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Reduction of the degrees of freedom in solving dynamic problems by the finite element method
Author(s) -
Vysloukh V. A.,
Kandidov V. P.,
Chesnokov S. S.
Publication year - 1973
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620070208
Subject(s) - degrees of freedom (physics and chemistry) , finite element method , mass matrix , reduction (mathematics) , vibration , point (geometry) , mixed finite element method , matrix (chemical analysis) , mathematics , mathematical analysis , finite element limit analysis , element (criminal law) , extended finite element method , geometry , physics , structural engineering , engineering , materials science , quantum mechanics , neutrino , political science , nuclear physics , law , composite material
The method of lowering the order of a matrix equation which describes the dynamics of a finite element model is presented. The finite element with a ‘truncated’ mass matrix is obtained for calculating thin plate vibrations. Such an element has one vibrational degree of freedom at each nodal point. In the case of uniform systems the accuracy provided by the suggested element is no less than that provided by the non‐conforming elements, which have three vibrational degrees of freedom at each nodal point, and in some cases it is greater. The finite elements with a ‘truncated’ mass matrix have essential advantages in the study of non‐uniform systems.