Fischer, P., Mergheim, J. and Steinmann, P. (2010) On the C1 continuous discretization of non-linear gradient elasticity: A comparison of NEM and FEM based on Bernstein-Bezier patches. International Journal for Numerical Methods in Engineering, 82(10), pp. 1282-1307. (doi: 10.1002/nme.2802)
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Abstract
In gradient elasticity, the appearance of strain gradients in the free energy density leads to the need of C1 continuous discretization m ethods. In the present work, the performances of C1 finite elements and the C1 Natural Element Method (NEM) are compared. The triangular Argyris and Hsieh-Clough-Tocher finite elements are reparametrized in terms of the Bernstein polynomials. The quadrilateral Bogner-Fox-Schmidt element is used in an isoparametric framework, for which a preprocessing algorithm is presented. Additionally, the C1-NEM is applied to non-linear gradient elasticity. Several numerical examples are analyzed to compare the convergence behavior of the different methods. It will be illustrated that the isoparametric elements and the NEM show a significantly better performance than the triangular elements.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Steinmann, Professor Paul |
| Authors: | Fischer, P., Mergheim, J., and Steinmann, P. |
| College/School: | College of Science and Engineering > School of Engineering > Infrastructure and Environment |
| Journal Name: | International Journal for Numerical Methods in Engineering |
| Publisher: | Wiley |
| ISSN: | 0029-5981 |
| ISSN (Online): | 1097-0207 |
| Related URLs: |
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