The accuracy and stability of time domain finite element solutions

The use of finite elements in the time domain provides a means of determining the response of a mechanical system to any forcing function. Two types of elements are used; a cubic element which maintains continuity of displacement and velocity between adjacent elements, and a quintic element which al...

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Bibliographic Details
Published in:Journal of sound and vibration 1978-12, Vol.61 (4), p.585-595
Main Authors: Howard, G.F., Penny, J.E.T.
Format: Article
Language:English
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Summary:The use of finite elements in the time domain provides a means of determining the response of a mechanical system to any forcing function. Two types of elements are used; a cubic element which maintains continuity of displacement and velocity between adjacent elements, and a quintic element which also ensures continuity of acceleration. The accuracy of solutions depends on the number of elements per unit time, errors being inversely proportional to the square of the number of elements for the cubic and inversely proportional to the fourth power of the number of elements for the quintic element. A condition for the stability of a solution is also established.
ISSN:0022-460X
1095-8568
DOI:10.1016/0022-460X(78)90457-1