A RANCF-Linear Complementarity Problem Framework for Modeling Incompressible Fluid–Structure Interactions

Abstract

Abstract. Accurate modeling of systems with interacting deformable solids and fluids is essential across various engineering disciplines. Applications such as control systems, high-fidelity simulators, and fluid–structure interactions depend on computationally efficient and precise representations of these systems. Traditional finite element methods face challenges when dealing with large deformations and rotations, particularly in scenarios involving fluid dynamics and complex geometries. This work introduces a numerical framework that integrates the rational absolute nodal coordinate formulation (RANCF) with linear complementarity problem (LCP) formulations to model incompressible Newtonian fluids interacting with multibody systems. The proposed approach incorporates interpolation functions such as nonuniform rational B-splines (NURBS) and enforces constraints through Lagrange multipliers, which addresses limitations in geometric flexibility and constraint handling found in prior methods. Benchmark problems, including fluid sloshing and dam break scenarios, demonstrate the framework's accuracy and stability. Compared to earlier absolute nodal coordinate formulation (ANCF)-based approaches, the proposed framework models large deformations and fluid–structure interactions with fewer degrees-of-freedom, resulting in improved numerical efficiency. Additionally, the method eliminates reliance on penalty methods for constraint enforcement, which addresses stability and accuracy concerns associated with them. These findings contribute to the broader field of multibody dynamics by providing a unified framework that integrates continuum mechanics and multibody formulations. The results lay the groundwork for future developments in integrating fluid simulations into multibody system models for engineering applications.