In this work, we propose an two-level computational approach to enrich a seven degree-of-freedom kinematically exact rod model for thin-walled members, allowing for a simple elastoplastic-hardening constitutive equation. The novelty lies in upper-level description, where the effects of coupled elastoplastic-local geometrical instabilities are characterized in terms of cross-sectional stress resultants and generalized rod strains in a fully 3D context. Torsion-warping degrees of freedom and arbitrary (plastic) failure mode capabilities are present, allowing for the modeling of complex structural behavior in thin-walled members. The lower level is based on a kinematically exact shell or 3D-solid model with usual von Mises plasticity and linear isotropic hardening. At such level, simulations are performed in a pre-process stage, with the resulting equivalent stress-resultant-based hardening plastic parameters directly transferred to the upper-level as input data. No iterative procedure further binding the upper/lower level representations is required. This rather phenomenological approach of incorporating local effects may satisfactorily replicate the overall behavior of thin-walled members consisted of ductile materials, such as, but not only, steel or aluminum beam/column profiles. Numerical solution of the upper-level is carried in the framework of operator split, whereby, the local variables are solved in an element-wise fashion through numerical condensation, thus not adding any extra DOFs to the upper-level. The model is implemented in an in-house finite element program for the analysis of flexible thin structures and is validated against reference solutions.

中文翻译：

---

通过两能级计算方法获得的几何精确的薄壁杆模型，具有翘曲和基于应力合力的塑性


在这项工作中，我们提出了一种两级计算方法，以丰富薄壁构件的七自由度运动学精确杆模型，从而允许一个简单的弹塑性硬化本构方程。新颖之处在于上层描述，其中耦合弹塑性-局部几何不稳定性的影响在全三维背景下根据横截面应力合力和广义杆应变来表征。存在扭转翘曲自由度和任意（塑性）失效模式功能，允许对薄壁构件中的复杂结构行为进行建模。下层基于运动学上精确的壳或 3D 实体模型，具有通常的 von Mises 塑性和线性各向同性硬化。在这样的级别上，在前处理阶段进行模拟，生成的基于应力合成的等效硬化塑性参数作为输入数据直接传输到上层。不需要进一步绑定上/下级表示的迭代过程。这种结合局部效应的相当现象学方法可以令人满意地复制由延展性材料组成的薄壁构件的整体行为，例如但不仅仅是钢或铝梁/柱型材。上层的数值解是在算子分裂的框架下进行的，其中，局部变量通过数值压缩以元素方式求解，因此不会向上层添加任何额外的 DOF。该模型在内部有限元程序中实现，用于分析柔性薄结构，并根据参考解决方案进行了验证。