Abstract
A new formulation for nonlinear, elastic wave propagation, based on the pressure and density, is introduced. The formulation accounts for a nonlinear relation between speed of sound and density. The pressure and density are interpolated by identical shape functions between the nodes. The equation of state is introduced in the discretized system, hence the nonlinearity is enforced point wise. This procedure concentrates on proper interpolation of the balance equations by relaxing the nonlinear constitutive relation between the nodes. A standard finite element procedure focuses on the constitutive equation and thereby produces a less consistent representation of the balance equation. In addition, the formulation accounts for fluid-structure interaction.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cole, R.H.: Underwater Explosions, Princeton University Press, 1948.
Plesset, M.S.: Cavitation in Real Liquids, Bubble Dynamics, Elsevier Publishing, Amsterdam, 1964.
Newton, R.E.: Effects of Cavitation on Underwater Shock Loading - Part 1. NPS-69–78–013, Naval Postgraduate School, Monterey, California, 1978.
Newton, R.E.: Effects of Cavitation on Underwater Shock Loading - Plane Problem, Part 1. NPS-69–79–007PR, Naval Postgraduate School, Monterey, California, 1979.
Newton, R.E.: Effects of Cavitation on Underwater Shock Loading - Plane Problem, Part 2. NPS-69–80–001, Naval Postgraduate School, Monterey, California, 1980.
Newton, R.E.: Effects of Cavitation on Underwater Shock Loading - Plane Problem - Final Report. NPS-69–81–001A, Naval Postgraduate School, Monterey, California, 1981.
Zienkiewicz, O.C., Paul, D.K., Hinton, E.: ‘Cavitation in Fluid-Structure Response (with particular reference to dams under earthquake loading)’, Earthquake Engineering and Structural Dynamics, Vol. 11, pp. 463–481, 1983.
Felippa, C.A., Deruntz, J.A.: Finite Element Analysis of Shock-Induced Hull Cavitation. Computer Methods in Applied Mechanics and Engineering, Vol. 44, pp. 297–337, 1984.
Hughes, T.J.R., Tezdugar, T.E.: Finite Element Methods for First-Order Hyperbolic Systems with Particular Emphasis on the Compressible Euler Equations. Computer Methods in Applied Mechanics and Engineering, Vol. 45, pp. 217–284, 1984.
Christie, I., Griffiths, D.F., Mitchell, A.R., Sanz-Serna, J.M.: Product Approximation for Non-Linear Problems in the Finite Element Method, IMA Journal of Numerical Analysis, Vol. 1, pp. 253–266, 1981.
Spradley, L.W., Stalnaker, J.F., Ratliff, A.W.: Computation of three-dimensional Viscous Flows with the Navier-Stokes Equations, AIAA-80–1348, AIAA 13th Fluid and Plasma Dynamics Conference, Snowmass, Colorado, 1980.
Fletcher, C.A.J.: The Group Finite Element Formulation, Computer Methods in Applied Mechanics and Engineering, Vol. 37, pp. 225–243, 1983.
Fletcher, C.A.J., Srinivas, K.: On the Role of Mass Operators in the Group Finite Element Formulation, Computer Methods in Applied Mechanics and Engineering, Vol. 46, pp. 313–327, 1984.
Bleich, H.H., Sandler, I.S.: Interaction Between Structures and Bilinear Fluids, International Journal of Solids and Structures, Vol. 6, pp. 617–639, 1970.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Computational Mechanics Publications
About this chapter
Cite this chapter
Sandberg, G. (1991). A Finite Element Formulation for Nonlinear Wave Propagation with Application to Cavitation. In: Brebbia, C.A., Peters, A., Howard, D. (eds) Applications of Supercomputers in Engineering II. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3660-0_32
Download citation
DOI: https://doi.org/10.1007/978-94-011-3660-0_32
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-85166-695-9
Online ISBN: 978-94-011-3660-0
eBook Packages: Springer Book Archive