利用矢量旋转变量的共旋转四边形壳元公式实现的准能量动量保守算法

IF 2.9 3区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
Zhongxue Li, Xunda Lin, Loc Vu-Quoc, Bassam A. Izzuddin, Haoyan Wei, Jin Xu, Hongtao Qian, Xin Zhuo
{"title":"利用矢量旋转变量的共旋转四边形壳元公式实现的准能量动量保守算法","authors":"Zhongxue Li,&nbsp;Xunda Lin,&nbsp;Loc Vu-Quoc,&nbsp;Bassam A. Izzuddin,&nbsp;Haoyan Wei,&nbsp;Jin Xu,&nbsp;Hongtao Qian,&nbsp;Xin Zhuo","doi":"10.1002/nme.70128","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>This paper proposes a flexible multi-body dynamics approach for elastic smooth and non-smooth shells undergoing large deformations and large overall motions. The formulation is based on a co-rotational curved quadrilateral shell element employing vectorial rotational variables and a quasi energy and momentum conservation algorithm. Hamilton's principle is adopted to derive the system's dynamic differential equations. When differentiating the kinetic energy functional with respect to time, the part involving the first-order differentiation of vectorial rotational variables with respect to time is integrated into an equivalent load vector, yielding a symmetric equivalent mass matrix. Accelerations, velocities, displacements, body, and surface loads of the generalized midpoints are generated by convex functions. The Newmark scheme is applied to transform the dynamic differential equations of the system into a set of nonlinear equations. Instead of using strains and their first/second derivatives with respect to local nodal variables at the midpoint configuration, the formulation employs time-averaged assumed strains (computed via the MITC method) and their corresponding derivatives evaluated at both ends of the time step for calculating the internal force vector and element tangent stiffness matrix in the local coordinate system. The transformation matrix from local to global coordinates, however, remains computed at the midpoint configuration. This approach ensures near-exact conservation of total energy and exact conservation of linear and angular momenta once the external loads vanish, while also yielding symmetric tangent stiffness matrices in both local and global coordinate systems. Finally, four examples of three smooth shells and one non-smooth shell problems subjected to impulse loads are solved to verify the proposed formulation for flexible multi-body dynamics of shells. It is shown that the results exhibit excellent agreement with those from other references, demonstrating the reliability, accuracy, and long-term stability of the proposed quasi energy and momentum conserving algorithm.</p>\n </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Quasi Energy and Momentum Conservative Algorithm Implemented With a Co-Rotational Quadrilateral Shell Element Formulation Using Vectorial Rotational Variables\",\"authors\":\"Zhongxue Li,&nbsp;Xunda Lin,&nbsp;Loc Vu-Quoc,&nbsp;Bassam A. Izzuddin,&nbsp;Haoyan Wei,&nbsp;Jin Xu,&nbsp;Hongtao Qian,&nbsp;Xin Zhuo\",\"doi\":\"10.1002/nme.70128\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n <p>This paper proposes a flexible multi-body dynamics approach for elastic smooth and non-smooth shells undergoing large deformations and large overall motions. The formulation is based on a co-rotational curved quadrilateral shell element employing vectorial rotational variables and a quasi energy and momentum conservation algorithm. Hamilton's principle is adopted to derive the system's dynamic differential equations. When differentiating the kinetic energy functional with respect to time, the part involving the first-order differentiation of vectorial rotational variables with respect to time is integrated into an equivalent load vector, yielding a symmetric equivalent mass matrix. Accelerations, velocities, displacements, body, and surface loads of the generalized midpoints are generated by convex functions. The Newmark scheme is applied to transform the dynamic differential equations of the system into a set of nonlinear equations. Instead of using strains and their first/second derivatives with respect to local nodal variables at the midpoint configuration, the formulation employs time-averaged assumed strains (computed via the MITC method) and their corresponding derivatives evaluated at both ends of the time step for calculating the internal force vector and element tangent stiffness matrix in the local coordinate system. The transformation matrix from local to global coordinates, however, remains computed at the midpoint configuration. This approach ensures near-exact conservation of total energy and exact conservation of linear and angular momenta once the external loads vanish, while also yielding symmetric tangent stiffness matrices in both local and global coordinate systems. Finally, four examples of three smooth shells and one non-smooth shell problems subjected to impulse loads are solved to verify the proposed formulation for flexible multi-body dynamics of shells. It is shown that the results exhibit excellent agreement with those from other references, demonstrating the reliability, accuracy, and long-term stability of the proposed quasi energy and momentum conserving algorithm.</p>\\n </div>\",\"PeriodicalId\":13699,\"journal\":{\"name\":\"International Journal for Numerical Methods in Engineering\",\"volume\":\"126 17\",\"pages\":\"\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2025-09-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal for Numerical Methods in Engineering\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/nme.70128\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal for Numerical Methods in Engineering","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/nme.70128","RegionNum":3,"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

摘要

针对大变形大整体运动的光滑和非光滑弹性壳,提出了一种柔性多体动力学方法。该公式基于一个共旋转的弯曲四边形壳单元,采用矢量旋转变量和准能量动量守恒算法。采用Hamilton原理推导了系统的动力学微分方程。当动能泛函相对于时间微分时,涉及矢量旋转变量相对于时间的一阶微分的部分被积分到一个等效载荷矢量中,产生一个对称的等效质量矩阵。广义中点的加速度、速度、位移、体和表面载荷由凸函数生成。采用Newmark格式将系统的动态微分方程转化为一组非线性方程。该公式不是在中点构型中使用应变及其对局部节点变量的一/二阶导数,而是在时间步长两端使用时间平均假设应变(通过MITC方法计算)及其对应的导数来计算局部坐标系中的内力矢量和单元切向刚度矩阵。然而,从局部坐标到全局坐标的变换矩阵仍然在中点配置处计算。这种方法确保了一旦外部载荷消失,总能量和线动量和角动量的精确守恒,同时也在局部和全局坐标系中产生对称的切线刚度矩阵。最后,对三个光滑壳和一个非光滑壳在冲击载荷作用下的四个算例进行了求解,验证了所提出的壳柔性多体动力学公式。计算结果与其他文献的结果非常吻合,证明了所提出的准能量动量守恒算法的可靠性、准确性和长期稳定性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Quasi Energy and Momentum Conservative Algorithm Implemented With a Co-Rotational Quadrilateral Shell Element Formulation Using Vectorial Rotational Variables

This paper proposes a flexible multi-body dynamics approach for elastic smooth and non-smooth shells undergoing large deformations and large overall motions. The formulation is based on a co-rotational curved quadrilateral shell element employing vectorial rotational variables and a quasi energy and momentum conservation algorithm. Hamilton's principle is adopted to derive the system's dynamic differential equations. When differentiating the kinetic energy functional with respect to time, the part involving the first-order differentiation of vectorial rotational variables with respect to time is integrated into an equivalent load vector, yielding a symmetric equivalent mass matrix. Accelerations, velocities, displacements, body, and surface loads of the generalized midpoints are generated by convex functions. The Newmark scheme is applied to transform the dynamic differential equations of the system into a set of nonlinear equations. Instead of using strains and their first/second derivatives with respect to local nodal variables at the midpoint configuration, the formulation employs time-averaged assumed strains (computed via the MITC method) and their corresponding derivatives evaluated at both ends of the time step for calculating the internal force vector and element tangent stiffness matrix in the local coordinate system. The transformation matrix from local to global coordinates, however, remains computed at the midpoint configuration. This approach ensures near-exact conservation of total energy and exact conservation of linear and angular momenta once the external loads vanish, while also yielding symmetric tangent stiffness matrices in both local and global coordinate systems. Finally, four examples of three smooth shells and one non-smooth shell problems subjected to impulse loads are solved to verify the proposed formulation for flexible multi-body dynamics of shells. It is shown that the results exhibit excellent agreement with those from other references, demonstrating the reliability, accuracy, and long-term stability of the proposed quasi energy and momentum conserving algorithm.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
5.70
自引率
6.90%
发文量
276
审稿时长
5.3 months
期刊介绍: The International Journal for Numerical Methods in Engineering publishes original papers describing significant, novel developments in numerical methods that are applicable to engineering problems. The Journal is known for welcoming contributions in a wide range of areas in computational engineering, including computational issues in model reduction, uncertainty quantification, verification and validation, inverse analysis and stochastic methods, optimisation, element technology, solution techniques and parallel computing, damage and fracture, mechanics at micro and nano-scales, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, and error estimation and mesh generation. It is emphasized that this is by no means an exhaustive list, and particularly papers on multi-scale, multi-physics or multi-disciplinary problems, and on new, emerging topics are welcome.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信