{"title":"Dynamic performance of circular cavity in an elastic half-space with initial stress","authors":"Xi-meng Zhang, Hui Qi, Zhiyu Fan","doi":"10.1007/s00707-025-04377-8","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, the dynamic problem of a circular cavity in an elastic half-space with initial stress is studied. Firstly, the equilibrium equation for the two-dimensional elastic medium with initial stress under the SH wave is obtained by tensor analysis. Then, the analytical expression of scattering wave is established by conformal mapping method and substitution method. Finally, based on the theory of incremental elasticity, the expression for the total stress is derived. The integral equations are set up through boundary conditions and solved by applying orthogonal function expansion technique and effective truncation. The calculation results analyzed and discussed the dynamic stress concentration factor around the circular cavity. Besides, the analytical solutions are compared with the finite element solutions to verify the accuracy of the conclusions in this article.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 7","pages":"3893 - 3909"},"PeriodicalIF":2.9000,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mechanica","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00707-025-04377-8","RegionNum":3,"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
In this paper, the dynamic problem of a circular cavity in an elastic half-space with initial stress is studied. Firstly, the equilibrium equation for the two-dimensional elastic medium with initial stress under the SH wave is obtained by tensor analysis. Then, the analytical expression of scattering wave is established by conformal mapping method and substitution method. Finally, based on the theory of incremental elasticity, the expression for the total stress is derived. The integral equations are set up through boundary conditions and solved by applying orthogonal function expansion technique and effective truncation. The calculation results analyzed and discussed the dynamic stress concentration factor around the circular cavity. Besides, the analytical solutions are compared with the finite element solutions to verify the accuracy of the conclusions in this article.
期刊介绍：
Since 1965, the international journal Acta Mechanica has been among the leading journals in the field of theoretical and applied mechanics. In addition to the classical fields such as elasticity, plasticity, vibrations, rigid body dynamics, hydrodynamics, and gasdynamics, it also gives special attention to recently developed areas such as non-Newtonian fluid dynamics, micro/nano mechanics, smart materials and structures, and issues at the interface of mechanics and materials. The journal further publishes papers in such related fields as rheology, thermodynamics, and electromagnetic interactions with fluids and solids. In addition, articles in applied mathematics dealing with significant mechanics problems are also welcome.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
