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Fundamentals of a Vector Form Intrinsic Finite Element: Part I. Basic Procedure and A Plane Frame Element

Published online by Cambridge University Press:  05 May 2011

Edward C. Ting ,
Chiang Shih  and
Yeon-Kang Wang
Edward C. Ting*
Affiliation:
School of Civil Engineering, Purdue University, West Lafayette, Indiana, U.S.A. Department of Civil Engineering, National Central University, Taoyuan, Taiwan 320, R.O.C.
Chiang Shih*
Affiliation:
Trinity Foundation Engineering, Consultants Co., Ltd., Taipei, Taiwan 106, R.O.C.
Yeon-Kang Wang*
Affiliation:
Department of Information Management, Fortune Institute of Technology, Kaohsiung County, Taiwan 831, R.O.C.
*
*Professor Emeritus, AOS Foundation Chair Professor (Ret.)
**Senior Engineer
***Associate Professor
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Abstract

In a series of three articles, fundamentals of a vector form intrinsic finite element procedure (VFIFE) are summarized. The procedure is designed to calculate motions of a system of rigid and deformable bodies. The motion may include large rigid body motions and large geometrical changes. Newton's law, or a work principle, for particle is assumed to derive the governing equations of motion. They are obtained by using a set of deformation coordinates for the description of kinematics. A convected material frame approach is proposed to handle very large deformations. Numerical results are calculated by using an explicit algorithm. In the first article, using the plane frame element as an example, basic procedures are described. In the accompanied articles, plane solid elements, convected material frame procedures and numerical results of patch tests are given.

Keywords

FrameFinite elementExplicit, Large displacement
Type
Articles
Information
Journal of Mechanics , Volume 20 , Issue 2 , June 2004 , pp. 113 - 122
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2004

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References

1.Kreig, R. D. and Key, S. W., “Transient Shell Response by Numerical Time Integration,” Int. J. Num. Meth. Eng., 7, pp. 273–286 (1973).CrossRefGoogle Scholar
2.Key, S. W., “Finite Element Procedure for Large Deformation Dynamic Response of Axisymmetric Solids,” Comp. Meth. Appl. Mech. Eng., 4, pp. 195–218 (1974).CrossRefGoogle Scholar
3.Key, S. W., “Computational Methods for Impact and Penetration,” Nucl. Eng. Design, 48, pp. 259–268 (1978).CrossRefGoogle Scholar
4.Key, S. W., “Concept Underlying Finite Element Methods for Structural Analysis,” Nucl. Eng. Design, 48(1), pp. 259–268 (1978).CrossRefGoogle Scholar
5.Key, S. W., “Improvements in Transient Dynamic Time Integration with Application to Nuclear Fuel Shipping Cask Impact Analysis,” Finite Element Methods for Nonlinear Problems, Bergen, Bathe and Wunderlich, , eds., Spring-Verlag, Berlin (1986).Google Scholar
6.Belytschko, T. and Hsieh, B. J., “Nonlinear Transient Finite Element Analysis with Convected Coordinates,” Int. J. Num. Meth. Eng., 7, pp. 255–271 (1973).CrossRefGoogle Scholar
7.Yang, Y. B. and Chiou, H. T., “Rigid Body Motion Test for Nonlinear Analysis with Beam Elements,” J. Struct. Eng., ASCE, 113, pp. 1404–1419 (1987).Google Scholar
8.Saha, N. and Ting, E. C., “Large Displacement Dynamic Analysis of Space Frames,” School of Civil Engineering, Purdue University Report, EC-SRT-83–5 (1983).Google Scholar
9.Rice, D. L. and Ting, E. C., “Large Displacement Transient Analysis of Flexible Structures,” Int. J. Num. Meth. Eng., 36, pp. 1541–1562 (1993).CrossRefGoogle Scholar