NONLINEAR-THEORY FOR ELASTIC SPATIAL RODS

Starting with a three-dimensional non-linear formulation of elasticity and employing the variational procedure together with a suitable and proper strain and displacement field, general forms of kinematical relations, equilibrium equations, and a set of one-dimensional constitutive equations have been derived for spatial rods undergoing small finite deformations. These equations can be employed to study different types of spatial rod elements for different geometries, loading, and cross-sectional shapes. The formulations take account of the influence of the loading behavior, either conservative or non-conservative loading. The corresponding equations for the classical rod theory are extracted from the derived, general non-linear equations. © 1990.