On a consistent theory, and variational formulation of finitely stretched and rotated 3-D space-curved beams
This paper deals with finite rotations, and finite strains of three- dimensional space-curved elastic beams, under the action of conservative as well as nonconservative type external distributed forces and moments. The plausible deformation hypothesis of ``plane sections remaining plane'' is invoked. Exact expressions for the curvature, twist, and transverse shear strains are given; as is a consistent set of boundary conditions. General mixed variational principles, corresponding to the stationarity of a functional with respect to the displacement vector, rotation tensor, stress-resultants, stress-couples, and their conjugate strain-measures, are stated for the case when conservative-type external moments act on the beam. The momentum-balance conditions arising out of these functionals, either coincide exactly with, or are equivalent to, those from the ``static method''. The incremental variational functionals, governing both the Total and Updated Lagrangian incremental finite element formulations, are given. An example of the case of the buckling of a beam subject to axial compression and non-conservative type axial twisting couple, is presented and discussed.
three-dimensional space-curved elastic beams
nonconservative type external distributed forces
Total and Updated Lagrangian incremental finite element formulations
scientific article; zbMATH DE number 4090908
scientific article