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.

我们提出了一套先进的分析公式，有助于精确分析和有效实施有限变形的薄基尔霍夫-洛夫梁。本文通过为空间梁的初始曲率，非零力切线和外部刚度矩阵贡献生成精确的几何公式​​，从而增强了基于流行的基于微分几何的大变形梁模型。尽管在现有的梁模型中未对其进行分析合并，但梁的初始曲率对梁截面上的力积分有重大影响。我们通过对梁力的体积积分中的雅可比行列式进行系统的推论来揭示这种影响。此外，本文还演示了通过对全局Hessian矩阵进行必要的调整，对梁施加跟随载荷的适用性。