In this work, an efficient and robust isogeometric three-dimensional solid-beam finite element is developed for large deformations and finite rotations with merely displacements as degrees of freedom. The finite strain theory and hyperelastic constitutive models are considered and B-Spline and NURBS are employed for the finite element discretization. Similar to finite elements based on Lagrange polynomials, also NURBS-based formulations are affected by the non-physical phenomena of locking, which constrains the field variables and negatively impacts the solution accuracy and deteriorates convergence behavior. To avoid this problem within the context of a solid-beam formulation, the Assumed Natural Strain (ANS) method is applied to alleviate membrane and transversal shear locking and the Enhanced Assumed Strain (EAS) method against Poisson thickness locking. Furthermore, the Mixed Integration Point (MIP) method is used to make the formulation more efficient and robust. The proposed novel isogeometric solid-beam element is tested on several single-patch and multi-patch benchmark problems, and it is validated against classical solid finite elements and first-order Lagrange solid-beam element. The results show that the proposed formulation can alleviate the locking effects and significantly improve the performance of the isogeometric solid-beam element. With the developed element, efficient and accurate predictions of mechanical properties of lattice-based structured materials can be achieved. The proposed solid-beam element inherits both the merits of solid elements e.g. flexible boundary conditions and of the beam elements i.e. higher computational efficiency.

中文翻译：

---

稳健的有限应变等几何实体梁单元


在这项工作中，开发了一种高效且鲁棒的等几何三维实体梁有限元，用于仅以位移作为自由度的大变形和有限旋转。考虑有限应变理论和超弹性本构模型，采用B样条和NURBS进行有限元离散。与基于拉格朗日多项式的有限元类似，基于 NURBS 的公式也受到锁定非物理现象的影响，这会限制场变量并对求解精度产生负面影响并恶化收敛行为。为了避免实体梁公式中的此问题，应用假设自然应变 (ANS) 方法来减轻膜和横向剪切锁定，并应用增强假设应变 (EAS) 方法来对抗泊松厚度锁定。此外，混合积分点（MIP）方法用于使配方更加高效和稳健。所提出的新型等几何实体梁单元在多个单面片和多面片基准问题上进行了测试，并针对经典实体有限元和一阶拉格朗日实体梁单元进行了验证。结果表明，所提出的公式可以减轻锁定效应并显着提高等几何实体梁单元的性能。利用所开发的元件，可以实现对基于晶格的结构材料的机械性能的高效和准确的预测。所提出的固体梁单元继承了固体单元的优点，例如：灵活的边界条件和梁单元，即更高的计算效率。