes, the robustness and stability of computation are important requirements since the computation time and convergency become major points of consideration besides the solution accuracy due to the complexity of geometry and boundary conditions. The implicit scheme employs a more reliable and rigorous scheme in considering the equilibrium at each step of deformation, while in the explicit scheme the problem of convergency is eliminated at the cost of solution accuracy. The explicit approach and the implicit approach have merits and demerits, respectively. In order to combine the merits of these two methods a step-wise combined implicit/explicit scheme has been developed.

• 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.

• Steel and Composite Structures
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• v.43 no.1
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• pp.1-17
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• 2022

The free and forced nonlinear dynamic behaviors of Porous Functionally Graded Material (PFGM) plates are examined by means of a High-Order Implicit Algorithm (HOIA). The formulation is developed using the Third-order Shear Deformation Theory (TSDT). Unlike previous works, the formulation is written without resorting to any homogenization technique neither rule of mixture nor considering FGM as a laminated composite, and the distribution of the porosity is assumed to be gradually variable through the thickness of the PFGM plates. Using the Hamilton principle, we establish the governing equations of motion. The Finite Element Method (FEM) is used to compute approximations of the resulting equations; FEM is adopted using a four-node quadrilateral finite element with seven Degrees Of Freedom (DOF) per node. Nonlinear equations are solved by a HOIA. The accuracy and the performance of the proposed approach are verified by presenting comparisons with literature results for vibration natural frequencies and dynamic response of PFGM plates under external loading. The influences of porosity volume fraction, porosity distribution, slenderness ratio and other parameters on the vibrations of PFGM plate are explored. The results demonstrate the significant impact of different physical and geometrical parameters on the vibration behavior of the PFGM plate.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.2
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• pp.197-215
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• 2015

Modeling water flow in variably saturated, porous media is important in many branches of science and engineering. Highly nonlinear relationships between water content and hydraulic conductivity and soil-water pressure result in very steep wetting fronts causing numerical problems. These include poor efficiency when modeling water infiltration into very dry porous media, and numerical oscillation near a steep wetting front. A one-dimensional finite element formulation is developed for the numerical simulation of variably saturated flow systems. First order backward Euler implicit and second order Crank-Nicolson time discretization schemes are adopted as a solution strategy in this formulation based on Picard and Newton iterative techniques. Five examples are used to investigate the numerical performance of two approaches and the different factors are highlighted that can affect their convergence and efficiency. The first test case deals with sharp moisture front that infiltrates into the soil column. It shows the capability of providing a mass-conservative behavior. Saturated conditions are not developed in the second test case. Involving of dry initial condition and steep wetting front are the main numerical complexity of the third test example. Fourth test case is a rapid infiltration of water from the surface, followed by a period of redistribution of the water due to the dynamic boundary condition. The last one-dimensional test case involves flow into a layered soil with variable initial conditions. The numerical results indicate that the Crank-Nicolson scheme is inefficient compared to fully implicit backward Euler scheme for the layered soil problem but offers same accuracy for the other homogeneous soil cases.

• 한국전산유체공학회:학술대회논문집
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• 2009.04a
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• pp.277-282
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• 2009

A temperature equation which is derived from an enthalpy transport equation by using an assumption of a constant specific heat is very attractive for analyses of heat and fluid flows. It can be used for an analysis of a solid-fluid conjugate heat transfer, and it does not need a numerical method to find temperature from a temperature-enthalpy relation. But its application is limited because of the assumption. A new method is derived in this study, which is a temperature-explicit formulation of the energy equation. The enthalpy form of the energy equation is used in the method. But the final discrete form of the equation is expressed with temperature. It can be used for a solid-fluid conjugate heat transfer and multiphase flows. It is found by numerical tests that it is very efficient and as accurate as the standard enthalpy formulation.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1992.03a
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• pp.201-212
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• 1992

The plane strain analysis for simulating the stretch/draw forming operation of arbitrarily-shaped tool profiles and arbitrarily draw-in conditions is introduced. An implicit, incremental, updated Lagrangian formulation is employed, introducing a rigid-viscoplastic constitutive equation. Contact and friction are considered through the mesh-normal, which compatibly describes arbitrary tool surfaces and FEM meshe without depending on the explicit spatial derivatives of tool surfaces. The FEM formulation is tested in the sections automotive inner panel and two-side draw-in. Not only the excellent agreement between measured and computed strains in the stretched section is obtained, but also the numerical stability of current formulation is verified in the two-side draw-in section.

• Transactions of Materials Processing
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• v.1 no.1
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• pp.95-103
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• 1992

The plane strain analysis for simulating the stretch/draw forming operation with an arbitrarily-shaped tool profile is introduced. An implicit, incremental, updated Lagrangian formulation with a rigid-viscoplastic constitutive equation is employed. Contact and friction are considered through the mesh-normal, which compatibly describes arbitrary tool surfaces and FEM meshes without depending on the explicit spatial derivatives of tool surfaces. The linear line elements are used for depicting the formed sheet, based on membrane approximation. The FEM formulation is tested in the sections of automotive inner panel and two-side draw-in. Not only the excellent agreement between measured and computed strains is obtained in the stretched section, but also the numerical stability of formulation is verified in the draw-in section.

• Structural Engineering and Mechanics
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• v.14 no.1
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• pp.71-84
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• 2002

A finite element formulation for the time-domain analysis of linear transient elastodynamic problems is presented based on the weak form obtained by applying the Galerkin's method to the integro-differential equations which contain the initial conditions implicitly and does not include the inertia terms. The weak form is extended temporally under the assumptions of the constant and linear time variations of field variables, since the time-stepping algorithms such as the Newmark method and the Wilson ${\theta}$-method are not necessary, obtaining two kinds of implicit finite element equations which are tested for numerical accuracy and convergency. Three classical examples having finite and infinite domains are solved and numerical results are compared with the other analytical and numerical solutions to show the versatility and accuracy of the presented formulation.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.4
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• pp.465-474
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• 2012

In this study, a dynamic simulation model that considers many spherical particles and multibody dynamics (MBD) entities is developed. Plenteous spherical particles are solved using the Discrete Element Method (DEM) technique and simulated on a GPU board in a PC. A fast algorithm is used to calculate the Hertzian contact forces between many spherical particles, and NVIDIA CUDA is used to increase the calculation speed. The explicit integration method is applied to solve the many spheres. MBD entities are simulated by recursive formulation. Constraints are reduced by recursive formulation, and the implicit generalized alpha method is applied to solve the dynamic model. A new algorithm is developed to simulate the DEM and MBD models simultaneously. As a numerical example, a truck car model and gear model are developed. The results show that the proposed algorithm using a general-purpose GPU in a PC has many advantages.