Nonlinearities as large structure deformations, shock waves, separation and viscous effects play an important role in the system dynamics. As the linear theory is not able to determine accurately the system behavior, it is necessary to develop new, accurate, robust and efficient numerical methods to solve these kind of problems.

One possible and very versatile solution is to use fluid structure interaction algorithms in the time domain such as the staggered algorithms. Within a fluid-structure interaction algorithm, the structure and fluid solutions are determined separately and each treats the interaction effects as external forces.

In the present article, large structural deformations are taken into account using the nonlinear corotational finite element method. In the finite element corotational description, one element displacement is considered to be composed of the element rigid body motion and of this element small elastic deformations(linear theory). The two dimensional formulation presented in the present article is based on the corotational theory developed by Crisfield and co-workers [1,2].

The structural problem is solved in the time domain using the energy conserving implicit algorithm developed by Crisfield and co-workers [3,2]. This algorithm is more stable than others nonlinear dynamic algorithms as the nonlinear trapezoidal rule. In this article some structural problems are solved using the corotational theory and the implicit algorithms already mentioned. It is shown the superior stability and accuracy of the energy conserving algorithm.

This article main contribution is to solve the fluid-structure interaction problem using the finite element corotational theory in conjunction with the fluid motion equations derived with respect to multiple moving frames of reference. The governing fluid movement equations are written with respect to multiple frames of reference, each attached to a structural node. Each frame is associated with designated fluid grid nodes. When the fluid flow equations are solved, the obtained solution at these nodes is determined with respect to the associated moving frame. As the structure takes new configurations, these reference frames move in a conforming way, transmitting to the fluid solver the new structure configuration. This is an alternative approach to the conventional methods where each time the structure takes a new configuration the fluid grid has to be deformed or regenerated. This is considerable time consuming and error generator. These two techniques association leads to a nonlinear fluid structure interaction solution procedure, with no fluid grid update.

To illustrate the multiple moving frames application, in this article it is studied the fluid flow around a NACA0012 airfoil with a prescribed pitch motion. Besides, linear and nonlinear NACA0012 aeroelastic results are also presented.

These methods association is very natural and allows a considerable safe in time and software reuse. Thus, an efficient, stable and accurate method is obtained.

1

M.A. Crisfield, quot;Non-linear finite element analysis of solids and structures, volume 1", John Wiley & Sons, 1991.

2

U. Galvanetto, M.A. Crisfield, "An energy-conserving co-rotational procedure for the dynamics of planar beam structures" International journal for numerical methods in engineering, 39:2265-2282, 1996. doi:10.1002/(SICI)1097-0207(19960715)39:13<2265::AID-NME954>3.0.CO;2-O

3

M. Crisfield, J. Shi, "A co-rotational element/time-integration strategy for non-linear dynamics", International journal for numerical methods in engineering, 37:1897-1913, 1994. doi:10.1002/nme.1620371108

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £95 +P&P)