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Analysis of fluid-structure interactions. A direct symmetric coupled formulation based on the fluid velocity potential. (English) Zbl 0568.73088
We present a symmetric finite element method for solving fluid-structure interaction problems. The formulation uses velocity potentials and a hydrostatic pressure as unknowns in each fluid region and displacements as unknowns in the solid. The hydrostatic pressure is an unknown variable at only one node per fluid region. A C matrix (multiplied by time derivatives of the nodal variables, but not a damping matrix) enforces the coupling between the variables. The resulting matrix equations are banded and symmetric, making them easy to incorporate in standard displacement-based finite element codes. Several test cases indicate that this approach works well for static, transient, and frequency analysis.

74S05 Finite element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S99 Numerical and other methods in solid mechanics
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