Implementation and verification of nonlinear spring–damper restraints in OpenFOAM's six-DOF rigid-body motion framework

Abstract

 This work presents the development of new OpenFOAM libraries that extend existing linear spring–damper models to incorporate nonlinear translational and rotational restraints in a 6-DOF rigid-body analysis case. The implementation allows arbitrary stiffness and damping relationships to be defined through analytical models, such as Duffing and Rayleigh formulations, or via user-specified interpolation tables. The libraries are embedded directly into the 6-DOF rigid body motion solver, enabling fluid–structure interaction simulations considering nonlinear dynamic oscillations, without relying on external structural solvers. Numerical verification against central difference schemes, analytical models, and preCICE-coupled OpenFOAM– CalculiX simulations demonstrates good agreement for linear and nonlinear single-DOF systems, with only minor deviations in amplitude response. Application cases, including wind-induced oscillations of airfoils and galloping of a 3:2 prism, further illustrate the ability of the libraries to capture nonlinear structural dynamics within realistic flow conditions. The proposed implementation extends the existing approach and provides an efficient and flexible framework for investigating nonlinear aeroelastic phenomena and energy harvesting concepts, modelling the dynamic system as a nonlinear 6-DOF system in OpenFOAM.