Efficient explicit integration for dynamics of inextensible ANCF beams with large deformations

Explicit integration in flexible multibody dynamics is highly attractive for real-time simulation but poses significant efficiency challenges. The bending and axial straining dynamics of slender structural components, such as beams and cables, operate on different time scales. As a result, axial straining—usually the higher-frequency one, though often of minor interest—imposes strict time step limitations for algorithmic stability in explicit integration schemes. This work achieves efficient explicit integration for inextensible flexible beams undergoing large deformations. The key is to develop a dynamic model optimized for explicit integrators by reducing the stiffness of the problem. To this end, an absolute nodal coordinate formulation for inextensible beams is proposed, where the elastic potential energy is derived from the direct multiplication of the first and second derivatives of the position vector with respect to the arc-length coordinate. This formulation results in equations of motion with moderate stiffness, making it well-suited for explicit schemes. Inextensibility is rigorously enforced through algebraic constraints on slope vector lengths, applied either at discrete points or via a fixed-length constraint on the entire span of the beam. A constraint stabilization technique is employed to transform the resulting system of differential-algebraic equations into a set of ordinary differential equations, ensuring numerical stability. The main advantage of this method is its ability to accommodate large time steps, significantly improving computational efficiency. This capability makes explicit simulation schemes more practical and contributes to enabling real-time simulation of mechanical systems with flexible beams or cables.