A non-linear implicit approach for modelling the dynamics of porous tensile structures interacting with fluids

Abstract

A new model for the simulation of large motions of porous tensile structures and their interaction with the surrounding fluid is developed in this paper. The discrete structure is represented by several non-linear elastic bars and knots connecting up to four bars. An implicit system of equations is derived from the fundamental relations of dynamics, kinematics and material and solved using an improved Newton’s method. The Navier–Stokes equations are solved in a numerical domain to account for the interaction with the fluid. The presence of the porous structure is respected in these equations through an additional forcing term based on a modified Lagrangian–Eulerian coupling algorithm. Here, the forces on the structure are distributed on multiple Lagrangian points embedded in the fluid domain. Integration over a suitable Kernel function is applied to distribute these forces on the surrounding fluid. The derived numerical model is suitable for simulating the interaction of porous tensile structures of arbitrary geometry, non-linear material and under large motion with fluids including complex free surfaces. This is in contrast to existing models which either neglect important non-linearities, the physical interaction with the fluid or rely on explicit time integration. The validation process shows excellent agreement between the numerical simulations and existing experimental data and demonstrates the applicability of the new methodology for a wide range of applications.