A Lagrangian quadratic triangular fluid finite element for fluid-structure interaction problems

Abstract

A quadratic triangular fluid element based on Lagrangian frame of reference is formulated for solving coupled fluid-structure interaction problems. The mesh-locking behavior due to simultaneous enforcement of the incompressibility and the irrotational constraints are studied in detail. In addition, their relationship to the number of active degrees of freedom and the number of integration points used to evaluate the stiffness matrix is established. It is found that the order of numerical integration used in the evaluation of stiffness matrix has pronounced effect on the element behavior. It is found that for a given mesh the formulated element does not lock in the absence of irrotationality constraints when the stiffness matrix is fully integrated. The same mesh locks when the stiffness matrix is fully integrated and both the constraints are enforced simultaneously. However, when the volumetric stiffness matrix is fully integrated and the rotational stiffness matrix is reduced integrated, the twin constraints are satisfied giving superior performance. The utility of the derived element to solve some coupled fluid-structure interaction problems is demonstrated and the solutions are compared with the available results.