On completeness of shape functions for finite element analysis

✍ Scribed by Robert L. Taylor

• Publisher: John Wiley and Sons
• Year: 1972
• Tongue: English
• Weight: 302 KB
• Volume: 4
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620040105

✦ Synopsis

Some elements commonly used for analysis are examined for completeness of polynomial interpolation and computational efficiency. Extensions to n-dimensional space are shown to be natural consequences of the interpolation, thus all elements considered here allow for finite element approximation in higher than three-dimensional spaces (e.g. space-time interpolations). From the study it is concluded that 'serendipity' class elements form the most efficient elements up to third-degree polynomial approximations. The method used here to develop the serendipity shape functions allows for different orders of interpolation along each edge. Thus, in zones where high accuracy is required meshes can now be easily changed from linear to quadratic or higher-order elements. Computations on some simple problems have demonstrated this to be a superior method than using large numbers of low ordered elements.

* Hermitian-type elements are similar to the Lagrangian elements and are not explicitly discussed herein.