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Some Two‐Field Variational Principles for Nonlinear Deformation Analysis of Shells
Author(s) -
Gass N.
Publication year - 1975
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.19750550907
Subject(s) - compatibility (geochemistry) , variational principle , nonlinear system , finite element method , displacement field , deflection (physics) , plane stress , stress field , mathematics , plane (geometry) , mathematical analysis , structural engineering , geometry , classical mechanics , physics , engineering , quantum mechanics , chemical engineering
Some two‐field variational principles for nonlinear deflection analysis are formulated. Based on a specific mixed variational principle, a rectangular finite element model has been developed. The variables employed are the out of plane displacement and a stress function. The former satisfies out of plane compatibility requirements of the element, while the latter ensures the equilibrium of the in‐plane stresses. The efficiency of this method is illustrated on two examples.