Analytical solution for the bending problem of micropolar plates based on the symplectic approach

IF 2.6 4区 工程技术 Q2 MECHANICS Journal of Applied Mechanics-Transactions of the Asme Pub Date : 2023-10-16 DOI:10.1115/1.4063398
Qiong Wu, Long Chen, Qiang Gao
{"title":"Analytical solution for the bending problem of micropolar plates based on the symplectic approach","authors":"Qiong Wu, Long Chen, Qiang Gao","doi":"10.1115/1.4063398","DOIUrl":null,"url":null,"abstract":"Abstract An analytical solution for the bending problem of micropolar plates is derived based on the symplectic approach. By applying Legendre's transformation, we obtain the Hamiltonian canonical equation for the bending problem of a micropolar plate. Utilizing the method of separation of variables, the homogeneous Hamiltonian canonical equation can be transformed into an eigenvalue problem of the Hamiltonian operator matrix. We derive the eigensolutions of the eigenvalue problem for the simply supported, free, and clamped boundary conditions at the two opposite sides. Based on the adjoint symplectic orthogonal relation of the eigensolutions, the solution of the bending problem of the micropolar plate is expressed as a series expansion of eigensolutions. Numerical results confirm the validity of the present approach for the bending problem of micropolar plates under various boundary conditions and demonstrate the capability of the proposed approach to capture the size-dependent behavior of micropolar plates.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mechanics-Transactions of the Asme","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1115/1.4063398","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0

Abstract

Abstract An analytical solution for the bending problem of micropolar plates is derived based on the symplectic approach. By applying Legendre's transformation, we obtain the Hamiltonian canonical equation for the bending problem of a micropolar plate. Utilizing the method of separation of variables, the homogeneous Hamiltonian canonical equation can be transformed into an eigenvalue problem of the Hamiltonian operator matrix. We derive the eigensolutions of the eigenvalue problem for the simply supported, free, and clamped boundary conditions at the two opposite sides. Based on the adjoint symplectic orthogonal relation of the eigensolutions, the solution of the bending problem of the micropolar plate is expressed as a series expansion of eigensolutions. Numerical results confirm the validity of the present approach for the bending problem of micropolar plates under various boundary conditions and demonstrate the capability of the proposed approach to capture the size-dependent behavior of micropolar plates.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
基于辛方法的微极板弯曲问题解析解
摘要基于辛方法导出了微极板弯曲问题的解析解。应用勒让德变换,得到了微极板弯曲问题的哈密顿正则方程。利用分离变量的方法,将齐次哈密顿正则方程转化为哈密顿算子矩阵的特征值问题。导出了简支、自由和固支边界条件下的特征值问题的本征解。基于特征解的伴随辛正交关系,将微极板弯曲问题的解表示为特征解的级数展开。数值结果证实了该方法在各种边界条件下求解微极板弯曲问题的有效性,并证明了该方法能够捕捉微极板的尺寸相关行为。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
4.80
自引率
3.80%
发文量
95
审稿时长
5.8 months
期刊介绍: All areas of theoretical and applied mechanics including, but not limited to: Aerodynamics; Aeroelasticity; Biomechanics; Boundary layers; Composite materials; Computational mechanics; Constitutive modeling of materials; Dynamics; Elasticity; Experimental mechanics; Flow and fracture; Heat transport in fluid flows; Hydraulics; Impact; Internal flow; Mechanical properties of materials; Mechanics of shocks; Micromechanics; Nanomechanics; Plasticity; Stress analysis; Structures; Thermodynamics of materials and in flowing fluids; Thermo-mechanics; Turbulence; Vibration; Wave propagation
期刊最新文献
Improved Ballistic Impact Resistance of Nanofibrillar Cellulose Films with Discontinuous Fibrous Bouligand Architecture. FAST OPTIMAL DESIGN OF SHELL-GRADED-INFILL STRUCTURES WITH EXPLICIT BOUNDARY BY A HYBRID MMC-AABH PLUS APPROACH The role of frequency and impedance contrasts in bandgap closing and formation patterns of axially-vibrating phononic crystals Head Injuries Induced by Tennis Ball Impacts: A Computational Study Experimental Validation of Reconstructed Microstructure via Deep Learning in Discontinuous Fiber Platelet Composite
×
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
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1