Uniqueness theorem in coupled strain gradient elasticity with mixed boundary conditions

Author:

Nazarenko LidiiaORCID,Glüge Rainer,Altenbach Holm

Abstract

AbstractThe equilibrium equations and the traction boundary conditions are evaluated on the basis of the condition of the stationarity of the Lagrangian for coupled strain gradient elasticity. The quadratic form of strain energy can be written as a function of the strain and the second gradient of displacement and contains a fourth-, a fifth- and a sixth-order stiffness tensor $${\mathbb {C}}_4$$ C 4 , $${\mathbb {C}}_5$$ C 5 and $${\mathbb {C}}_6$$ C 6 , respectively. Assuming invariance under rigid body motions the balance of linear and angular momentum is obtained. The uniqueness theorem (Kirchhoff) for the mixed boundary value problem is proved for the case of the coupled linear strain gradient elasticity (novel). To this end, the total potential energy is altered to be presented as an uncoupled quadratic form of the strain and the modified second gradient of displacement vector. Such a transformation leads to a decoupling of the equation of the potential energy density. The uniqueness of the solution is proved in the standard manner by considering the difference between two solutions.

Funder

deutsche forschungsgemeinschaft

Publisher

Springer Science and Business Media LLC

Subject

General Physics and Astronomy,Mechanics of Materials,General Materials Science

Cited by 9 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3