Hyper-reduced arc-length algorithm for stability analysis in elastoplasticity

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:208

Article

Launay, H.¹  Besson, J.¹  Ryckelynck, D.¹  Willot, F.^1,2 

[1] PSL Res Univ, Ctr Mat, CNRS, MINES ParisTech,UMR 7633, F-91003 Evry, France

[2] Ctr Morphol Math, F-77300 Fontainebleau, France

关键词: Model order reduction;    Hyper-reduction;    Reduced integration domain;    Crisfield algorithm;    POD;    Plastic instability;    Buckling;    Limit load;   

DOI  :  10.1016/j.ijsolstr.2020.10.014

来源: Elsevier

【 摘 要 】

In this article an hyper-reduced scheme for the Crisfield's algorithm (Crisfield, 1981) applied to buckling simulations and plastic instabilities is presented. The two linear systems and the ellipse equation entering the algorithm are projected on a reduced space and solved in a reduced integration domain, resulting in a system of hyper-reduced equations. Use is made of the Gappy proper orthogonal decomposition to recover stresses outside the reduced integration domain. Various methods are proposed to construct a reduced bases, making use of simulation data obtained with standard finite element method and a stress-based error criterion for the hyper reduced calculations is proposed. A greedy algorithm coupled with this error criterion is used to generate intelligently full standard finite element simulations and enrich the reduced base, demonstrating the adequacy of the error criterion. Finally, numerical results pertaining to elastoplastic structures undergoing finite strains, with emphasis on buckling and limit load predictions are presented. A parametric study on the geometry of the structure is carried out in order to determine the domain of validity of the proposed hyper-reduced modeling approach. (C) 2020 Elsevier Ltd. All rights reserved.

【 授权许可】

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