Germain, S. and Steinmann, P. (2012) On a recursive algorithm for avoiding mesh distortion in inverse form finding. Journal of the Serbian Society for Computational Mechanics, 6(1), pp. 216-234.
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Abstract
A challenge in the design of functional parts is the determination of the initial, undeformed shape such that under a given load a part will obtain the desired deformed shape. A shape optimization formulation might be used to determine the initial shape in the sense of an inverse problem via successive iterations of a direct mechanical problem. In this paper, we present a shape optimization formulation for elastoplastic materials with a constitutive model for anisotropic additive elastoplasticity in the logarithmic strain space. A discrete sensitivity analysis is performed and gives the analytical gradient of the objective function needed in the optimization algorithm. We found that the use of the coordinates of the functional component as design variables led to mesh distortions. Without a split of the total force applied on the component and an update of the undeformed configuration between two steps the optimization algorithm is not able to find an appropriate minimum. Three numerical examples in isotropic and anisotropic elastoplasticity illustrate the structure of such a recursive algorithm for avoiding mesh distortions.
| Item Type: | Articles |
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| Additional Information: | s This work is supported by the German Research Foundation (DFG) within the Collaborative Research Centre SFB Transregio 73: ''Manufacturing of Complex Functional Components with Variants by Using a New Sheet Metal Forming Process - Sheet-Bulk Metal Forming''. |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Steinmann, Professor Paul |
| Authors: | Germain, S., and Steinmann, P. |
| College/School: | College of Science and Engineering > School of Engineering > Infrastructure and Environment |
| Journal Name: | Journal of the Serbian Society for Computational Mechanics |
| Publisher: | Serbian Society for Computational Mechanics |
| ISSN: | 1820-6530 |
| ISSN (Online): | 1820-6530 |
| Copyright Holders: | Copyright © 2012 The Authors |
| First Published: | First published in Journal of the Serbian Society for Computational Mechanics 6:216-234 |
| Publisher Policy: | Reproduced in accordance with the copyright policy of the publisher |
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