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An eigenanalysis-based bifurcation indicator proposed in the framework of a reduced-order modeling technique for non-linear structural analysis |
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| Affiliation: | 1. Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology, Beijing 100094, China;2. Aerospace Structures and Computational Mechanics, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands;3. School of Engineering, University of Glasgow, Rankine Building, Oakfield Avenue, Glasgow G12 8LT, United Kingdom;1. Department of Mathematics G. Castelnuovo, Sapienza Roma University, Roma, Italy;2. In Unam Sapientiam, Roma, Italy;3. IAPS, Istituto Nazionale di Astrofisica INAF, Roma, Italy;4. IASF, Istituto Nazionale di Astrofisica INAF, Palermo, Italy;5. INFN, Sezione Roma1, Roma, Italy;1. SEMTE, Faculties of Mechanical and Aerospace Engineering, Arizona State University, 501 E. Tyler Mall, Tempe, AZ 85287-6106, United States;2. Universal Technology Corporation, 1270 North Fairfield Road, Dayton, OH 45432, United States |
| Abstract: | The Koiter–Newton method is a reduced order modeling technique which allows us to trace efficiently the entire equilibrium path of a non-linear structural analysis. In the framework of buckling the method is capable to handle snap-back and snap-through phenomena but may fail to predict reliably bifurcation branches along the equilibrium path. In this contribution we extend the original Koiter–Newton approach with a reliable and accurate bifurcation indicator which is based on an eigenanalysis of the reduced order tangent stiffness matrix. The proposed indicator has a negligible numerical effort since all computations refer to the reduced order model which is typically of very small dimension. The extension allows the identification of bifurcation points and a tracing of corresponding bifurcation branches in each sector of the equilibrium path. The performance of the method in terms of reliability, accuracy and computational effort is demonstrated with several examples. |
| Keywords: | Koiter–Newton method Bifurcation indicator Eigenanalysis Tangent stiffness Reduced order model |
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