The Koiter-Newton method had recently demonstrated a superior performance for nonlinear 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 postbuckling theory that 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.

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

Magisano, D.
Conceptualization
;
Garcea, G.
Methodology
;
Leonetti, L.
Validation
;
2018

Abstract

The Koiter-Newton method had recently demonstrated a superior performance for nonlinear 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 postbuckling theory that 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.
buckling; geometrically nonlinear analysis; mixed formulation; reduced-order model; solid-shell; Numerical Analysis; Engineering (all); Applied Mathematics
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Descrizione: This is the pre-peer reviewed version of the following article: [Magisano, D, Liang, K, Garcea, G, Leonetti, L, Ruess, M. An efficient mixed variational reduced-order model formulation for nonlinear analyses of elastic shells. Int J Numer Meth Engng. 2018; 113: 634– 655. https://doi.org/10.1002/nme.5629], which has been published in final form at [https://onlinelibrary.wiley.com/doi/10.1002/nme.5629]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. Source: Wiley
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/269430
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