On the geometrically exact formulations of finite deformable isogeometric beams

Abstract

We present a set of advanced analytical formulations that facilitates the accurate analysis and efficient implementation of finite deformable thin Kirchhoff–Love beams. This paper enhances the prevailing differential geometry based large deformation beam models by producing geometrically exact formulations for initial curvatures, non-zero force tangents and external stiffness matrix contributions of spatial beams. Though it is not analytically merged in existing beam models, initial curvatures of beams have a significant influence on the integration of forces over beam cross-sections. We reveal this influence through the systematic deduction of the Jacobian in volume integrals of beam forces. Also, this paper demonstrates the applicability of follower loads on beams with necessary adjustments to the global Hessian matrix. We adopt the isogeometric analysis formalism in beam body discretisation and algorithmic implementation of the presented formulations.