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

Dejan Zupan in Miran Saje (2003) The three-dimensional beam theory: Finite element formulation based on curvature. Computers & Structures, 81 (18-19). str. 1875-1888. ISSN 00457949

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article introduces a new finite element formulation of the three-dimensional `geometrically exact finite-strain beam theory'. 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 Newton'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. (C) 2003 Civil-Comp Ltd. and Elsevier Ltd. All rights reserved.

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