Constraint Realization-Based Hamel Field Integrator for Geometrically Exact Planar Euler–Bernoulli Beam Dynamics

Abstract

In this article, we first introduce a Hamel field integrator designed for a geometrically exact Euler–Bernoulli beam with infinite-dimensional holonomic constraints, constructed using a Lagrange multiplier. This method addresses the complexities introduced by constraints, but the additional multiplier introduces a new degree of freedom and hence results in a system with mixed-type partial differential equations. To address this issue, we further propose a constraint realization method based on perturbation theory for infinite-dimensional mechanical systems within the framework of Hamel's formalism. This method circumvents the use of additional Lagrange multiplier, significantly reducing the computational complexity of modeling problems. Building on this, we construct a perturbed Hamel field integrator optimized for parallel computing and incorporate artificial viscosity to accelerate constraint convergence. While applicable to three dimensions, our method is demonstrated in a simplified context using planar Euler–Bernoulli beam examples to illustrate the effectiveness of the unified mathematical framework.