论文标题
具有可扩展董事的几何精确的Timoshenko梁的等质测量有限元公式
An isogeometric finite element formulation for geometrically exact Timoshenko beams with extensible directors
论文作者
论文摘要
提出了用于几何和物质非线性的Timoshenko梁的同几何有限元公式，该公式构成了两个可扩展导向矢量描述的横截面的平面内变形。由于这些董事属于Space $ {\ bbb r}^3 $，因此可以将配置加上更新。开发的公式允许直接应用非应力条件的无应力条件的非线性三维本构方程。特别是，研究了正确的表面载荷而不是直接在中央轴上施加等效载荷的重要性。通过使用增强的假定菌株（EAS）方法，已添加了横截面的不兼容的线性内平面应变成分，以减轻泊松锁定。在表现出较大变形的各种数值示例中，与砖元素相比，评估了所提出的光束公式的准确性和效率。我们特别使用St. Venant-Kirchhoff的热弹性材料和可压缩的新霍克类型。
An isogeometric finite element formulation for geometrically and materially nonlinear Timoshenko beams is presented, which incorporates in-plane deformation of the cross-section described by two extensible director vectors. Since those directors belong to the space ${\Bbb R}^3$, a configuration can be additively updated. The developed formulation allows direct application of nonlinear three-dimensional constitutive equations without zero stress conditions. Especially, the significance of considering correct surface loads rather than applying an equivalent load directly on the central axis is investigated. Incompatible linear in-plane strain components for the cross-section have been added to alleviate Poisson locking by using an enhanced assumed strain (EAS) method. In various numerical examples exhibiting large deformations, the accuracy and efficiency of the presented beam formulation is assessed in comparison to brick elements. We particularly use hyperelastic materials of the St. Venant-Kirchhoff and compressible Neo-Hookean types.
