• Interaction and multiscale mechanics
• /
• 제6권2호
• /
• pp.83-105
• /
• 2013

In this paper, a multi-scale meshfree-enriched finite element formulation is presented for the analysis of acoustic wave propagation problem. The scale splitting in this formulation is based on the Variational Multi-scale (VMS) method. While the standard finite element polynomials are used to represent the coarse scales, the approximation of fine-scale solution is defined globally using the meshfree enrichments generated from the Generalized Meshfree (GMF) approximation. The resultant fine-scale approximations satisfy the homogenous Dirichlet boundary conditions and behave as the "global residual-free" bubbles for the enrichments in the oscillatory type of Helmholtz solutions. Numerical examples in one dimension and two dimensional cases are analyzed to demonstrate the accuracy of the present formulation and comparison is made to the analytical and two finite element solutions.

• Journal of applied mathematics & informatics
• /
• 제24권1_2호
• /
• pp.191-207
• /
• 2007

Based on a mixed Galerkin approximation, we construct the fully discrete approximations of $U_y$ as well as U to a single-phase quasilinear Stefan problem with a forcing term in non-divergence form. We prove the optimal convergence of approximation to the solution {U, S} and the superconvergence of approximation to $U_y$.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2004년도 춘계학술대회
• /
• pp.551-556
• /
• 2004

We propose a 2D 'crack' element for the simulation of propagating crack with minimal remeshing. A regular finite element containing the crack tip is replaced with this novel crack element, while the elements which the crack has passed are split into two transition elements. Singular elements can easily be implemented into this crack element to represent the crack-tip singularity without enrichment. Both crack element and transition element proposed in our formulation are mapped from corresponding master elements which are commonly built using the moving least-square (MLS) approximation only in the natural coordinate. In numerical examples, the accuracy of stress intensity factor $K_I$ is demonstrated and the crack propagation in a plate is simulated.

• 한국정밀공학회지
• /
• 제27권9호
• /
• pp.103-110
• /
• 2010

This paper presents the optimized approximation of finite element modeling for a complex tool holder spindle using both DOE (Design of Experiment) with Optimal Latin Hypercube (OLH) method and approximation modeling method with Radial Basis Function (RBF) neural network structure. The complex tool holder is used for holding a (milling/drilling) tool of a machine tool. The engineering problem of complex tool holder results from the twisting of spindle of tool holder. For this purpose, we present the optimized approximation of finite element modeling for a complex tool holder spindle using both DOE (Design of Experiment) with Optimal Latin Hypercube (OLH) method (specifically a module of $iSight^{(R)}$ FD-3.1) and approximation modeling method with Radial Basis Function (RBF) (another module of $iSight^{(R)}$ FD-3.1) neural network structure

• Journal of Electrical Engineering and Technology
• /
• 제4권2호
• /
• pp.229-233
• /
• 2009

This paper proposes a correction method for the error inherently created by time-step approximation in finite element analysis (FEA). For a simple RL and RLC linear circuit, the error in time-step analysis is analytically investigated, and a correction method is proposed for a non-linear system as well as a linear one. Then, for a practical inductor model, linear and non-linear time-step analyses are performed and the calculation results are corrected by the proposed methods. The accuracy of the corrected results is confirmed by comparing the electric input and output powers.

• Journal of applied mathematics & informatics
• /
• 제8권3호
• /
• pp.935-942
• /
• 2001

A finite element approximation of a fourth-order nonlinear boundary value problem is given. In the direct implementation, a nonlinear system will be obtained and also a full size matrix will be introduced when Newton’s method is adopted to solve the system. To avoid this difficulty we introduce an iterative scheme which can be shown to converge the positive solution of the system lying between 0 and $sin{\pi}x$.

• Structural Engineering and Mechanics
• /
• 제5권2호
• /
• pp.127-135
• /
• 1997

Patch recovery attempts to derive a more accurate stress filed over a particular element than the finite element shape function used for that particular element. Elements that have a free edge being the boundary to the structure have particular stress relationship that can be incorporated to the stress field to improve the accuracy of the approximation.

• 한국소성가공학회:학술대회논문집
• /
• 한국소성가공학회 1994년도 추계학술대회 논문집
• /
• pp.133-140
• /
• 1994

In this paper, we have proposed a new method to determine the initial billet for the forged products using a function approximation in neural networks. the architecture of neural network is a three-layer neural network and the back propagation algorithm is employed to train the network. By utilizing the ability of function approximation of neural network, an optimal billet is determined by applying nonlinear mathematical relationship between shape ratio in the initial billet and the final products. A volume of incomplete filling in the die is measured by the rigid-plastic finite element method. The neural network is trained with the initial billet shape ratio and that of the un-filled volume. After learning, the system is able to predict the filling region which are exactly the same or slightly different to results of finite element method. It is found that the prediction of the filling shape ratio region can be made successfully and the finite element method results are represented better by the neural network.

• 대한기계학회논문집A
• /
• 제25권4호
• /
• pp.574-581
• /
• 2001

Transient linear elastodynamic problems are numerically analyzed in a time-domain by the Finite Element Method, for which the variational formulation based upon the equations of motion in convolution integral is newly derived. This formulation is implicit and does not include the time derivative terms so that the computation procedure is simple and less assumptions are required comparing to the conventional time-domain dynamic numerical algorithms, being able to get the improved numerical accuracy and stability. That formulation is expanded using the semi-discrete approximation to obtain the finite element equations. In the temporal approximation, the time axis is divided equally and constant and linear time variations are assumed in those intervals. It is found that unconditionally stable numerical results are obtained in case of the constant time variation. Some numerical examples are given to show the versatility of the presented formulation.

• Journal of applied mathematics & informatics
• /
• 제26권5_6호
• /
• pp.1057-1069
• /
• 2008

We consider singularly perturbed Boundary Value Problems (BVPs) for third and fourth order Ordinary Differential Equations(ODEs) of convection-diffusion type with discontinuous source term and a small positive parameter multiplying the highest derivative. Because of the type of Boundary Conditions(BCs) imposed on these equations these problems can be transformed into weakly coupled systems. In this system, the first equation does not have the small parameter but the second contains it. In this paper a computational method named as 'An asymptotic finite element method' for solving these systems is presented. In this method we first find an zero order asymptotic approximation to the solution and then the system is decoupled by replacing the first component of the solution by this approximation in the second equation. Then the second equation is independently solved by a fitted mesh Finite Element Method (FEM). Numerical experiments support our theoritical results.