• Title/Summary/Keyword: conventional finite element method

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Bending Vibration Analysis of a Rotating Cantilever Beam Employing Finite Element Method (유한 요소법을 사용한 회전 외팔보의 굽힘 진동 해석)

  • Park, Jeong-Hun;Yu, Hong-Hui
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.7 s.178
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    • pp.1826-1832
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    • 2000
  • A modelling method for the bending vibration analysis of rotating cantilever beams employing finite element method is presented in this paper. Different from the conventional modelling method in wh ich only Cartesian deformation variables are used, a non-Cartesian deformation variable is introduced and approximated to derive the equations of motion. Numerical results obtained by using the presented modelling method are compared to those obtained by using other methods in the related literature, and the accuracy of the presented method is verified through the comparison study. The presented modelling method is superior to other previous methods in a sense that several advantages of the previous methods are incorporated into the presented method.

A MASS LUMPING AND DISTRIBUTING FINITE ELEMENT ALGORITHM FOR MODELING FLOW IN VARIABLY SATURATED POROUS MEDIA

  • ISLAM, M.S.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.20 no.3
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    • pp.243-259
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    • 2016
  • The Richards equation for water movement in unsaturated soil is highly nonlinear partial differential equations which are not solvable analytically unless unrealistic and oversimplifying assumptions are made regarding the attributes, dynamics, and properties of the physical systems. Therefore, conventionally, numerical solutions are the only feasible procedures to model flow in partially saturated porous media. The standard Finite element numerical technique is usually coupled with an Euler time discretizations scheme. Except for the fully explicit forward method, any other Euler time-marching algorithm generates nonlinear algebraic equations which should be solved using iterative procedures such as Newton and Picard iterations. In this study, lumped mass and distributed mass in the frame of Picard and Newton iterative techniques were evaluated to determine the most efficient method to solve the Richards equation with finite element model. The accuracy and computational efficiency of the scheme and of the Picard and Newton models are assessed for three test problems simulating one-dimensional flow processes in unsaturated porous media. Results demonstrated that, the conventional mass distributed finite element method suffers from numerical oscillations at the wetting front, especially for very dry initial conditions. Even though small mesh sizes are applied for all the test problems, it is shown that the traditional mass-distributed scheme can still generate an incorrect response due to the highly nonlinear properties of water flow in unsaturated soil and cause numerical oscillation. On the other hand, non oscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped finite element method.

A Study on the Analysis and Improvement of Forming Processes of a Steel Shell Body (강철재 약협의 공정해석 및 성형공정 개선에 관한 연구)

  • Jang, Dong Hwan;Yu, Tae Gon;Hwang, Byeong Bok
    • Transactions of Materials Processing
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    • v.10 no.3
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    • pp.246-246
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    • 2001
  • The conventional and new forming processes of a steel shell body are analyzed by the rigid-plastic finite element method. The conventional process contains five forming stages such as bending, drawing, ironing, heading and sizing, which was designed by a forming equipment expert. The results of simulation of the conventional forming process are summarized in terms of deformation patterns and load-stroke relationships for each forming operation. Based on the simulation results of the current five-stage, the shell body forming Process including backward extrusion is designed for improving the conventional process sequence. Forming loads of the proposed process are within the limit value, which is proposed by experts and the proposed process is found to be proper for manufacturing steel shell body.

A Study on the Analysis and Improvement of Forming Processes of a Steel Shell Body (강철재 약협의 공정해석 및 성형공정 개선에 관한 연구)

  • 장동환;유태곤;황병복
    • Transactions of Materials Processing
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    • v.10 no.3
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    • pp.245-252
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    • 2001
  • The conventional and new forming processes of a steel shell body are analyzed by the rigid-plastic finite element method. The conventional process contains five forming stages such as bending, drawing, ironing, heading and sizing, which was designed by a forming equipment expert. The results of simulation of the conventional forming process are summarized in terms of deformation patterns and load-stroke relationships for each forming operation. Based on the simulation results of the current five-stage, the shell body forming Process including backward extrusion is designed for improving the conventional process sequence. Forming loads of the proposed process are within the limit value, which is proposed by experts and the proposed process is found to be proper for manufacturing steel shell body.

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A Time-Domain Finite Element Formulation for Transient Dynamic Linear Elasticity (과도 선형 동탄성 문제의 시간영역 유한요소해석)

  • Sim, U-Jin;Lee, Seong-Hui
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.25 no.4
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    • pp.574-581
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    • 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.

An efficient adaptive finite element method based on EBE-PCG iterative solver for LEFM analysis

  • Hearunyakij, Manat;Phongthanapanich, Sutthisak
    • 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.

Metal forming analysis using meshfree-enriched finite element method and mortar contact algorithm

  • Hu, Wei;Wu, C.T.
    • Interaction and multiscale mechanics
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    • v.6 no.2
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    • pp.237-255
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    • 2013
  • In this paper, a meshfree-enriched finite element method (ME-FEM) is introduced for the large deformation analysis of nonlinear path-dependent problems involving contact. In linear ME-FEM, the element formulation is established by introducing a meshfree convex approximation into the linear triangular element in 2D and linear tetrahedron element in 3D along with an enriched meshfree node. In nonlinear formulation, the area-weighted smoothing scheme for deformation gradient is then developed in conjunction with the meshfree-enriched element interpolation functions to yield a discrete divergence-free property at the integration points, which is essential to enhance the stress calculation in the stage of plastic deformation. A modified variational formulation using the smoothed deformation gradient is developed for path-dependent material analysis. In the industrial metal forming problems, the mortar contact algorithm is implemented in the explicit formulation. Since the meshfree-enriched element shape functions are constructed using the meshfree convex approximation, they pose the desired Kronecker-delta property at the element edge thus requires no special treatments in the enforcement of essential boundary condition as well as the contact conditions. As a result, this approach can be easily incorporated into a conventional displacement-based finite element code. Two elasto-plastic problems are studied and the numerical results indicated that ME-FEM is capable of delivering a volumetric locking-free and pressure oscillation-free solutions for the large deformation problems in metal forming analysis.

Prestressed Concrete Girder Bridges Strengthened by External Post-tensioning Method

  • Kim, Kwang-Soo;Park, Sun-Kyu;Kim, Hyeong-Yeol
    • KCI Concrete Journal
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    • v.12 no.1
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    • pp.17-22
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    • 2000
  • This Paper deals with the analysis of both unstrengthened and strengthened prestressed concrete girder bridges. Finite element method is utilized to perform the analysis of superstructures. Based on the grillage method of analysis. emphasis is Placed on the modeling techniques for structures. The conventional grillage method of analysis is modif'=ed so that the interaction between the slab and gilder behaviors can be taken into account in the analysis A Prototype of simply supported prestressed I-type girder bridge is selected for the analysis. The results of numerical analyses are compared with those of load test. The results of analysis indicate that the proposed method of analysis gives more realistic response of bridges than the conventional grillage method.

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The Elastic Critical Loads of Sinusolidally Tapered Symmetric Compression Members (정현상 대칭으로 Taper진 변단면 압축재의 임계하중)

  • 오금열;홍종국;김순철;이수곤
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2000.04b
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    • pp.27-34
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    • 2000
  • The elastic critical loads of prismatic compression members can be easily determined by the conventional analytic method. In the cases of sinusoidally tapered members, however, the determination of elastic critical loads become impossible when one relies on the analytic method. In this paper, the critical loads of sinusoidally tapered members were determined by finite element method. Generally the output or results of numerical analysis are valid only when the governing parameters of a given system(or problem) have particular values. To make the practical applications easy, the critical loads determined by finite element method are expressed by some algebraic equations. The constants contained in the algebraic equations were determined by regression technique. The elastic critical loads estimated by the proposed algebraic equations coincide well with those by finite element method.

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An Application of the Localized Finite Element Method to 3-dimensional Free Surface Wave Problems (3차원 자유표면파 문제에서의 국소유한요소법의 응용)

  • K.J.,Bai;Se-Eun,Kim
    • Bulletin of the Society of Naval Architects of Korea
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    • v.24 no.3
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    • pp.1-8
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    • 1987
  • In this paper, the localized finite element method(LFEM) is applied to 3-dimensional ship motion problems in water of infinite depth. The LFEM used here is based on the functional constructed by Bai & Yeung(1974). To test the present numerical scheme, a few vertical axisymmetric bodies are treated by general 3-dimensional formulation. The computed results of hydrodynamic coefficients for a few vertical spheroids and vertical circular cylinders show good agreement with results obtained by others. The advantages of the present numerical method compared with the method of integral equation are as follows; (i) The cumbersome existence of irregular frequencies in the method of conventional integral equation is removed. (ii) The final matrix is banded and symmetric and the computation of the matrix elements is comparatively easier, whereas the size of the matrix in the present scheme is much larger. (iii) In the future research, it is possible to accommodate with the nonlinear exact free surface boundary condition in the localized finite element subdomain, whereas the linear solution is assumed in the truncated(far field) subdomain.

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