发表机构
Institute for Mathematics and Computer-Based Simulation (IMCS), University of the Bundeswehr Munich; Institute of Technical Mechanics, Johannes Kepler University Linz（联邦国防大学数学与计算机仿真研究所; 林茨约翰内斯·开普勒大学技术力学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种时空有限元方法，统一处理空间和时间，用于几何精确剪切变形梁的瞬态分析，支持弯曲结构、时变域，并通过数值示例验证其收敛性、客观性和适用性。
AI 中文摘要
我们提出了一种用于几何精确剪切变形梁瞬态分析的时空有限元公式。该公式在统一的有限元框架内处理空间和时间，并采用混合方法，其中平移速度和角速度被引入为独立场。旋转场使用节点旋转（伪）向量进行参数化，并采用合适的客观插值的三元组场。所提出的公式支持一般弯曲的梁结构，包括几何扭结和刚性连接。此外，时变材料域可以直接通过时空表面的几何形状来表示，从而无需修改底层梁公式即可处理非材料边界。数值示例证明了收敛到经典时间步进方案获得的解、公式的客观性以及时空稳定的影响。最后，滑动意大利面条问题说明了所提出方法对轴向运动连续体的适用性。
英文摘要
We present a space-time finite element formulation for the transient analysis of geometrically exact shear-deformable beams. The formulation treats space and time within a unified finite element framework and employs a mixed approach in which translational and angular velocities are introduced as independent fields. The rotation field is parametrized using nodal rotation (pseudo-)vectors and a suitable objective interpolation of the triad field is employed. The resulting formulation supports generally curved beam structures, including geometric kinks and rigid joints. Furthermore, time-dependent material domains can be represented directly through the geometry of the space-time surface, enabling the treatment of non-material boundaries without modifying the underlying beam formulation. Numerical examples demonstrate convergence to solutions obtained with classical time-stepping schemes, objectivity of the formulation, and the influence of the space-time stabilization. Finally, the sliding spaghetti problem illustrates the applicability of the proposed approach to axially moving continua.
