• Structural Engineering and Mechanics
• /
• v.19 no.3
• /
• pp.281-295
• /
• 2005

An analytical method is presented to solve the elastodynamic problem of finitely long hollow cylinder subjected to torsional impact often occurs in engineering mechanics. The analytical solution is composed of a solution of quasi-static equation satisfied with the non-homogeneous boundary condition and a solution of dynamic equation satisfied with homogeneous boundary condition. The quasi-static solution is obtained directly by solving the quasi-static equation satisfied with the non-homogeneous boundary condition. The solution of the non-homogeneous dynamic equation is obtained by means of finite Hankel transform on the radial variable, r, Laplace transform on time variable, t, and finite Fourier transform on axial variable, z. Thus, the solution for finitely long, hollow cylinder subjected to torsion impact is obtained. In the calculating examples, the response histories and distributions of shear stress in the finitely long hollow cylinder subjected to an exponential decay torsion load are obtained, and the results have been analyzed and discussed. Finally, a dynamic finite element for the same problem is carried out by using ABAQUS finite element analysis. Comparing the analytical solution with the finite element solution, it can be found that two kinds of results obtained by means of two different methods agree well. Therefore, it is further concluded that the analytical method and computing process presented in the paper are effective and accurate.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.24 no.2
• /
• pp.215-227
• /
• 2020

A new multiscale finite element method for elliptic problems with highly oscillating coefficients are introduced. A hybridization yields a locally flux-conserving numerical scheme for multiscale problems. Our approach naturally induces a homogenized equation which facilitates error analysis. Complete convergence analysis is given and numerical examples are presented to validate our analysis.

• Proceedings of the KIEE Conference
• /
• 1999.07a
• /
• pp.217-219
• /
• 1999

This paper presents a study of 2-dimensional(2-D) eddy current problem using boundary element method(BEM). When compared with finite element method(FEM), there are only a few unknown variables in BEM because it implements numerical analysis only for the surface or boundary of a model. As a result, a lot of computational memory and time can be saved. In order to analyze 2-D eddy current problem, potentials and its derivatives(flux) in a boundary are used as variables. The Mantel function of the second kind of the zero order is used here as a fundamental solution. In order to remove singularity and to solve the integral equations in a boundary, Subtracting Singularity Method and Gauss Quadrature Formula are adopted in this paper.

• Journal of the Korean Mathematical Society
• /
• v.50 no.1
• /
• pp.81-93
• /
• 2013

We consider a distributed optimal flux control problem: finding the potential of which gradient approximates the target vector field under an elliptic constraint. Introducing the Lagrange multiplier and a change of variables the Euler-Lagrange equation turns into a coupled equation of an elliptic equation and a reaction diffusion equation. The change of variables reduces iteration steps dramatically when the Gauss-Seidel iteration is considered as a solution method. For the elliptic equation solver we consider the Cell Boundary Element (CBE) method, which is the finite element type flux preserving methods.

• Structural Engineering and Mechanics
• /
• v.6 no.6
• /
• pp.633-641
• /
• 1998

Finite element solutions are presented for the optimal design of symmetrically laminated rectangular plates with various types of internal line supports. These plates are subject to a combination of simply supported, clamped and free boundary conditions. The design objective is the maximisation of the biaxial buckling load. This is achieved by determining the fibre orientations optimally with the effects of bending-twisting coupling taken into account. The finite element method coupled with an optimisation routine is employed in analysing and optimising the laminated plate designs. The effect of internal line support type and boundary conditions on the optimal ply angles and the buckling load are numerically studied. The laminate behavior with respect to fibre orientation changes significantly in the presence of internal line supports as compared to that of a laminate where there is no internal supporting. This change in behavior has significant implications for design optimisation as the optimal values of design variables with or without internal supporting differ substantially.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 1995.10a
• /
• pp.102-108
• /
• 1995

Internal contact scheme between two free surfaces on one deforming body has been proposed by using the penalty method. It has been imposed to be internal boundary condition on two-dimensional thermo-viscoplastic finite element method so as to analyze one deforming body, which has two free surfaces penetrating each others. Analysis of side pressing with a circular void and a inclined elliptic hole have been carried out in order to verity the proposed contact scheme. A finite element code imposed internal boundary condition has been applied to two-dimensional analysis of free forging of large ingot with a void. Through the analysis, effects of working parameters in order to consolidate voids have been investigated.

• Journal of applied mathematics & informatics
• /
• v.7 no.2
• /
• pp.493-506
• /
• 2000

Recently the first author and his coworker report a new finite element method for the Poisson equations with homogeneous Dirichlet boundary conditions on a polygonal domain with one re-entrant angle [7], They use the well-known fact that the solution of such problem has a singular representation, deduced a well-posed new variational problem for a regular part of solution and an extraction formula for the so-called stress intensity factor using tow cut-off functions. They use Fredholm alternative an Garding's inequality to establish the well-posedness of the variational problem and finite element approximation, so there is a maximum bound for mesh h theoretically. although the numerical experiments shows the convergence for every reasonable h with reasonable size y imposing a restriction to the support of the extra cut-off function without using Garding's inequality. We also give error analysis with similar results.

• Structural Engineering and Mechanics
• /
• v.6 no.2
• /
• pp.173-183
• /
• 1998

In the shape design of flexible structures, it is useful to predict the initial shape from the desirable large deformed shapes under some loading conditions. In this paper, we present a numerical procedure of an initial shape determination problem for hyperelastic materials which enables us to calculate an initial shape corresponding to the prescribed deformed shape and boundary condition. The present procedure is based on an Arbitrary Lagrangian-Eulerian (ALE) finite element method for hyperelasticity, in which arbitrary change of shapes in both the initial and deformed states can be treated by considering the variation of geometric mappings in the equilibrium equation. Then the determination problem of the initial shape can be formulated as a nonlinear problem to solve the unknown initial shape for the specified deformed shape that satisfies the equilibrium equation. The present approach can be implemented easily to the finite element method by employing the isoparametric hypothesis. Some basic numerical results are also given to characterize the present procedure.

• International Journal of Automotive Technology
• /
• v.7 no.4
• /
• pp.423-439
• /
• 2006

This paper proposes a hybrid analytic method for the prediction of vibrational and acoustic responses of reverberant system in the medium-to-high frequency ranges by using the PFA(Power Flow Analysis) algorithm and SEA(Statistical Energy Analysis) coupling concepts. The main part of this method is the application of the coupling loss factor(CLF) of SEA to the boundary condition of PFA in reverberant system. The hybrid method developed shows much more promising results than the conventional SEA and equivalent results to the classical PFA for various damping loss factors in a wide range of frequencies. Additionally, this paper presents applied results of hybrid power flow finite element method(hybrid PFFEM) by formulating the new joint element matrix with CLF to analyze the vibrational responses of built-up structures. Finally, the analytic results of coupled plate structures and an automobile-shaped structure using hybrid PFFEM were predicted successively.

• Journal of Mechanical Science and Technology
• /
• v.16 no.5
• /
• pp.683-695
• /
• 2002

The objective of the present study is to analyze the fluid flow with moving boundary using a finite element method. The algorithm uses a fractional step approach that can be used to solve low-speed flow with large density changes due to intense temperature gradients. The explicit Lax-Wendroff scheme is applied to nonlinear convective terms in the momentum equations to prevent checkerboard pressure oscillations. The ALE (Arbitrary Lagrangian Eulerian) method is adopted for moving grids. The numerical algorithm in the present study is validated for two-dimensional unsteady flow in a driven cavity and a natural convection problem. To extend the present numerical method to engine simulations, a piston-driven intake flow with moving boundary is also simulated. The density, temperature and axial velocity profiles are calculated for the three-dimensional unsteady piston-driven intake flow with density changes due to high inlet fluid temperatures using the present algorithm. The calculated results are in good agreement with other numerical and experimental ones.