Operator matrix and non-uniqueness of Beltrami–Schaefer stress functions
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- 作者：Yuan Wang (1) (2)
Jonny Rutqvist (2) - 刊名：Acta Mechanica
- 出版年：2014
- 出版时间：June 2014
- 年：2014
- 卷：225
- 期：6
- 页码：1761-1768
- 全文大小：
- 参考文献：1. Beltrami E.: Osservazioni sulla nota precedente. Atti Accad. Lincei Rend. Ser. 5 1, 141-42 (1892)
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3. Gurtin M.E.: A generalization of the Beltrami stress functions in continuum mechanics. Arch. Ration. Mech. Anal. 13, 321-29 (1963) CrossRef
4. Gurtin M.E.: The Linear Theory of Elasticity, Encyclopedia of Physics, Vol. VI a/2, Chief ed. S. Flugge. Springer, New York (1972)
5. Wang, Y., Rutqvist, J.: Non-uniqueness of Beltrami–Schaefer stress functions. J. Elast. 113(2), 283-88 (2013). doi:10.1007/s10659-012-9422-1
6. Wang M.Z., Xu B.X., Gao C.F.: Recent general solutions in linear elasticity and their applications. Appl. Mech. Rev. 61, 030803.1-30803.20 (2008) CrossRef
7. Rao C.R., Mitra S.K.: Generalized Inverse of Matrices and its Applications. Wiley Press, New York (1974) - 作者单位：Yuan Wang (1) (2)
Jonny Rutqvist (2)
1. Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, College of Civil and Transportation Engineering, Hohai University, Nanjing, 210098, China
2. Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA - ISSN：1619-6937
文摘
Beltrami–Schaefer stress functions are general solutions of the equilibrium equations of an elastic body without body force. In this paper, the representation of the non-uniqueness of these solutions is deduced by converting the equations into operator matrix form—including an operator matrix and its generalized inverse—and then deriving the representation using linear algebra. The completeness of the representation is proved in the process. In addition, the non-uniqueness of Helmholtz’s decomposition of a vector is proved.