Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 192, Issue 49-50, Pages 5209-5248Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2003.07.008
Keywords
non-linear beam theory; finite-element method; three-dimensional rotation; rotational invariant; strain measure
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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. (C) 2003 Elsevier B.V. All rights reserved.
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