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Transient shell response by numerical time integration
Author(s) -
Krieg Raymond D.,
Key Samuel W.
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.1620070305
Subject(s) - mass matrix , diagonal , finite element method , matrix (chemical analysis) , transient (computer programming) , mathematics , main diagonal , differential (mechanical device) , diagonal matrix , numerical integration , element (criminal law) , mathematical analysis , computer science , structural engineering , geometry , engineering , physics , materials science , aerospace engineering , nuclear physics , law , political science , neutrino , composite material , operating system
In using the finite element method to compute a transient response, two choices must be made. First, some form of mass matrix must be decided upon. Either the consistent mass matrix prescribed by the finite element method can be employed or some form of diagonal mass matrix may be introduced. Secondly, some particular time integration procedure must be adopted. The procedures available divide themselves into two classes: the conditionally stable explicit schemes and the unconditionally or conditionally stable implicit schemes. The choices should be guided by both economy and accuracy. Using exact discrete solutions compared to the exact solutions of the differential equations, the results of these choices are displayed. Concrete examples of well‐matched methods, as well as ill‐matched methods, are identified and demonstrated. In particular, the diagonal mass matrix and the explicit central difference time integration method are shown to be a good combination in terms of accuracy and economy.