• Magazine of the Korean Society of Agricultural Engineers
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• v.22 no.2
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• pp.83-100
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• 1980

This study was intended to computerize the structural analysis of two-dimensional continuum by finite element method, and to provide a preparatory basis for more sophisticated and more generalized computer programs of this kind. A computer program, applicable to any shape of two-dimensional continuum, was formulated on the basis of 16-degree-of- freedom rectangular element. Various computational aspects pertaining to the implementation of finite element method were reviewed and settled in the course of programming. The validity of the program was checked through several case studies. To assess the accuracy and the convergence characteristics of the method, the results computed by the program were compared with solutions by other methods, namely the analytical Navier's method and the framework method. Through actual programming and analysis of the computed results, the following facts were recognized; 1) The stiffness matrix should necessarily be assembled in a condensed form in order to make it possible to discretize the continuum into practically adequate number of elements without using back-up storage. 2) For minimization of solution time, in-core solution of the equilibrium equation is essential. LDLT decomposition is recommended for stiffness matrices condensed by the compacted column storage scheme. 3) As for rectangular plates, the finite element method shows better performances both in the accuracy and in the rate of convergence than the framework method. As the number of elements increases, the error of the finite element method approaches around 1%. 4) Regardless of the structural shape, there is a uniform tendency in convergence characteristics dependent on the shape of element. Square elements show the best performance. 5) The accuracy of computation is independent of the interpolation function selected.

• Magazine of the Korean Society of Agricultural Engineers
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• v.27 no.2
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• pp.38-46
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• 1985

The reinforced concrete farm silos on the elastic foundatin are widely used in agricultural engineering because of their superior structural performance, economy and attractive appearance. Various methods for the analysis and design of farm silo, such as the analytical method, the finite difference method, and the finite element methods, can be used. But the analytical procedure can not be applied for the intricate conditions in practice. Therefore lately the finite element method has been become in the structural mechanics. In this paper, a method of finite element analysis for the cylindrical farm silo on ffness matrix for the elastic foundation governed by winkler's assumption. A complete computer programs have been developed in this paper can be applicable not only to the shell structures on elastic foundation but also to the arbitrary three dimensional structures. Assuming the small deflection theory, the membrane and plate bending behaviours of flat plate element can be assumed mutually uncoupled. In this case, the element has 5 degrees of freedom per node when defined in the local coordinate system. However, when the element properties are transformed to the global coordinates for assembly, the 6th degree of freedom should be considered. A problem arises in this procedure the resultant stiffness in the 6th degree of freedom at this node will be zero. But this singularity of the stiffness matrix can be eliminated easily by merely replacing the zero diagonal by dummy stiffness.

• Structural Engineering and Mechanics
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• v.83 no.3
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• pp.353-361
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• 2022

Linear Elastic Fracture Mechanics (LEFM) has been developed by applying stress analysis to determine the stress intensity factor (SIF, K). The finite element method (FEM) is widely used as a standard tool for evaluating the SIF for various crack configurations. The prediction accuracy can be achieved by applying an adaptive Delaunay triangulation combined with a FEM. The solution can be solved using either direct or iterative solvers. This work adopts the element-by-element preconditioned conjugate gradient (EBE-PCG) iterative solver into an adaptive FEM to solve the solution to heal problem size constraints that exist when direct solution techniques are applied. It can avoid the formation of a global stiffness matrix of a finite element model. Several numerical experiments reveal that the present method is simple, fast, and efficient compared to conventional sparse direct solvers. The optimum convergence criterion for two-dimensional LEFM analysis is studied. In this paper, four sample problems of a two-edge cracked plate, a center cracked plate, a single-edge cracked plate, and a compact tension specimen is used to evaluate the accuracy of the prediction of the SIF values. Finally, the efficiency of the present iterative solver is summarized by comparing the computational time for all cases.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.1022-1027
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• 2007

This paper presents a method to analyze the unbalance response of a high speed polygon mirror scanner motor supported by sintered metal bearing and flexible structures by using the finite element method and the mode superposition method considering the asymmetry of the gyroscopic effect and sintered metal bearing. The eigenvalues and eigenvectors are calculated by solving the eigenvalue problem and the adjoint eigenvalue problem by using the restarted Arnoldi iteration method. The decoupled equations of motion can be obtained from global finite element motion equations by using the orthogonal relation between the right eigenvectors and left eigenvectors. The decoupled equations of motion are used to analyze the unbalance response of a high speed polygon mirror scanner motor. The validity of the proposed method is verified by comparing the simulated unbalance response with the experimental results.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.29-51
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• 2004

In this paper, we propose a new mixed finite element method, called the characteristics-mixed method, for approximating the solution to Burgers' equation. This method is based upon a space-time variational form of Burgers' equation. The hyperbolic part of the equation is approximated along the characteristics in time and the diffusion part is approximated by a mixed finite element method of lowest order. The scheme is locally conservative since fluid is transported along the approximate characteristics on the discrete level and the test function can be piecewise constant. Our analysis show the new method approximate the scalar unknown and the vector flux optimally and simultaneously. We also show this scheme has much smaller time-truncation errors than those of standard methods. Numerical example is presented to show that the new scheme is easily implemented, shocks and boundary layers are handled with almost no oscillations. One of the contributions of the paper is to show how the optimal error estimates in $L^2(\Omega)$ are obtained which are much more difficult than in the standard finite element methods. These results seem to be new in the literature of finite element methods.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1994.04a
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• pp.128-136
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• 1994

In this study, dynamic boundary element method using mass matrix is derived, using fundamental solutions for the semi-infinite domain. In constituting boundary integral equations for the dynamic equilibrium condition, inertia term in the form of domain integral is transformed into boundary integral form. Corresponding system equations are derived, and a boundary element program is developed. In addition, equations for free vibration is formulated, and eigenvalue analysis is performed. The results from the dynamic boundary element analysis for a tunnel problem are compared with those from the finite element analysis. According to the comparison, boundary element method using mass matrix is consistent with the results of finite element method. Consequently, in tunnel vibration problems, it results in reasonable solution compared with other methods where relatively higher degree of freedoms are employed.

• Journal of Advanced Marine Engineering and Technology
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• v.27 no.6
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• pp.790-796
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• 2003

As a fluid machinery for piping liquid in the reactor cooling system, multi-stage centrifugal pump requires the structural dynamic stability against external dynamic excitation. This paper is concerned with the finite element analysis of its eigen behavior and seismic response to RRS(Required Response Spectrum) curves in the case of SSE (Safe Shutdown Earthquake). Through the finite element analysis, the major vibration characteristics of multi-stage centrifugal pump(MSCP) are investigated and seismic qualification based on the IEEE codes is executed. The numerical results show that the MSCP used in this study has enough seismic strength.

• Transactions of the Korean Society of Automotive Engineers
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• v.16 no.4
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• pp.14-20
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• 2008

Fatigue fracture of engine connecting-rod bolts is encountered frequently during the developement of high-speed engines. Only the engine dyno test is a currently reliable fatigue durability assessment method. It is because the available rig tests cannot mimic the engine running condition completely, and because the finite element analysis cannot provide realistic stresses near the bolt thread that is modeled as a cylinder. This paper introduces a methodology to assess the fatigue durability of the connecting-rod bolts using the finite element analysis. The methods to contruct the bolt model, to extract the critical bolt stresses for the fatigue analysis, and to obtain the bolt fatigue endurance limit experimentally are discussed. Reliability of the method is verified indirectly.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• v.5B no.1
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• pp.90-94
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• 2005

As the structure of the piezoelectric bimorph cantilever becomes increasingly more complicated, a more accurate and efficient analysis of piezoelectric media is needed. In this paper, the piezoelectric transducer is analyzed by using the three-dimensional finite element method. The validity of the three-dimensional finite element routine is confirmed by comparing the experimental result. The resonance characteristics, such as resonance frequency and anti-resonance frequency, of the piezoelectric cantilever are calculated by the experimentally verified three dimensional finite element method. Subsequently, the characteristics, such as mechanical displacement and impedance, are calculated at the resonance frequency. Besides, to design the piezoelectric bimorph cantilever shape that maximizes displacement at the tip, the ES (Evolution Strategy) algorithm is applied. Finally, optimal design for the fan of the piezoelectric cantilever is fulfilled to obtain maximum displacement at the tip. From these results, the application potentiality of the piezoelectric bimorph cantilever fan is identified.

• Steel and Composite Structures
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• v.35 no.1
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• pp.43-59
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• 2020

In this study, free vibration analysis of laminated composite parabolic thick plate frames by using finite element method is introduced. Governing equations of an eigenvalue problem are obtained from First Order Shear Deformation Theory (FSDT). Finite element method is employed to obtain natural frequency values from the governing differential equations. The frames consist of two flat square plates and one singly curved plate. Parameters like radii of curvature, aspect ratio, ply orientation and boundary conditions are investigated to understand their effect on dynamic behavior of such a structure. In addition, multi-bay structures of such geometry with different stacking order are also taken into account. The composite frame structures are also modeled and simulated via ANSYS to verify the accuracy of the present study.