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.
翻译:提出了几何和物质上非线性Timoshenko波束的等离子计量有限元素配方,其中包括两个可扩展的导体矢量描述的横截面的平面变形。由于这些导体属于面积$_Bbb R ⁇ 3美元,因此可以对配置进行添加更新。开发的配方允许直接应用非线性三维构形方程式,而没有零压力条件。特别是,对考虑正确表面负荷而不是直接在中央轴上应用同等负荷的重要性进行了调查。通过使用增强的假定压力(EAS)法,增加了跨轴线性平面阵列线性阵列组件,以缓解Poisson的锁定。在显示大形变形的各种数字实例中,对所呈现的波束配方的准确性和效率进行了比重评估。我们特别使用St. Venant-Kirchhoff和可压缩的Ne-Hookean型超弹性材料。