Behaviour of isoparametric quadrilateral family of Lagrangian fluid finite elements

Abstract

This paper presents the formulation of both the consistent and inconsistent four-, eight- and nine-noded isoparametric quadrilateral fluid finite elements that are based on Lagrangian frame of reference. The mesh locking phenomenon due to simultaneous enforcement of twin constraints, namely the incompressibility and irrotationality constraints, is studied in detail. The study shows that the characteristic of the locked fluid elements is that it always generates numerous spurious acoustic (volume change) modes upon the enforcement of rotational constraints. That is, the rotational constraints change the character of certain volume change modes. The study further reinforces the necessity of rotational constraints in not only identifying the spurious pressure modes, but also in reducing the computational effort for determining the eigenvalues and eigenvectors. It is found that all fully integrated inconsistent models exhibit locking behaviour. However, the inconsistent eight- and nine-noded elements, integrated with full integration of volumetric stiffness and one point integration of the rotational stiffness matrices, gives excellent performance, although they do not pass the inf–sup test. The four- and nine-noded consistent models are found to give locking free performance while their eight-noded counterpart exhibited locking behaviour. The study shows that only consistent nine-noded element models pass the inf–sup test. The utility of these elements in the coupled fluid–structure interaction problem is also demonstrated.