On a consistent theory, and variational formulation of finitely stretched and rotated 3-D space-curved beams
type: Item
instance of: scholarly article
title: On a consistent theory, and variational formulation of finitely stretched and rotated 3-D space-curved beams
zbMATH Open document ID: 0666.73015
DOI: 10.1007/BF00282411
published in: Computational Mechanics
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74G60
zbMATH DE Number: 4090908
zbMATH Keywords: finite rotations
zbMATH Keywords: finite strains
zbMATH Keywords: three-dimensional space-curved elastic beams
zbMATH Keywords: nonconservative type external distributed forces
zbMATH Keywords: moments
zbMATH Keywords: curvature
zbMATH Keywords: twist
zbMATH Keywords: transverse shear strains
zbMATH Keywords: consistent set of boundary conditions
zbMATH Keywords: General mixed variational principles
zbMATH Keywords: conservative-type external moments
zbMATH Keywords: momentum-balance conditions
zbMATH Keywords: incremental variational functionals
zbMATH Keywords: Total and Updated Lagrangian incremental finite element formulations
author: M. Iura
author: Satya N. Atluri
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4090908