{"title":"A geometrically exact thin-walled rod model with warping and stress-resultant-based plasticity obtained with a two-level computational approach","authors":"","doi":"10.1016/j.cma.2024.117497","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9000,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Methods in Applied Mechanics and Engineering","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0045782524007515","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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,并允许使用简单的弹塑性硬化构成方程。新颖之处在于上层描述,即在全三维背景下,通过横截面应力结果和广义杆应变来描述弹塑性耦合局部几何不稳定性的影响。此外,还具有扭转自由度和任意(塑性)失效模式功能,可对薄壁构件的复杂结构行为进行建模。较低层次基于运动学上精确的壳体或三维实体模型,具有通常的 von Mises 塑性和线性各向同性硬化。在这一层次中,模拟在预处理阶段进行,由此产生的基于等效应力结果的硬化塑性参数作为输入数据直接传输到上一层次。无需迭代程序进一步绑定上层/下层表示。这种包含局部效应的现象学方法可以令人满意地复制由韧性材料组成的薄壁构件的整体行为,例如但不仅限于钢或铝梁/柱型材。上层的数值求解是在算子拆分的框架下进行的,即通过数值凝聚以元素为单位的方式求解局部变量,从而不会给上层增加任何额外的 DOF。该模型在内部有限元程序中实施,用于分析柔性薄结构,并根据参考解法进行了验证。
期刊介绍:
Computer Methods in Applied Mechanics and Engineering stands as a cornerstone in the realm of computational science and engineering. With a history spanning over five decades, the journal has been a key platform for disseminating papers on advanced mathematical modeling and numerical solutions. Interdisciplinary in nature, these contributions encompass mechanics, mathematics, computer science, and various scientific disciplines. The journal welcomes a broad range of computational methods addressing the simulation, analysis, and design of complex physical problems, making it a vital resource for researchers in the field.