Non-linear exact geometry 12-node solid-shell element with three translational degrees of freedom per node

International Journal for Numerical Methods in EngineeringVolume 88, Issue 13 p. 1363-1389 Research Article Non-linear exact geometry 12-node solid-shell element with three translational degrees of freedom per node G. M. Kulikov, Corresponding Author G. M. Kulikov [email protected] Department of Applied Mathematics and Mechanics, Tambov State Technical University, Sovetskaya Street, 106, Tambov 392000, RussiaDepartment of Applied Mathematics and Mechanics, Tambov State Technical University, Sovetskaya Street, 106, Tambov 392000, RussiaSearch for more papers by this authorS. V. Plotnikova, S. V. Plotnikova Department of Applied Mathematics and Mechanics, Tambov State Technical University, Sovetskaya Street, 106, Tambov 392000, RussiaSearch for more papers by this author G. M. Kulikov, Corresponding Author G. M. Kulikov [email protected] Department of Applied Mathematics and Mechanics, Tambov State Technical University, Sovetskaya Street, 106, Tambov 392000, RussiaDepartment of Applied Mathematics and Mechanics, Tambov State Technical University, Sovetskaya Street, 106, Tambov 392000, RussiaSearch for more papers by this authorS. V. Plotnikova, S. V. Plotnikova Department of Applied Mathematics and Mechanics, Tambov State Technical University, Sovetskaya Street, 106, Tambov 392000, RussiaSearch for more papers by this author First published: 26 May 2011 https://doi.org/10.1002/nme.3226Citations: 18Read the full textAboutPDF 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 presents the finite rotation exact geometry (EG) 12-node solid-shell element with 36 displacement degrees of freedom. The term 'EG' reflects the fact that coefficients of the first and second fundamental forms of the reference surface and Christoffel symbols are taken exactly at each element node. The finite element formulation developed is based on the 9-parameter shell model by employing a new concept of sampling surfaces (S-surfaces) inside the shell body. We introduce three S-surfaces, namely, bottom, middle and top, and choose nine displacements of these surfaces as fundamental shell unknowns. Such choice allows one to represent the finite rotation higher order EG solid-shell element formulation in a very compact form and to derive the strain–displacement relationships, which are objective, that is, invariant under arbitrarily large rigid-body shell motions in convected curvilinear coordinates. The tangent stiffness matrix is evaluated by using 3D analytical integration and the explicit presentation of this matrix is given. The latter is unusual for the non-linear EG shell element formulation. 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