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 employed 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 isoparametric solid-beam elements. 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.

翻译：本文开发了一种高效且鲁棒的等几何三维实体-梁有限单元，适用于仅以位移为自由度的大变形和有限转动问题。考虑了有限应变理论和超弹性本构模型，并采用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，NURBS基公式化也受到锁定的非物理现象影响，这会约束场变量，负向影响求解精度并恶化收敛行为。为避免此问题，在实体-梁公式化框架下，采用假定自然应变法缓解薄膜和横向剪切锁定，采用增强假定应变法克服泊松厚度锁定。此外，采用混合积分点法使公式化更具效率和鲁棒性。所提出的新型等几何实体-梁单元在多个单块和多块基准问题中进行了测试，并与经典实体有限元和等参实体-梁单元进行了验证。结果表明，所提公式化能缓解锁定效应，显著提升等几何实体-梁单元的性能。利用所开发单元，可实现基于晶格的结构材料力学性能的高效、精确预测。所提出的实体-梁单元兼具实体单元（如灵活边界条件）和梁单元（即更高计算效率）的双重优势。