Abstract
The deformation and strength of generalized curved rods are examined in order to apply for the design of springs. The analysis by three-dimensional elasticity has considerable error because of neglecting the cross-sectional deformation. In this study, a rod is regared as one-dimensional Cosserat's continuum which has bending, torsional and axial rigidities.
Curvature and torsion which are connected with the principal axes are defined and strain energy is described by the variation of these values. Through the principle of virtual work, the fourth order simultaneous differential equations are derived as fundamental equations and the equations for the boundary conditions are also obtained.
In these approaches, we used the tensorial relation of differential geometry for the general curves. In the analysis, strain energy by the distortion and shearing deformation are not counted. Nonlinear terms are neglected and the analysis is based on the infinitesimal theory, but we think the finite deformation theory will be able to introduce on the line of this theory. Simple special cases are analyzed to verify above equations and analytical solutions are obtained in closed forms.
