Abstract

A new formulation for two-dimensional fluid-rigid body interaction problems is developed. In particular, vortex-induced oscillations of a rigid boy in viscous incompressible flow are studied. The incompressible Naiver-Stokes equations are used to describe the motion of the fluid, while it is assumed that the rigid body is mounted on a system consisting of a spring and a dashpot. An arbitrary Lagrangian-Eulerian formulation (ALE) is used in order to account for large boundary motion. A general formulation for coupled problem is obtained by uncoupling the translation motion of the body from its rotational motion and developing a specific algorithm to efficiently handle the nonlinear dependence of the rotations. This general formulation ca be easily applied to multi-body problems. Two numerical examples involving either translations and rotations are presented as an illustration of the proposed methodologies for fluid-rigid body interaction.

Abstract

The arbitrary Lagrangian—Eulerian (ALE) formulation, which is already well established in the hydrodynamics and fluid-structure interaction fields, is extended to materials with memory, namely, non- linear path-dependent materials. Previous attempts to treat non- linear solid mechanics with the ALE description have, in common, the implicit interpolation technique employed. Obviously, this implies a numerical burden which may be uneconomical and may induce to give up this formulation, particularly in fast-transient dynamics where explicit algorithms are usually employed. Here, several applications are presented to show that if adequate stress updating techniques are implemented, the ALE formulation could be much more competitive than classical Lagrangian computations when large deformations are present. Moreover, if the ALE technique is interpreted as a simple interpolation enrichment, adequate—in opposition to distorted or locally coarse—meshes are employed. Notice also that impossible computations (or at least very involved numerically) with a Lagrangian code are easily implementable in an ALE analysis. Finally, it is important to observe that the numerical examples shown range from a purely academic test to real engineering simulations. They show the effective applicability of this formulation to non-linear solid mechanics and, in particular, to impact, coining or forming analysis.

Abstract

A new formulation for two-dimensional fluid–rigid body interaction problems is developed. In particular, vortex-induced oscillations of a rigid body in viscous incompressible flow are studied. The incompressible Navier–Stokes equations are used to describe the motion of the fluid, while it is assumed that the rigid body is mounted on a system consisting of a spring and a dashpot. An arbitrary Lagrangian–Eulerian formulation (ALE) is used in order to account for large boundary motion. A general formulation for the coupled problem is obtained by uncoupling the translation motion of the body from its rotational motion and developing a specific algorithm to efficiently handle the nonlinear dependence of the rotations. This general formulation can be easily applied to multi-body problems. Two numerical examples involving either translations and rotations are presented as an illustration of the proposed methodologies for fluid–rigid body interaction.