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Direct computation of critical equilibrium states for spatial beams and frames
Author(s) -
Mäkinen Jari,
Kouhia Reijo,
Fedoroff Alexis,
Marjamäki Heikki
Publication year - 2011
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3233
Subject(s) - eigenvalues and eigenvectors , critical load , computation , mathematics , criticality , state variable , critical point (mathematics) , residual , mathematical analysis , stability (learning theory) , state (computer science) , physics , buckling , computer science , algorithm , quantum mechanics , machine learning , nuclear physics , thermodynamics
SUMMARY In this paper, explicit formulas for second order derivatives of the residual vector with respect to the state variables for a geometrically exact 3D beam element based on the Reissner's model are presented. These derivatives are required when a direct non‐linear stability eigenvalue problem is solved by the Newton's method. If the external load is parametrized by a single parameter, such an eigenvalue problem consists of solving the critical state variables, the eigenmode, and the critical load parameter from the equation system consisting of the equilibrium equations, the criticality condition, and some auxiliary conditions depending on the type of a critical point. Copyright ©2011 John Wiley & Sons, Ltd.