{"title":"A review of the three-dimensional elasticity analysis of a rotating annular disk","authors":"Marko V. Lubarda, Vlado A. Lubarda","doi":"10.1007/s00419-025-02896-3","DOIUrl":null,"url":null,"abstract":"<div><p>Novel stress-based derivations of three-dimensional elastic stress and displacement fields in an isotropic annular disk of uniform thickness, rotating around its axis of symmetry with constant angular speed, are presented, which complement other more involved derivations available in the literature. The first derivation is based on the direct integration of two partial differential equations for the sum and difference of the in-plane stresses, which are obtained by combining the equation of motion and the compatibility condition. In the second derivation the stresses are obtained by using a simple form of the stress function satisfying a first-order nonhomogeneous partial differential equation following from the Beltrami–Michell compatibility equations, which can be solved readily. The third derivation is based on Love’s stress function of axisymmetric three-dimensional elasticity, generalized to include a rotational inertia force. The resulting nonhomogeneous biharmonic partial differential equation is solved by two alternative methods of constructing its particular and complementary solution. The derived expression for Love’s function has not been reported in the literature before. The displacement-based derivation of elastic fields is also presented, including a construction of the corresponding Papkovich–Neuber potentials.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 8","pages":""},"PeriodicalIF":2.5000,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00419-025-02896-3.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive of Applied Mechanics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00419-025-02896-3","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
Novel stress-based derivations of three-dimensional elastic stress and displacement fields in an isotropic annular disk of uniform thickness, rotating around its axis of symmetry with constant angular speed, are presented, which complement other more involved derivations available in the literature. The first derivation is based on the direct integration of two partial differential equations for the sum and difference of the in-plane stresses, which are obtained by combining the equation of motion and the compatibility condition. In the second derivation the stresses are obtained by using a simple form of the stress function satisfying a first-order nonhomogeneous partial differential equation following from the Beltrami–Michell compatibility equations, which can be solved readily. The third derivation is based on Love’s stress function of axisymmetric three-dimensional elasticity, generalized to include a rotational inertia force. The resulting nonhomogeneous biharmonic partial differential equation is solved by two alternative methods of constructing its particular and complementary solution. The derived expression for Love’s function has not been reported in the literature before. The displacement-based derivation of elastic fields is also presented, including a construction of the corresponding Papkovich–Neuber potentials.
期刊介绍:
Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.