{"title":"任意弯曲粘弹性梁非线性动力分析的任意拉格朗日-欧拉公式","authors":"Lanfeng Deng, Mu-Qing Niu, Xin Yang, Yimin Fan, Li-Qun Chen","doi":"10.1016/j.finel.2024.104303","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, a three-dimensional arbitrary Lagrangian-Eulerian (ALE) formulation based on the consistent corotational method for flexible structures' large deformation problems is proposed. In contrast with the Lagrangian formulations, the proposed formulation can accurately describe moving boundary and load problems using moving nodes. The ALE formulation for flexible structures with an arbitrarily curved initial geometry is derived for the first time. Moreover, internal and external dampings are integrated into the ALE formulation to consider the energy dissipation induced by the structures' deformation and spatial motion. In addition, the rigid-body motion energy dissipation of the internal damping can be avoided by measuring the element's deformation rate in a corotational frame. Kelvin-Voigt model and the interdependent interpolation element are embedded into the element-independent framework of the corotational method. Then, a general beam element model is established to account for the beam's rotary inertia, viscoelasticity, and shear, bending, torsional, and axial deformations in the ALE formulation. Four examples are provided to validate the proposed formulation. The numerical results obtained using the proposed method are compared with those from the commercial software ANSYS and previously published methods. This comparison illustrates the enhanced efficiency in computation time and computer memory.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"244 ","pages":"Article 104303"},"PeriodicalIF":3.5000,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An arbitrary Lagrangian-Eulerian corotational formulation for nonlinear dynamic analysis of arbitrarily curved viscoelastic beams\",\"authors\":\"Lanfeng Deng, Mu-Qing Niu, Xin Yang, Yimin Fan, Li-Qun Chen\",\"doi\":\"10.1016/j.finel.2024.104303\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, a three-dimensional arbitrary Lagrangian-Eulerian (ALE) formulation based on the consistent corotational method for flexible structures' large deformation problems is proposed. In contrast with the Lagrangian formulations, the proposed formulation can accurately describe moving boundary and load problems using moving nodes. The ALE formulation for flexible structures with an arbitrarily curved initial geometry is derived for the first time. Moreover, internal and external dampings are integrated into the ALE formulation to consider the energy dissipation induced by the structures' deformation and spatial motion. In addition, the rigid-body motion energy dissipation of the internal damping can be avoided by measuring the element's deformation rate in a corotational frame. Kelvin-Voigt model and the interdependent interpolation element are embedded into the element-independent framework of the corotational method. Then, a general beam element model is established to account for the beam's rotary inertia, viscoelasticity, and shear, bending, torsional, and axial deformations in the ALE formulation. Four examples are provided to validate the proposed formulation. The numerical results obtained using the proposed method are compared with those from the commercial software ANSYS and previously published methods. This comparison illustrates the enhanced efficiency in computation time and computer memory.</div></div>\",\"PeriodicalId\":56133,\"journal\":{\"name\":\"Finite Elements in Analysis and Design\",\"volume\":\"244 \",\"pages\":\"Article 104303\"},\"PeriodicalIF\":3.5000,\"publicationDate\":\"2025-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Finite Elements in Analysis and Design\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0168874X24001975\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Finite Elements in Analysis and Design","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168874X24001975","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
本文针对柔性结构的大变形问题,提出了一种基于一致矢量法的三维任意拉格朗日-欧拉(ALE)公式。与拉格朗日公式相比,本文提出的公式可以精确描述移动边界和使用移动节点的荷载问题。首次推导出了具有任意弯曲初始几何形状的柔性结构的 ALE 公式。此外,ALE 公式还集成了内部和外部阻尼,以考虑结构变形和空间运动引起的能量耗散。此外,内部阻尼的刚体运动能量耗散可以通过在惯性框架中测量元素的变形率来避免。Kelvin-Voigt 模型和相互依存的插值元素被嵌入到相关性方法的元素无关框架中。然后,建立了一个通用梁元素模型,以在 ALE 公式中考虑梁的旋转惯性、粘弹性以及剪切、弯曲、扭转和轴向变形。本文提供了四个示例来验证所提出的公式。将使用建议方法获得的数值结果与商业软件 ANSYS 和以前发布的方法进行了比较。比较结果表明,计算时间和计算机内存的效率都有所提高。
An arbitrary Lagrangian-Eulerian corotational formulation for nonlinear dynamic analysis of arbitrarily curved viscoelastic beams
In this paper, a three-dimensional arbitrary Lagrangian-Eulerian (ALE) formulation based on the consistent corotational method for flexible structures' large deformation problems is proposed. In contrast with the Lagrangian formulations, the proposed formulation can accurately describe moving boundary and load problems using moving nodes. The ALE formulation for flexible structures with an arbitrarily curved initial geometry is derived for the first time. Moreover, internal and external dampings are integrated into the ALE formulation to consider the energy dissipation induced by the structures' deformation and spatial motion. In addition, the rigid-body motion energy dissipation of the internal damping can be avoided by measuring the element's deformation rate in a corotational frame. Kelvin-Voigt model and the interdependent interpolation element are embedded into the element-independent framework of the corotational method. Then, a general beam element model is established to account for the beam's rotary inertia, viscoelasticity, and shear, bending, torsional, and axial deformations in the ALE formulation. Four examples are provided to validate the proposed formulation. The numerical results obtained using the proposed method are compared with those from the commercial software ANSYS and previously published methods. This comparison illustrates the enhanced efficiency in computation time and computer memory.
期刊介绍:
The aim of this journal is to provide ideas and information involving the use of the finite element method and its variants, both in scientific inquiry and in professional practice. The scope is intentionally broad, encompassing use of the finite element method in engineering as well as the pure and applied sciences. The emphasis of the journal will be the development and use of numerical procedures to solve practical problems, although contributions relating to the mathematical and theoretical foundations and computer implementation of numerical methods are likewise welcomed. Review articles presenting unbiased and comprehensive reviews of state-of-the-art topics will also be accommodated.