This paper presents two numerical models (Model L and Model N) and its application in the analysis of dynamic stability of beam-type structures. Both numerical models use two-noded rotation-free finite elements and take into account the exact formulation for finite displacement, finite rotations, and finite strains. Model L was previously developed and is intended for linear elastic material behavior, whereas Model N is newly developed, considers laminar cross sections, and takes into account the nonlinear material behavior. Both models have been implemented into the open-source finite discrete element package Y-FDEM. Performance and conditions under which both numerical models can be used for the analysis of dynamic stability are presented by numerical examples which show good agreement in comparison with the analytical solutions.

本文介绍了两个数值模型（L型和N型）及其在梁型结构动力稳定性分析中的应用。两种数值模型均使用两节点无旋转有限元，并考虑了有限位移，有限旋转和有限应变的精确公式。模型L是先前开发的，用于线性弹性材料的行为，而模型N是新开发的，考虑了层状横截面，并考虑了非线性材料的行为。两种模型都已实现到开源有限离散元素包Y-FDEM中。通过数值示例介绍了两个数值模型都可用于动态稳定性分析的性能和条件，这些数值示例与解析解相比具有很好的一致性。