Fluid‐structure interaction analysis by the finite element method–a variational approach

We have developed a finite element method for analysing non-linear and linear fluid-structure interaction problems by working directly from a variational indicator based on Hamilton's principle. We restrict our analyses to inviscid, irrotational and isentropic fluid flows. The variational indicator includes the fluid potential energy due to gravity, which is often ignored. This and the fact that we consider our domain to be variable provide us with the capability to model free surfaces. We demonstrate the effectiveness of both linear and non-linear finite element formulations in analysing a variety of fluid-structure interaction problems.

[1]  Anil Chaudhary,et al.  A SOLUTION METHOD FOR PLANAR AND AXISYMMETRIC CONTACT PROBLEMS , 1985 .

[2]  Mohammad Aslam,et al.  Finite element analysis of earthquake‐induced sloshing in axisymmetric tanks , 1981 .

[3]  G. C. Everstine.  A symmetric potential formulation for fluid-structure interaction , 1981 .

[4]  J. C. Luke.  A variational principle for a fluid with a free surface , 1967, Journal of Fluid Mechanics.

[5]  K. Bathe,et al.  On transient analysis of fluid-structure systems , 1979 .

[6]  Ted Belytschko,et al.  A fluid-structure finite element method for the analysis of reactor safety problems , 1976 .

[7]  M. Ikegawa,et al.  Finite element method applied to analysis of flow over a spillway crest , 1973 .

[8]  Ted Belytschko,et al.  COMPUTER MODELS FOR SUBASSEMBLY SIMULATION , 1978 .

[9]  Ted Belytschko,et al.  Fluid-structure interaction , 1980 .

[10]  Edward L. Wilson,et al.  Finite elements for the dynamic analysis of fluid‐solid systems , 1983 .

[11]  James Serrin,et al.  Mathematical Principles of Classical Fluid Mechanics , 1959 .

[12]  Lorraine G. Olson,et al.  A study of displacement-based fluid finite elements for calculating frequencies of fluid and fluid-structure systems , 1983 .

[13]  L. E. Malvern.  Introduction to the mechanics of a continuous medium , 1969 .

[14]  John W. Miles,et al.  On Hamilton's principle for surface waves , 1977, Journal of Fluid Mechanics.

[15]  K. Washizu.  Variational Methods in Elasticity and Plasticity , 1982 .

[16]  O. C. Zienkiewicz,et al.  Fluid‐structure dynamic interaction and wave forces. An introduction to numerical treatment , 1978 .

[17]  R. Ohayon.  Fluid-Structure Modal Analysis. New Symmetric Continuum-Based Formulations. Finite Element Applications , 1987 .

[18]  R. A. Uras,et al.  Variational approach to fluid-structure interaction with sloshing , 1988 .

[19]  K. Bathe,et al.  Analysis of fluid-structure interactions. a direct symmetric coupled formulation based on the fluid velocity potential , 1985 .

[20]  Yves Ousset,et al.  A displacement method for the analysis of vibrations of coupled fluid-structure systems , 1978 .

[21]  R. Ohayon,et al.  Substructure variational analysis of the vibrations of coupled fluid–structure systems. Finite element results , 1979 .