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Notes on the stability of non‐rectangular space–time finite elements
Author(s) -
Bajer Czesław I.
Publication year - 1987
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.1620240909
Subject(s) - partition (number theory) , mathematics , spacetime , dimension (graph theory) , instability , finite element method , simple (philosophy) , stability (learning theory) , space time , space (punctuation) , mathematical analysis , partition of unity , computer science , engineering , structural engineering , physics , mechanics , philosophy , epistemology , quantum mechanics , combinatorics , machine learning , chemical engineering , pure mathematics , operating system
The method of space–time finite elements enables the simple solution of quite new problems. It is possible to assume the arbitrary partition of the structure area in each moment of integration of the motion equation. Instability is caused by a too large time step and too great changes of joint locations in successive time steps. A changeable spatial partition is useful in contact dynamic problems, in the case of a travelling support, generally in problems with movable edges. In this paper a stability problem is described and some investigations for chosen types of non‐rectangular space–time finite elements are carried out. Linear and surface elements which in time space gain an additional time dimension are presented. Some numerical examples prove the efficiency of the described method under determined limitations.