Advanced SearchSearch Tips
A Time-Domain Finite Element Formulation for Transient Dynamic Linear Elasticity
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
A Time-Domain Finite Element Formulation for Transient Dynamic Linear Elasticity
Sim, U-Jin; Lee, Seong-Hui;
  PDF(new window)
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.
Transient;Dynamic Elasticity;Finite Element Method;Elastic Wave;
 Cited by
시간적분형 운동방정식을 바탕으로 한 동적 응력확대계수의 계산,심우진;이성희;

대한기계학회논문집A, 2002. vol.26. 5, pp.904-913 crossref(new window)
축대칭 문제에서의 동적 응력집중 해석,심우진;이성희;

대한기계학회논문집A, 2002. vol.26. 11, pp.2364-2373 crossref(new window)
유한요소법을 이용한 이방성 재료에서의 초음파 전파 거동 해석,정현조;박문철;

대한기계학회논문집A, 2002. vol.26. 10, pp.2201-2210 crossref(new window)
시간적분형 운동방정식에 근거한 동점탄성 문제의 응력해석,이성희;심우진;

대한기계학회논문집A, 2003. vol.27. 9, pp.1579-1588 crossref(new window)
Reddy, J.N., 1993, An Introduction to the Finite Element Method, McGraw-Hill, New York, Chap. 10

Zienkiewicz, O.C. and Taylor, R.L., 1991, The Finite Element Method(4th edn), Vol. 2, Dynamics and Nonlinearity, McGraw-Hill, London, Chap. 9-10

Fu, C.C., 1970, 'A Method for the Numerical Integration of the Equations of Motion Arising From a Finite-Element Analysis,' Trans. ASME, J. Appl. Mech. pp. 599-605

Ahmad, S., 1986, Linear and Nonlinear Dynamic Analysis by Boundary Element Method, Ph.D. Thesis, SUNY at Buffalo, Chap. VIII

Lee, T.W. and Sim, W.J., 1992, 'Efficient Time-Domain Finite Element Analysis for Dynamic Coupled Thermoelasticity,' Computers and Structures, Vol. 45, No. 4, pp. 785-793 crossref(new window)

김진석, 1998, '라플라스 변환을 이용한 단순한 지지보의 동적 변형률 해석,' 대한기계학회논문집, 제22권, 제10호, pp. 1858-1865

Bedford, A. and Drumheller, D. S., 1994, Introduction to Elastic Wave Propagation, John Wiley, Chichester, Chap. 4

Gurtin, M. E., 1964, 'Variational Principles for Linear Elastodynamics,' Archive for Rational Mechanics and Analysis, Vol. 16, pp. 234-250 crossref(new window)

Achenbach, J. D., 1975, Wave Propagation in Elastic Solids, North-Holland, Amsterdam, Chap. 2

Timoshenko, S.P. and Goodier, J.N., 1970, Theory of Elasticity, 3rd Edn., McGraw-Hill, New York

Mansur, W.J., 1983, A Time-stepping Technique to Solve Wave Propagation Problems Using the Boundary Element Method, Ph.D. Dissertation, University of Southhampton, U.K.

Israil, A.S.M. and Banerjee, P.K., 1990, 'Advanced Development of Time-Domain BEM for Two-Dimensional Scalar Wave Propagation,' Int. J. Num. Eng., Vol. 29, pp. 1003-1020 crossref(new window)

Chou, P.E. and Koenig, H.A., 1966, 'A Unified Approach to Cylindrical and Spherical Elastic Waves by Method of Characteristics,' Trans. ASME, J. Appl. Mech., pp. 159-167