• Structural Engineering and Mechanics
• /
• v.17 no.6
• /
• pp.735-749
• /
• 2004

This work presents a direct integration scheme, based on a fourth order finite difference approach, for elastodynamics. The proposed scheme was chosen as an alternative for attenuating the errors due to the use of the central difference method, mainly when the time-step length approaches the critical time-step. In addition to eliminating the spurious numerical oscillations, the fourth order finite difference scheme keeps the advantages of the central difference method: reduced computer storage and no requirement of factorisation of the effective stiffness matrix in the step-by-step solution. A study concerning the stability of the fourth order finite difference scheme is presented. The Finite Element Method and the Boundary Element Method are employed to solve elastodynamic problems. In order to verify the accuracy of the proposed scheme, two examples are presented and discussed at the end of this work.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.12 no.2
• /
• pp.69-79
• /
• 2008

Multigrid methods finite element/finite volume methods and their convergence properties are reviewed in a general setting. Some early theoretical results in simple finite element methods in variational setting method are given and extension to nonnested-noninherited forms are presented. Finally, the parallel theory for nonconforming element[13] and for cell centered finite difference methods [15, 23] are discussed.

• Journal of KSNVE
• /
• v.8 no.2
• /
• pp.267-273
• /
• 1998

This study aims at performing sensitivity analysis of piezoelectric smart structure for minimizing radiated noise from the structure, The structure consists of a flat plate on which disk shaped piezoelectric actuator is mounted, and finite element modeling is used for the structure. The finite element modeling uses a combination of three dimensional piezoelectric, flat shell and transition elements so thus it can take into account the coupling effects of the piezoelectric device precisely and it can also reduce the degrees of freedom of the finite element model. Electric potential on the piezoelectric actuator is taken as a design variable and total radiated power of the structure is chosen as an objective function. The objective function can be represented as Rayleigh's integral equation and is a function of normal displacements of the structure. For the convenience of computation, all degrees of freedom of the finite element equation is condensed out except the normal displacements of the structure. To perform the design sensitivity analysis, the derivative of the objective function with respect to the normal displacements is found, and the derivative of the norma displacements with respect to the design variable is calculated from the finite element equation by using so called the adjoint variable method. The analysis results are compared with those of the finite difference method, and shows a good agreement. This sensitivity analysis is faster and more accurate than the finite difference method. Once the sensitivity analysis program is used for gradient-based optimizations, one could achieve a better convergence rate than non-derivative methods for optimal design of piezoelectric smart structures.

• Transactions of Materials Processing
• /
• v.16 no.8
• /
• pp.590-595
• /
• 2007

This paper introduces a new approach to take account of bending history in finite element inverse analysis during sheet metal forming process. A modified membrane element was adopted for finite element inverse analysis so that bending-unbending energy was additionally imposed in the total plastic energy, predicting bending-unbending regions using the geometry of the final shape and tools. An algorithm was applied to a cylindrical cup deep drawing process. The blank shape and the distribution of the thickness strain were compared with those obtained from the incremental finite element analysis in order to evaluate the effect of the bending history. The algorithm reduced the difference between the results of the inverse analysis from those of the incremental analysis due to bending history. The analysis was also carried out with the variation of the thickness of the initial blank to investigate the effect of bending deformation. The results showed that the difference was remarkably reduced as the thickness of the initial blank increased. This indicates that the finite element inverse analysis cooperated with the suggested scheme is useful to obtain more accurate results, especially when bending effects are significant.

• Structural Engineering and Mechanics
• /
• v.83 no.2
• /
• pp.273-282
• /
• 2022

In this paper, we propose a new concept for error estimation in finite element solutions, which we call mode-based error estimation. The proposed error estimation predicts a posteriori error calculated by the difference between the direct finite element (FE) approximation and the recovered FE approximation. The mode-based FE formulation for the recently developed self-updated finite element is employed to calculate the recovered solution. The formulation is constructed by searching for optimal bending directions for each element, and deep learning is adopted to help find the optimal bending directions. Through various numerical examples using four-node quadrilateral finite elements, we demonstrate the improved predictive capability of the proposed error estimator compared with other competitive methods.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.19 no.4
• /
• pp.19-29
• /
• 1982

Galerkin's finite element method is applied to a two-dimensional heat convection-diffusion problem arising in the hydrodynamic lubrication of thrust bearings used in naval vessels. A parabolized thermal energy equation for the lubricant, and thermal diffusion equations for both bearing pad and the collar are treated together, with proper juncture conditions on the interface boundaries. it has been known that a numerical instability arises when the classical Galerkin's method, which is equivalent to a centered difference approximation, is applied to a parabolic-type partial differential equation. Probably the simplest remedy for this instability is to use a one-sided finite difference formula for the first derivative term in the finite difference method. However, in the present coupled heat convection-diffusion problem in which the governing equation is parabolized in a subdomain(Lubricant), uniformly stable numerical solutions for a wide range of the Peclet number are obtained in the numerical test based on Galerkin's classical finite element method. In the present numerical convergence errors in several error norms are presented in the first model problem. Additional numerical results for a more realistic bearing lubrication problem are presented for a second numerical model.

• Transactions of the Korean Society of Pressure Vessels and Piping
• /
• v.13 no.1
• /
• pp.84-91
• /
• 2017

This paper is proposed to select the optimal finite element type in finite element analysis. Based on the NUREG reports, static analyses were performed using a commercial analysis program, $ABAQUS^{TM}$. In this study, we used a nonlinear kinematic hardening model proposed by Chaboche. The analysis result of solid elements by inputting the same material constants was different from the results of the NUREG report. This is resulted from the difference between shell element and solid element. Therefore, the material constants that have similar result to the experimental result were determined and compared according to element type. In case of using solid element for efficient finite element analysis, we confirmed that the use of C3D8I element type(incompatible mode 8-node linear brick element) leads the accurate result while reducing the analysis time.

• Journal of the Korean Society for Nondestructive Testing
• /
• v.20 no.2
• /
• pp.116-129
• /
• 2000

Due to the great complexity of the physical phenomena involved in most ultrasonic nondestructive testing, the numerical method is effective in many cases of their theoretical modeling. A brief overview is provided in this paper of the numerical methods used in modeling ultrasonic nondestructive testing, with an emphasis on the finite difference and the finite element methods. The procedures of execution, special considerations required, and some previous research results of the finite difference and the finite element methods are presented, with a rather extensive list of work reported in the literature. These numerical modeling techniques for ultrasonic nondestructive testing are expected to be more reliable and more convenient, as a result of the continuing technological development of computers.

• Journal of Mechanical Science and Technology
• /
• v.17 no.5
• /
• pp.679-690
• /
• 2003

As the rate of increase in areal density of the HDD has accelerated, dynamic characteristics of the HDD actuator need to be improved with respect to the performance of the tracking servo and shock transmission. Therefore, it is important to analyze the vibration characteristic of the HDD actuator that consists of the VCM part, E-block and pivot bearing. In this paper, vibration modes of the HDD actuator are investigated the using finite element and experimental modal analyses methods. To develop a detailed finite element model, finite element models of each components of the actuator assembly are constructed and tuned to the results of the EMA. The VCM coil is modeled as an equivalent finite element model that has an orthotropic material property using auto-model updating program. Auto-model updating program with improved sensitivity based iterative method is applied to build a detailed finite element model using the result of the EMA. A detailed finite element model of the HDD actuator is then constructed and analyzed.

• Journal of the korean Society of Automotive Engineers
• /
• v.3 no.3
• /
• pp.24-29
• /
• 1981

This paper is studied an efficient temperature distribution and heat transfer of two-dimensional rectangular cross-section by the higher-order triangular finite dynamic element and finite difference. This is achieved by employing a discretization technique based on a recently developed concept of finite dynamic elements, involving higher order dynamic correction terms in the associated stiffness and convection matrices. Numerical solution results of temperature distribution presented herein clearly optimum element and show that FEM10 is the most accurate temperature distribution, but heat transfer and computational effort is the most acquired.