An efficient mixed variational reduced order model formulation for non-linear analyses of elastic shells

Magisano, D., Liang, K., Garcea, G., Leonetti, L. and Ruess, M. (2018) An efficient mixed variational reduced order model formulation for non-linear analyses of elastic shells. International Journal for Numerical Methods in Engineering, 113(4), pp. 634-655. (doi: 10.1002/nme.5629)

Abstract

The Koiter-Newton method had recently demonstrated a superior performance for non-linear analyses of structures, compared to traditional path-following strategies. The method follows a predictor-corrector scheme to trace the entire equilibrium path. During a predictor step a reduced order model is constructed based on Koiter's asymptotic post-buckling theory which is followed by a Newton iteration in the corrector phase to regain the equilibrium of forces. In this manuscript, we introduce a robust mixed solid-shell formulation to further enhance the efficiency of stability analyses in various aspects. We show that a Hellinger-Reissner variational formulation facilitates the reduced order model construction omitting an expensive evaluation of the inherent fourth order derivatives of the strain energy. We demonstrate that extremely large step sizes with a reasonable out-of-balance residual can be obtained with substantial impact on the total number of steps needed to trace the complete equilibrium path. More importantly, the numerical effort of the corrector phase involving a Newton iteration of the full order model is drastically reduced thus revealing the true strength of the proposed formulation. We study a number of problems from engineering and compare the results to the conventional approach in order to highlight the gain in numerical efficiency for stability problems.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Ruess, Dr Martin
• Authors: Magisano, D., Liang, K., Garcea, G., Leonetti, L., and Ruess, M.
• 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
• Published Online: 25 July 2017
• Copyright Holders: Copyright © 2017 John Wiley and Sons Ltd
• First Published: First published in International Journal for Numerical Methods in Engineering 113(4): 634-655
• Publisher Policy: Reproduced in accordance with the publisher copyright policy