• Coupled systems mechanics
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• v.9 no.1
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• pp.5-28
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• 2020

Despite a widely-held belief that the finite element method is the method for the solution of solid mechanics problems, which has for 30 years dissuaded solid mechanics scientists from paying any attention to the finite volume method, it is argued that finite volume methods can be a viable alternative. It is shown that it is simple to understand and implement, strongly conservative, memory efficient, and directly applicable to nonlinear problems. A number of examples are presented and, when available, comparison with finite element methods is made, showing that finite volume methods can be not only equal to, but outperform finite element methods for many applications.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.55-78
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• 2001

Given the anisotropic Poisson equation $-{\nabla}{\cdot}{\mathcal{K}}{\nabla}p=f$, one can convert it into a system of two first order PDEs: the Darcy law for the flux $u=-{\mathcal{K}{\nabla}p$ and conservation of mass ${\nabla}{\cdot}u=f$. A very natural mixed finite volume method for this system is to seek the pressure in the nonconforming P1 space and the Darcy velocity in the lowest order Raviart-Thomas space. The equations for these variables are obtained by integrating the two first order systems over the triangular volumes. In this paper we show that such a method is really a standard finite element method with local recovery of the flux in disguise. As a consequence, we compare two approaches in analyzing finite volume methods (FVM) and shed light on the proper way of analyzing non co-volume type of FVM. Numerical results for Dirichlet and Neumann problems are included.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1411-1429
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• 2016

We consider the nite volume element method for elliptic problems using isoparametric bilinear elements on quadrilateral meshes. A gradient recovery method is presented by using the patch interpolation technique. Based on some superclose estimates, we prove that the recovered gradient $R({\nabla}u_h)$ possesses the superconvergence: ${\parallel}{\nabla}u-R({\nabla}u_h){\parallel}=O(h^2){\parallel}u{\parallel}_3$. Finally, some numerical examples are provided to illustrate our theoretical analysis.

• Nuclear Engineering and Technology
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• v.45 no.7
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• pp.839-846
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• 2013

This paper describes a finite element model of the microstructure of dispersion type nuclear fuels, which can be used to determine the effective thermal conductivity of the fuels during irradiation. The model simulates a representative region of the fuel as a prism shaped unit cell made of brick elements. The elements within the unit cell are assigned material properties of either the fuel or the matrix depending on position, in such a way as to represent randomly distributed fuel particles with a size distribution similar to that of the as manufactured fuel. By applying an appropriate heat flux across the unit cell it is possible to determine the effective thermal conductivity of the unit cell as a function of the volume fraction of the fuel particles. The presence of a fuel/matrix interaction layer is simulated by the addition of a third set of material properties that are assigned to the finite elements that surround each fuel particle. In this way the effective thermal conductivity of the material may also be determined as a function of the volume fraction of the interaction layer. Work is on going to add fission gas bubbles in the fuel as a fourth phase to the model.

• Computers and Concrete
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• v.19 no.4
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• pp.375-385
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• 2017

In the present paper experimental and numerical analysis of hook-ended steel fiber reinforced concrete is carried out. The experimental tests are performed on notched beams loaded in 3-point bending using fiber volume fractions up to 1.5%. The numerical analysis of fiber reinforced concrete beams is performed at meso scale. The concrete is discretized with 3D solid finite elements and microplane model is used as a constitutive law. The fibers are modelled by randomly generated 1D truss finite elements, which are connected with concrete matrix by discrete bond-slip relationship. It is demonstrated that the presented approach, which is based on the modelling of concrete matrix using microplane model, able to realistically replicate experimental results. In all investigated cases failure is due to the pull-out of fibers. It is shown that with increase of volume content of fibers the effective bond strength and slip capacity of fibers decreases.

• Structural Engineering and Mechanics
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• v.53 no.4
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• pp.703-723
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• 2015

In this paper optimization of volume fraction distribution in a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) and subjected to steady state thermal and mechanical loadings is considered. The finite element method with graded material properties within each element (graded finite elements) is used to model the structure. Volume fractions of constituent materials on a finite number of design points are taken as design variables and the volume fractions at any arbitrary point in the cylinder are obtained via cubic spline interpolation functions. The objective function selected as having the normalized effective stress equal to one at all points that leads to a uniform stress distribution in the structure. Genetic Algorithm jointed with interior penalty-function method for implementing constraints is effectively employed to find the global solution of the optimization problem. Obtained results indicates that by using the uniform distribution of normalized effective stress as objective function, considerably more efficient usage of materials can be achieved compared with the power law volume fraction distribution. Also considering uniform distribution of safety factor as design criteria instead of minimizing peak effective stress affects remarkably the optimum volume fractions.

• Geomechanics and Engineering
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• v.12 no.6
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• pp.1021-1046
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• 2017

The assessment of slope stability is an essential task in geotechnical engineering. In this paper, a three-dimensional (3D) finite element analysis (FEA) was employed to investigate the performance of different shear pin arrangements to increase the stability of a soil block resting on an inclined plane with a low-interface friction plane. In the numerical models, the soil block was modeled by volume elements with linear elastic perfectly plastic material in a drained condition, while the shear pins were modeled by volume elements with linear elastic material. Interface elements were used along the bedding plane (bedding interface element) and around the shear pins (shear pin interface element) to simulate the soil-structure interaction. Bedding interface elements were used to capture the shear sliding of the soil on the low-interface friction plane while shear pin interface elements were used to model the shear bonding of the soil around the pins. A failure analysis was performed by means of the gravity loading method. The results of the 3D FEA with the numerical models were compared to those with the physical models for all cases. The effects of the number of shear pins, the shear pin locations, the different shear pin arrangements, the thickness and the width of the soil block and the associated failure mechanisms were discussed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.5
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• pp.735-745
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• 1997

In this study, the compressibility of resin was considered in filling analysis to account for the possible packing type flow. A numerical simulation program employing a hybrid finite element/finite difference scheme was developed to solve Hele-Shaw flow of the compressible viscous fluid at non-isothermal conditions. To advance the melt front, a control volume approach was adopted. Thin complex 3-D shapes of cavities, runners, and sprues were discretized by employing triangular, cylindrical and/or rectangular strip elements. Mass conservation was applied to each control volume to solve for the pressure distribution. Directly applying a constant mass flow rate at the inlet removes calculation of the apparent pressure boundary conditions, resulting in better simulation condition. The Cross model was used to model viscosity and the Tait equation was employed to represent density as a function of temperature and pressure. The validity of the developed program was verified through comparisons with available data in the literature and the effect of compressibility on the pressure distribution was discussed. To reduce computation time, 1-D and 2-D elements were used instead of applying triangular elements and the numerical results were compared to each other.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.4
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• pp.395-405
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• 2004

The filling pattern and an adaptive grid refinement based on the finite element method and Eulerian mesh advancement approach have been developed to analyze incompressible transient viscous flow with free surfaces. The governing equation for flow analysis is Navier-Stokes equation including inertia and gravity effects. The mixed FE formulation and predictor-corrector method are used effectively for unsteady numerical simulation. The flow front surface and the volume inflow rate are calculated using the filling pattern technique to select an adequate pattern among four filling patterns at each triangular control volume. By adaptive grid refinement, the new flow field that renders better prediction in flow surface shape is generated and the velocity field at the flow front part is calculated more exactly. In this domain the elements in the surface region are made finer than those in the remaining regions for more efficient computation. Using the proposed numerical technique, the collapse of a water dam has been analyzed to predict flow phenomenon of fluid and the predicted front positions with respect to time have been compared with the reported experimental results.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.891-897
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• 2006

The volume control method which utilize a pressure node added into a finite shell element can overcome the drawbacks of conventional load control method and displacement control method. In this study, an improved volume control method is introduced for effective analysis of path-dependant behaviors of RC structures subjected to cyclic loading. RC shell structures including RC hollow columns are anlayized by discretizing the structures with layered shell elements and by applying in-plane two dimensional constitutive equations for concrete layers and reinforcement layers of the shell elements. The so-called path dependant volume control method is verified by comparing analysis results with other data including experimental results.