Finite Element Analysis with Paraxial & Viscous Boundary Conditions for Elastic Wave Propagation

Hee Seok Kim

Structural Engineering Research Division, Korea Institute of Construction Technology, Ilsan, Republic of Korea.

DOI: 10.4236/eng.2012.412107                

Abstract

In this study, two studies are performed. One is to apply paraxial boundary conditions which are local boundary conditions based on paraxial approximations of the one-way wave equations to finite element analysis. To do this, a penalty functional is proposed and the existence and uniqueness of the extremum of the proposed functional is demonstrated. The other is to improve the capacity of viscous boundary conditions using dashpots. To do this, customary viscous boundary conditions are modified to maximize the efficiency according to angles of incidence and materials. For the numerical analysis of elasticity with paraxial boundary conditions and the modified viscous boundary conditions, the coding of the finite element models is implemented, and the efficiency of those boundary conditions is investigated.

Keywords

Paraxial Boundary; Local Boundary; Penalty Functional; Viscous Boundary

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. F. Claerbout, “Coarse Grid Calculations of Waves in Inhomogeneous Media with Application to Delineation of Complicated Seismic Structure,” Geophysics, Vol. 35, No. 3, 1970, pp. 407-418. doi:10.1190/1.1440103
[2]	J. F. Claerbout, “Fundamentals of Geophysical Data Processing,” McGraw-Hill, New York, 1976.
[3]	J. F. Claerbout and A. G. Johnson, “Extrapolation of Time Dependent Waveforms along Their Path of Propagation,” Geophysical Journal of the Royal Astron Society, Vol. 26, No. 1-4, 1971, pp. 285-293. doi:10.1111/j.1365-246X.1971.tb03402.x
[4]	R. Clayton and B. Engquist, “Absorbing Boundary Conditions for Acoustic and Elastic Wave Equations,” Bulletin of the Seismological Society of America, Vol. 67, No. 6, 19977, pp. 1529-1540.
[5]	B. Engquist and A. Majda, “Absorbing Boundary Conditions for the Numerical Simulation of Waves,” Mathematics of Computation, Vol. 31, No. 139, 1977, pp. 629-651. doi:10.1090/S0025-5718-1977-0436612-4
[6]	H. S. Kim and J. S. Lee, “Finite Element Analysis with Paraxial Boundary Conditions for Elastic Wave Propagation,” Proceedings of 15 International Congress on Sound and Vibration, Daejeon, 6-10 June 2008.
[7]	J. Lysmer and R. L. Kuhlemeyer, “Finite Dynamic Model for Infinite Media,” Journal of the Engineering Mechanics Division, Vol. 95, No. EM4, 1969, pp. 859-877.
[8]	W. White, S. Valliappan and I. K. Lee, “Unified Boundary for Finite Dynamic Models,” Journal of the Engineering Mechanics Division, Vol. 103, No. EM5, 1977, pp. 949- 964.