• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.299-309
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• 2013

In this paper, we introduce a new numerical technique which we call fractional Chebyshev finite difference method (FChFD). The algorithm is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. We tested this technique to solve numerically fractional BVPs. The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the fractional derivatives. This operational matrix method can be regarded as a non-uniform finite difference scheme. The error bound for the fractional derivatives is introduced. The fractional derivatives are presented in terms of Caputo sense. The application of the method to fractional BVPs leads to algebraic systems which can be solved by an appropriate method. Several numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method.

• Transactions of Materials Processing
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• v.21 no.7
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• pp.447-452
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• 2012

This paper is concerned with forming of Al-Zn-Mg-Sc aluminum alloy bolts, focusing on the effects of heat treatment and age-hardening on the formability and ductile damage evolution. Both experimental and finite element studies were performed. From the experiments, it is observed that the heat treatment or the normalization of Al-Zn-Mg-Sc aluminum alloy increases its formability dramatically resulting in successful bolt forming, while the effects of age-hardening at room temperature on the stress-strain relationship and formability are not very critical. Deformation characteristics such as distribution of effective stress and strain, material flow, and ductile damage evolution during bolt forming are examined using a commercial finite element package, Deform-2D. It should be noted that the extrusion load predicted by the finite element method matches well the experiment results. The finite element predictions on the deformation characteristics support the experimental observations such as fracture of bolt head flange, material flow, and distribution of hardness.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.2 s.233
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• pp.350-359
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• 2005

Finite element method is a very effective method to simulate the forming processes with good prediction of the deformation behaviour. For the finite element modeling of sheet mental forming the accurate die model is required. Among finite element method, the static-implicit finite element method is applied effectively to analyze real-size auto-body panel stamping processes, which include the forming stage. This study is about analyzing the stamping process problems by using AutoForm commercial software which used static-implicit method. According to this study, the results of simulation will give engineers good information to access the die design of optimization.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1103-1119
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• 2007

We consider multiscale mortar mixed finite element discretizations for slightly compressible Darcy flows in porous media. This paper is an extension of the formulation introduced by Arbogast et al. for the incompressible problem [2]. In this method, flux continuity is imposed via a mortar finite element space on a coarse grid scale, while the equations in the coarse elements (or subdomains) are discretized on a fine grid scale. Optimal fine scale convergence is obtained by an appropriate choice of mortar grid and polynomial degree of approximation. Parallel numerical simulations on some multiscale benchmark problems are given to show the efficiency and effectiveness of the method.

• Structural Engineering and Mechanics
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• v.66 no.5
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• pp.665-676
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• 2018

In this study, a four-node quadrilateral partial mixed plate element with low degrees of freedom (dofs) is developed for static and free vibration analysis of functionally graded material (FGM) plates rested on Winkler-Pasternak elastic foundations. The formulation of the presented finite element model is based on a parametrized mixed variational principle which is developed recently by the first author. The presented finite element model considers the effects of shear deformations and normal flexibility of the FGM plates without using any shear correction factor. It also fulfills the boundary conditions of the transverse shear and normal stresses on the top and bottom surfaces of the plate. Beside these capabilities, the number of unknown field variables of the plate is only six. The presented partial mixed finite element model has been validated through comparison with the results of the three-dimensional (3D) theory of elasticity and the results obtained from the classical and high-order plate theories available in the open literature.

• Journal of the Korean Society for Advanced Composite Structures
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• v.6 no.1
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• pp.45-50
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• 2015

This study performed a finite element crash analysis of support structures made of various composite materials for road facilities. The effects of different material properties of composites for various parameters are studied using the finite element commercial package for this study. In this study, the existing finite element analysis of composite post structures using the LS-DYNA program is further extended to compare dynamic behaviors against car crash of the structures made of various composite materials. The several numerical examples show the comparison of the nonlinear dynamic effects for different materials.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1375-1382
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• 2015

We investigate what happens when we try to work with continuing block codes (i.e., left or right continuing factor maps) between shift spaces that may not be shifts of finite type. For example, we demonstrate that continuing block codes on strictly sofic shifts do not behave as well as those on shifts of finite type; a continuing block code on a sofic shift need not have a uniformly bounded retract, unlike one on a shift of finite type. A right eresolving code on a sofic shift can display any behavior arbitrary block codes can have. We also show that a right continuing factor of a shift of finite type is always a shift of finite type.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.3 no.2
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• pp.97-102
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• 1991

Finite element method has been developed recently for the solution of the convection-diffusion problems. Finite element method has several advantages over finite difference method, but its requirement of the larger memory size of the computer has prevented from wide application. In the present study, line-by-line technique has been implemented to finite element method to overcome this disadvantage. Two dimensional laminar natural convection in square cavity was chosen as an example in this study. The numerical result shows good agreement with bench mark solution and the size of the coefficient marix has been reduced drastically.

• Advances in aircraft and spacecraft science
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• v.3 no.4
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• pp.379-397
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• 2016

In this manuscript, free vibrations of a unidirectional composite orthotropic Timoshenko beam based on finite strain have been studied. Using Green-Lagrange strain tensor and comprising all of the nonlinear terms of the tensor and also applying Hamilton's principle, equations of motion and boundary conditions of the beam are obtained. Using separation method in single-harmonic state, time and locative variables are separated from each other and finally, the equations of motion and boundary conditions are gained according to locative variable. To solve the equations, generalized differential quadrature method (GDQM) is applied and then, deflection and cross-section rotation of the beam in linear and nonlinear states are drawn and compared with each other. Also, frequencies of carbon/epoxy and glass/epoxy composite beams for different boundary conditions on the basis of the finite strain are calculated. The calculated frequencies of the nonlinear free vibration of the beam utilizing finite strain assumption for various geometries have been compared to von Karman one.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2001.10a
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• pp.58-61
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• 2001

An implicit finite element formulation for axisymmetric tube hydroforming is investigated. In order to describe normal anisotropy of the tube, Hill's non-quadratic yield function is employed. The frictional contact between die and tube and frictionless contact between tube and fluid are considered using the mesh-normal vector computed from finite element mesh of the tube. In order to verify the validity of the developed finite element formulation, the axisymmetric tube bulge test is simulated and simulation results are compared with experimental measurements. In the axisymmetric tube hydroforming process, an optimal hydraulic curve is pursued by performing the simulation with various internal pressures and axial forces.