Geometrically exact static 3D Cosserat rods problem solved using a shooting method

TL;DR

This paper introduces a novel shooting method for solving geometrically exact 3D static Cosserat rods, effectively handling large displacements, rotations, and discontinuities without finite element meshes.

Contribution

It presents a new multiple shooting method with dual MRP and SMRP rotation parameterizations for large rotations and discontinuities in 3D Cosserat rods.

Findings

Method accurately models large displacements and rotations.

Handles geometrical discontinuities and beam assemblies.

Demonstrates high performance and validity through numerical examples.

Abstract

This paper aims to solve the equations of geometrically exact 3D nonlinear Cosserat static rods under large displacements with a mesh free alternative method to finite elements: the shooting method. One of the main goal of the work presented is to introduce a new multiple shooting method to handle geometrical discontinuities as well as beams assembled through mechanical linkages in a multi-body framework. An additional purpose is to propose a new shooting method algorithm in which the dual set of Modified Rodrigues Parameters (MRP) and Shadow Modified Rodrigues Parameters (SMRP) are used for rotations parameterization along the length of the beam in order to model extremely large rotations. Several numerical examples demonstrate the validity, the performance and accuracy of the proposed approach.