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Finite element modeling of Kirchhoff‐Love shells as smooth material surfaces
Author(s) -
Vetyukov Yu.
Publication year - 2014
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201200179
Subject(s) - surface (topology) , finite element method , convergence (economics) , simple (philosophy) , benchmark (surveying) , mathematical analysis , element (criminal law) , position (finance) , mathematics , geometry , boundary (topology) , scheme (mathematics) , field (mathematics) , range (aeronautics) , pure mathematics , structural engineering , materials science , engineering , geology , philosophy , epistemology , geodesy , finance , political science , law , economics , composite material , economic growth
We consider large deformations of curved thin shells in the framework of a classical Kirchhoff‐Love theory for material surfaces. The geometry of the element is approximated via the position vector and its derivatives with respect to the material coordinates at the four nodes, and C 1 continuity of the surface over the interfaces between the elements is guaranteed. Theoretical background provides certainty concerning the boundary conditions, the range of applicability of the model, extensions to multi‐field problems, etc. Robust convergence and accuracy of the resulting simple numerical scheme is demonstrated by the analysis of benchmark problems in comparison with other solutions.