On the Theory of Rods. Part I. Derivations from the Three-Dimensional Equations.
Abstract
Starting with the three-dimensional theory of classical continuum mechanics, some aspects of both the nonlinear and the linear theories of elastic rods are discussed. Detailed attention is given to the derivation of constitutive equations for the linear isothermal theory of elastic rods of an isotropic material and of variable cross-section, deduced by an approximation procedure from the three-dimensional equations. Explicit linear constitutive relations are obtained for straight circular rods of non-uniform cross-section; the calculation is carried out (in terms of an approximate specific Gibbs free energy function) in four distinct parts, since the complete system of equations involved separate into those appropriate for extensional, torsional and two flexural modes of deformation. A system of displacement differential equations are derived for flexure of a beam of variable circular cross-section; they reduce to those of the Timoshenko beam theory when the radius of the cross-section is constant. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1973
- Accession Number
- AD0770047
Entities
People
- Alex E.S. Green
- M. L. Wenner
- Paul M. Naghdi
Organizations
- University of California, Berkeley