后屈曲薄复合板的互补能量定理

IF 0.6 4区 工程技术 Q4 MECHANICS Mechanics of Solids Pub Date : 2024-11-01 DOI:10.1134/S0025654424602957
S. V. Selyugin
{"title":"后屈曲薄复合板的互补能量定理","authors":"S. V. Selyugin","doi":"10.1134/S0025654424602957","DOIUrl":null,"url":null,"abstract":"<p>The thin composite von Kármán plates in postbuckling are considered. Using the first Piola stress tensor and the displacement gradient tensor, the complementary energy variational theorem is proven. The Kirchhoff assumptions are adopted. The plate lay-up is symmetric and pointwise. According to the theorem, at the actual stress state of the plate the complementary energy (as a functional of the internal forces and of the moments) reaches its stationary value. The stationary feature of the actual state is valid as compared to other feasible states satisfying the static equilibrium and the static boundary conditions. The theorem is a consent of the static variational principle. The principle leads to the linear relations between forces/moments, created by the corresponding first Piola stress tensor components, and the 2D-strains/curvatures. An illustrative plate example is given.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 3","pages":"1290 - 1300"},"PeriodicalIF":0.6000,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Complementary Energy Theorem for Thin Composite Plates in Postbuckling\",\"authors\":\"S. V. Selyugin\",\"doi\":\"10.1134/S0025654424602957\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The thin composite von Kármán plates in postbuckling are considered. Using the first Piola stress tensor and the displacement gradient tensor, the complementary energy variational theorem is proven. The Kirchhoff assumptions are adopted. The plate lay-up is symmetric and pointwise. According to the theorem, at the actual stress state of the plate the complementary energy (as a functional of the internal forces and of the moments) reaches its stationary value. The stationary feature of the actual state is valid as compared to other feasible states satisfying the static equilibrium and the static boundary conditions. The theorem is a consent of the static variational principle. The principle leads to the linear relations between forces/moments, created by the corresponding first Piola stress tensor components, and the 2D-strains/curvatures. An illustrative plate example is given.</p>\",\"PeriodicalId\":697,\"journal\":{\"name\":\"Mechanics of Solids\",\"volume\":\"59 3\",\"pages\":\"1290 - 1300\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mechanics of Solids\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S0025654424602957\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanics of Solids","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1134/S0025654424602957","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0

摘要

考虑了后屈曲中的薄复合 von Kármán 板。利用第一皮奥拉应力张量和位移梯度张量,证明了补能变分定理。采用基尔霍夫假设。板的铺设是对称和点对点的。根据该定理,在板的实际应力状态下,互补能(作为内力和力矩的函数)达到其静止值。与满足静态平衡和静态边界条件的其他可行状态相比,实际状态的静止特征是有效的。该定理是对静态变分原理的认可。该原理导致了由相应的第一皮奥拉应力张量分量产生的力/力矩与二维应变/曲率之间的线性关系。给出了一个示例板。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

摘要图片

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
Complementary Energy Theorem for Thin Composite Plates in Postbuckling

The thin composite von Kármán plates in postbuckling are considered. Using the first Piola stress tensor and the displacement gradient tensor, the complementary energy variational theorem is proven. The Kirchhoff assumptions are adopted. The plate lay-up is symmetric and pointwise. According to the theorem, at the actual stress state of the plate the complementary energy (as a functional of the internal forces and of the moments) reaches its stationary value. The stationary feature of the actual state is valid as compared to other feasible states satisfying the static equilibrium and the static boundary conditions. The theorem is a consent of the static variational principle. The principle leads to the linear relations between forces/moments, created by the corresponding first Piola stress tensor components, and the 2D-strains/curvatures. An illustrative plate example is given.

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
Mechanics of Solids
Mechanics of Solids 医学-力学
CiteScore
1.20
自引率
42.90%
发文量
112
审稿时长
6-12 weeks
期刊介绍: Mechanics of Solids publishes articles in the general areas of dynamics of particles and rigid bodies and the mechanics of deformable solids. The journal has a goal of being a comprehensive record of up-to-the-minute research results. The journal coverage is vibration of discrete and continuous systems; stability and optimization of mechanical systems; automatic control theory; dynamics of multiple body systems; elasticity, viscoelasticity and plasticity; mechanics of composite materials; theory of structures and structural stability; wave propagation and impact of solids; fracture mechanics; micromechanics of solids; mechanics of granular and geological materials; structure-fluid interaction; mechanical behavior of materials; gyroscopes and navigation systems; and nanomechanics. Most of the articles in the journal are theoretical and analytical. They present a blend of basic mechanics theory with analysis of contemporary technological problems.
期刊最新文献
Proper Motions of the Flat Structure of Cosserat Type Expansion of a Spherical Cavity in an Infinite Dilatant Medium Obeying the Drucker–Prager Yield Criterion and a Non-Associated Plastic Flow Rule Investigation of Thermoelastic behavior in a Three-Dimensional Homogeneous Half-Space with Reference Temperature-Dependent Material Properties Dynamic modeling and Multi-Objective Optimization of a 3DOF Reconfigurable Parallel Robot Nonlinear Poro-Visco-Thermal Vibrations in Piezo-Thermoelastic Hygroscopic Sandwich Shells
×
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