On the Theory of Rods. Part I. Derivations from the Three-Dimensional Equations.
CALIFORNIA UNIV BERKELEY DEPT OF MECHANICAL ENGINEERING
Pagination or Media Count:
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