Open AccessNonlinear deformation of a solid body on the basis of flow theory and realization of FEM in mixed formulation
Author(s) -
Н. А. Гуреева,
Р З Киселева,
А. П. Николаев
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/675/1/012059
Subject(s) - curvilinear coordinates , hexahedron , finite element method , deformation (meteorology) , mixed finite element method , body force , realization (probability) , mathematics , work (physics) , stress (linguistics) , flow (mathematics) , nonlinear system , matrix (chemical analysis) , coordinate system , mathematical analysis , geometry , mechanics , structural engineering , physics , materials science , engineering , mechanical engineering , linguistics , statistics , philosophy , quantum mechanics , meteorology , composite material
In the mixed formulation, an algorithm for the formation of a hexahedral finite element deformation matrix at the loading step to determine the stress-strain state of a solid body beyond the elastic limit based on the theory of plastic flow is developed in a curvilinear coordinate system. Stresses and displacements are taken as nodal unknowns. The approximation of the required values of the inner point of the finite element through the nodal unknowns was carried out by trilinear functions. To obtain the deformation matrix of the hexahedral finite element, a mixed functional on the equality of the real and possible works of external and internal forces with the replacement of the actual work of internal forces by the difference of the total and additional work of internal forces at the loading step is used.