The objective of this research is the development of a geometrically exact model for the analysis of arbitrarily curved spatial Bernoulli-Euler beams. The complete metric of the beam is utilized in order to include the effect of curviness on the nonlinear distribution of axial strain over the cross section. The exact constitutive relation between energetically conjugated pairs is employed, along with four reduced relations. The isogeometric approach, which allows smooth connections between finite elements, is used for the spatial discretization of the weak form. Two methods for updating the local basis are applied and discussed in the context of finite rotations. All the requirements of geometrically exact beam theory are satisfied, such as objectivity and path-independence. The accuracy of the formulation is verified by a thorough numerical analysis. The influence of the curviness on the structural response is scrutinized for two classic examples. If the exact response of the structure is sought, the curviness must be considered when choosing the appropriate beam model.

翻译：这项研究的目标是开发一个精确的几何模型,用于分析任意弯曲的空间Bernoulli-Euler光束。光束的完整度量是用来包括曲线对横截段轴承菌株的非线性分布的影响。采用了强力共生配对之间确切的构成关系,并减少了四条关系。使有限元素之间能够顺利连接的等离子测量方法,用于弱形的空间分解。两种更新当地基础的方法在有限的旋转中应用和讨论。几何精确的波束理论的所有要求都得到满足,例如客观性和路径独立性。配方的准确性通过彻底的数字分析加以验证。对结构反应的曲线影响进行仔细审查,以两种典型的例子为例。如果寻求结构的准确反应,则在选择适当的波束模型时必须考虑曲线。