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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.

MSC:
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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