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The three-dimensional beam theory: Finite element formulation based on curvature

✍ Scribed by D. Zupan; M. Saje

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
519 KB
Volume
81
Category
Article
ISSN
0045-7949

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✦ Synopsis

The article introduces a new finite element formulation of the three-dimensional Γ”geometrically exact finite-strain beam theoryΓ•. The formulation employs the generalized virtual work principle with the pseudo-curvature vector as the only unknown function. The solution of the governing equations is obtained by using a combined Galerkin-collocation algorithm. The collocation ensures that the equilibrium and the constitutive internal force and moment vectors are equal at a set of chosen discrete points. In NewtonΓ•s iteration special update procedures for the pseudo-curvature and rotational vectors have to be employed because of the non-linearity of the configuration space. The accuracy and the efficiency of the derived numerical algorithm are demonstrated by several examples.

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