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Dual-energy extension of the uniform-approximation approach

Schneider, P. and Kienzler, R. (2019):
Dual-energy extension of the uniform-approximation approach.
In: PAMM — Proceedings in Applied Mathematics and Mechanics, 19 (1), Wiley, pp. e201900222, ISSN 1617-7061,
DOI: 10.1002/pamm.201900222,
[Online-Edition: https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.2019002...],
[Article]

Abstract

Abstract In the talk an extension of the uniform-approximation approach, that relies on the truncation of the elastic energy after a certain power of a geometric scaling factor, towards an analogous truncation of the dual energy is proposed. On the one hand, this allows for a derivation of fully defined boundary value problems including compatible displacement boundary conditions. On the other hand, the extension enables us to provide an a priori error estimate for the systematic error of the arising approximative models with respect to the exact three-dimensional solution. The approach is compared to the approach of a fixed kinematic assumption for the displacement field which is widely used in engineering. We show that the later approach leads in general to a more complex model for a comparable approximation accuracy so that the consistent approximation approach is to prefer.

Item Type: Article
Erschienen: 2019
Creators: Schneider, P. and Kienzler, R.
Title: Dual-energy extension of the uniform-approximation approach
Language: English
Abstract:

Abstract In the talk an extension of the uniform-approximation approach, that relies on the truncation of the elastic energy after a certain power of a geometric scaling factor, towards an analogous truncation of the dual energy is proposed. On the one hand, this allows for a derivation of fully defined boundary value problems including compatible displacement boundary conditions. On the other hand, the extension enables us to provide an a priori error estimate for the systematic error of the arising approximative models with respect to the exact three-dimensional solution. The approach is compared to the approach of a fixed kinematic assumption for the displacement field which is widely used in engineering. We show that the later approach leads in general to a more complex model for a comparable approximation accuracy so that the consistent approximation approach is to prefer.

Journal or Publication Title: PAMM — Proceedings in Applied Mathematics and Mechanics
Volume: 19
Number: 1
Publisher: Wiley
Divisions: 16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Institute for Lightweight Construction and Design (KluB)
Date Deposited: 21 Nov 2019 12:07
DOI: 10.1002/pamm.201900222
Official URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.2019002...
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