A study of finite element spaces of uniform bars in free axial or torsional vibration from the viewpoint of bracketing of eigenvalues by ultimate and initial enforcement of bounds
✍ Scribed by E. Dokumaci
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 865 KB
- Volume
- 112
- Category
- Article
- ISSN
- 0022-460X
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✦ Synopsis
This paper introduces the notions of ultimately true and practically true upper and lower bound elements with reference to two point boundary elements. Explicit criteria are presented for the formulation of two point boundary elements which are ultimately true upper or lower bound elements on uniform finite element meshes. It is shown that element space models which are based on refined displacement or dynamic discrctization models are ultimately true lower bound elements if the space parameter is positive. The idea of initial enforcement of lower bounds is introduced for such elements as a device for assigning a specific numerical value to the space parameter. The form of the initial bound criterion, which is determined by the free-free or fixed-fixed element eigenvalues, suggests its use for the formulation of practically true lower bound elements. The extension of this criterion to more complicated elements is discussed.