Finite-element formulation of geometrically exact three-dimensional beam theories based on interpolation of strain measures

This paper presents a new finite element formulation of the ‘geometrically exact finite-strain beam theory’. The governing equations of the beam element are derived in which the strain vectors are the only unknown functions. The consistency condition that the equilibrium and the constitutive interna...

Full description

Saved in:
Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2003-01, Vol.192 (49), p.5209-5248
Main Authors: Zupan, D., Saje, M.
Format: Article
Language:English
Subjects:
Computational techniques
Exact sciences and technology
Finite-element and galerkin methods
Finite-element method
Fundamental areas of phenomenology (including applications)
Mathematical methods in physics
Non-linear beam theory
Physics
Rotational invariant
Solid mechanics
Static elasticity
Static elasticity (thermoelasticity...)
Strain measure
Structural and continuum mechanics
Three-dimensional rotation
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:This paper presents a new finite element formulation of the ‘geometrically exact finite-strain beam theory’. The governing equations of the beam element are derived in which the strain vectors are the only unknown functions. The consistency condition that the equilibrium and the constitutive internal force and moment vectors are equal, is enforced to be satisfied at chosen points. The solution is found by a collocation algorithm. The linearity of the strain space not only simplifies the application of Newton’s method on the non-linear configuration space, but also leads to the strain-objectivity of the proposed method. The accuracy and the efficiency of the derived numerical algorithm are demonstrated by several examples.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2003.07.008