DOI QR코드

DOI QR Code

Transient linear elastodynamic analysis in time domain based on the integro-differential equations

  • Sim, Woo-Jin (Department of Engineering Science and Mechanics, School of Mechanical Engineering Kum-Oh National University of Technology) ;
  • Lee, Sung-Hee (Department of Engineering Science and Mechanics, School of Mechanical Engineering Kum-Oh National University of Technology)
  • 투고 : 2001.04.02
  • 심사 : 2002.04.24
  • 발행 : 2002.07.25

초록

A finite element formulation for the time-domain analysis of linear transient elastodynamic problems is presented based on the weak form obtained by applying the Galerkin's method to the integro-differential equations which contain the initial conditions implicitly and does not include the inertia terms. The weak form is extended temporally under the assumptions of the constant and linear time variations of field variables, since the time-stepping algorithms such as the Newmark method and the Wilson ${\theta}$-method are not necessary, obtaining two kinds of implicit finite element equations which are tested for numerical accuracy and convergency. Three classical examples having finite and infinite domains are solved and numerical results are compared with the other analytical and numerical solutions to show the versatility and accuracy of the presented formulation.

키워드

참고문헌

  1. Achenbach, J.D. (1975), Wave Propagation in Elastic Solids, North-Holland, Amsterdam.
  2. Atluri, S., (1973), "An assumed stress hybrid finite element model for linear elastodynamic analysis", AIAA J., 11(7), 1028-1031. https://doi.org/10.2514/3.6865
  3. Argyris, J.H. and Mlejnek, H.P. (eds.) (1991), "Dynamics of Structures": Proc. 2nd World Conference, Stuttgart, Germany, 27-31 Aug., 1990, Elsevier, Amsterdam.
  4. Banerjee, P.K. (1994), Boundary Element Methods in Engineering, McGraw-Hill, London.
  5. Baron, M.L. and Matthews, A.T. (1961), "Diffraction of a pressure wave by a cylindrical cavity in an elastic medium", Trans. ASME, J. Appl. Mech., 28, 347-354. https://doi.org/10.1115/1.3641710
  6. Bathe, K.J. (1996), Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs.
  7. Bedford, A. and Drumheller, D.S. (1994), Elastic Wave Propagation, John Wiley & Sons, Chichester.
  8. Belytschko, T. and Hughes, T.J.R. (eds.) (1983), Computational Methods for Transient Analysis, North-Holland, Amsterdam.
  9. Beskos, D.E. (1997), "Boundary element methods in dynamic analysis: Part II (1986-1996)", Trans ASME, Appl. Mech. Rev., 50(3), 149-197. https://doi.org/10.1115/1.3101695
  10. Carrer, J.A.M. and Mansur, W.J. (1999), "Stress and velocity in 2D transient elastodynamic analysis by the boundary element method", Engineering Analysis with Boundary Elements, 23, 233-245. https://doi.org/10.1016/S0955-7997(98)00080-0
  11. Chou, P.C. and Koenig, H.A. (1966), "A unified approach to cylindrical and spherical elastic waves by method of characteristics", Trans. ASME, J. Appl. Mech., 159-167.
  12. Dauksher, W. and Emery, A.F. (2000), "The solution of elastostatic and elastodynamic problems with Chebyshev spectral finite elements", Comp. Meth. Appl. Mech. Eng., 188, 217-233. https://doi.org/10.1016/S0045-7825(99)00149-8
  13. Dominguez, J. (1993), Boundary Elements in Dynamics, Elsevier, Amsterdam.
  14. Fu, C.C. (1970), "A method for the numerical integration of the equations of motion arising from a finiteelement analysis", Trans. ASME, J. Appl. Meth., 37, 599-605. https://doi.org/10.1115/1.3408586
  15. Gurtin, M.E. (1964), "Variational principles for linear elastodynamics", Archive for Rational Mechanics and Analysis, 16(1), 34-50.
  16. Harari, I., Hughes, T.J.R., Grosh, K., Malhotra, M., Pinsky, P.M., Stewart, J.R. and Thompson, L.L. (1996), "Recent developments in finite element methods for structural acoustics", Archives of Computational Methods in Engineering, 3, 131-309. https://doi.org/10.1007/BF03041209
  17. Hughes, T.J.R. (1987), The Finite Element Method, Englewood Cliffs, Prentice-Hall.
  18. Israil, A.S.M. and Banerjee, P.K. (1990), "Advanced development of time-domain BEM for two-dimensional scalar wave propagation", Int. J. Num. Meth. Eng., 29, 1003-1020. https://doi.org/10.1002/nme.1620290507
  19. Manolis, G.D. and Beskos, D.E. (1981), "Dynamic stress concentration studies by boundary integrals and Laplace transform", Int. J. Num. Meth. Eng., 17, 573-599. https://doi.org/10.1002/nme.1620170407
  20. Manolis, G.E. (1983), "A comparative study on three boundary element method approaches to problems in elastodynamics", Int. J. Num. Meth. Eng., 19, 73-91. https://doi.org/10.1002/nme.1620190109
  21. Miles, J.W. (1961), Modern Mathematics for the Engineer, Beckenback, E.F. (ed.), McGraw-Hill, London.
  22. Nickell, R.E. and Sackman, J.L. (1968), "Approximate solutions in linear coupled thermoelasticity", Trans. ASME, J. Appl. Mech., 35, 255-266. https://doi.org/10.1115/1.3601189
  23. Oden, J.T. and Reddy, J.N. (1976), Variational Methods in Theoretical Mechanics, Springer-Verlag, Berlin.
  24. Pao, Y.H. and Mow, C.C. (1972), Diffraction of Elastic Waves and Dynamic Stress Concentrations, Crane-Russak, New York.
  25. Reddy, J.N. (1993), An Introduction to the Finite Element Method (2nd edn.), McGraw-Hill, London.
  26. Wang, C.C., Wang, H.C. and Liou, G.S. (1997), "Quadratic time domain BEM formulation for 2D elastodynamic transient analysis", Int. J. Solids Structures, 34(1), 129-151. https://doi.org/10.1016/0020-7683(95)00293-6
  27. Washizu, K. (1975), Variational Methods in Elasticity and Plasticity (2nd edn.), Pergamon Press, Oxford.
  28. Zienkiewicz, O.C. and Taylor, R.L. (1991), The Finite Element Method Vol. II (4th edn.), McGraw-Hill, London.

피인용 문헌

  1. Finite element analysis of transient dynamic viscoelastic problems in time domain vol.19, pp.1, 2005, https://doi.org/10.1007/BF02916105
  2. 시간적분형 운동방정식에 근거한 동점탄성 문제의 응력해석 vol.27, pp.9, 2003, https://doi.org/10.3795/ksme-a.2003.27.9.1579