A modified Newton-type Koiter-Newton method for tracing the geometrically nonlinear response of structures

Journal Article (2018)
Author(s)

K. Liang (Northwestern Polytechnical University)

M.M. Abdalla (TU Delft - Aerospace Structures & Computational Mechanics)

Qin Sun (Northwestern Polytechnical University)

Research Group
Aerospace Structures & Computational Mechanics
DOI related publication
https://doi.org/10.1002/nme.5709
More Info
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Publication Year
2018
Language
English
Research Group
Aerospace Structures & Computational Mechanics
Issue number
10
Volume number
113
Pages (from-to)
1541–1560

Abstract

The Koiter-Newton (KN) method is a combination of local multimode polynomial approximations inspired by Koiter's initial postbuckling theory and global corrections using the standard Newton method. In the original formulation, the local polynomial approximation, called a reduced-order model, is used to make significantly more accurate predictions compared to the standard linear prediction used in conjunction with Newton method. The correction to the exact equilibrium path relied exclusively on Newton-Raphson method using the full model. In this paper, we proposed a modified Newton-type KN method to trace the geometrically nonlinear response of structures. The developed predictor-corrector strategy is applied to each predicted solution of the reduced-order model. The reduced-order model can be used also in the correction phase, and the exact full nonlinear model is applied only to calculate force residuals. Remainder terms in both the displacement expansion and the reduced-order model are well considered and constantly updated during correction. The same augmented finite element model system is used for both the construction of the reduced-order model and the iterations for correction. Hence, the developed method can be seen as a particular modified Newton method with a constant iteration matrix over the single KN step. This significantly reduces the computational cost of the method. As a side product, the method has better error control, leading to more robust step size adaptation strategies. Numerical results demonstrate the effectiveness of the method in treating nonlinear buckling problems.

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