Stochastic finite element method for elasto-plastic body

International Journal for Numerical Methods in EngineeringVolume 46, Issue 11 p. 1897-1916 Research Article Stochastic finite element method for elasto-plastic body Maciej Anders, Maciej Anders Earthquake Research Institute, The University of Tokyo, JapanSearch for more papers by this authorMuneo Hori, Corresponding Author Muneo Hori [email protected] Earthquake Research Institute, The University of Tokyo, JapanEarthquake Research Institute, The University of Tokyo, 1-1-1-Yayoi, Bunkyo, Tokyo 113-0032, JapanSearch for more papers by this author Maciej Anders, Maciej Anders Earthquake Research Institute, The University of Tokyo, JapanSearch for more papers by this authorMuneo Hori, Corresponding Author Muneo Hori [email protected] Earthquake Research Institute, The University of Tokyo, JapanEarthquake Research Institute, The University of Tokyo, 1-1-1-Yayoi, Bunkyo, Tokyo 113-0032, JapanSearch for more papers by this author First published: 09 November 1999 https://doi.org/10.1002/(SICI)1097-0207(19991220)46:11<1897::AID-NME758>3.0.CO;2-3Citations: 73AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract This paper proposes a Stochastic Finite Element Method (SFEM) for non-linear elasto-plastic bodies, as a generalization of the SFEM for linear elastic bodies developed by Ghanem and Spanos who applied the Karhunen–Loeve expansion and the polynomial chaos expansion for stochastic material properties and field variables, respectively. The key feature of the proposed SFEM is the introduction of two fictitious bodies whose behaviours provide upper and lower bounds for the mean of field variables. The two bounding bodies are rigorously obtained from a given distribution of material properties. The deformation of an ideal elasto-plastic body of the Huber–von Mises type is computed as an illustrative example. The results are compared with Monte-Carlo simulation. It is shown that the proposed SFEM can satisfactorily estimate means, variances and other probabilistic characteristics of field variables even when the body has a larger variance of the material properties. Copyright © 1999 John Wiley & Sons, Ltd. REFERENCES 1 Der Kiureghian A, Ke BJ. The stochastic finite element method in structural reliability. Journal of Probabilistic Engineering Mechanics 1988; 3(2): 83–91. 2 Liu PL, Der Kiureghian A. Finite element reliability of geometrically nonlinear uncertain structures. Journal of Engineering Mechanics ASCE 1991; 117(8): 1806–1825. 3 Hisada T, Nakagiri S. Stochastic finite element method developed for structural safety and reliability. Proceedings of the Third International Conference on Structural Safety and Reliability, Trondheim, Norway, 1981; 395–308. 4 Liu WK, Mani A, Belytschko T. Finite element methods in probabilistic mechanics. Journal of Probabilistic Engineering Mechanics 1987; 2(4): 201–213. 5 Yamazaki F, Shinozuka M. 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