Direct computation of critical equilibrium states for spatial beams and frames

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 pr...

Full description

Saved in:
Bibliographic Details
Published in:International journal for numerical methods in engineering 2012-01, Vol.89 (2), p.135-153
Main Authors: Mäkinen, Jari, Kouhia, Reijo, Fedoroff, Alexis, Marjamäki, Heikki
Format: Article
Language:English
Subjects:
Algebra
critical points
equilibrium equations
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
geometrically exact kinematics
Linear and multilinear algebra, matrix theory
Mathematics
Newton'smethod
Physics
Reissner's beam model
rotation manifold
Sciences and techniques of general use
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.3233