A reduced angular-coordinate equilibrium formulation with exact embedding of prescribed angular data for inextensible Kirchhoff rods

Abstract

In the reduced-order static analysis of inextensible Kirchhoff rods, locally prescribed tangent directions and material-twist angles are still often enforced only after discretization as external constraints. This increases the constrained-system burden and can offset the benefit of a reduced representation. This paper proposes the Reduced Angular-Coordinate Equilibrium Formulation (RACEF). The rod configuration is represented in a low-dimensional interpolatory angular trial space; prescribed angular data at the corresponding arc-length locations are included in the interpolation grid and imposed as fixed coordinates, so that the associated angular constraints are satisfied at the parameterization stage and do not enter the external nonlinear equality system. Representative planar and spatial examples, compared with independent high-fidelity references, show that RACEF solves large-deformation equilibrium problems with locally prescribed angular constraints using fewer configuration variables at matched accuracy, and reduces constrained-system size and solution cost under high prescribed-angle density. RACEF thus provides a reduced-order route for many-query analyses such as parameter sweeps and design optimization.