A GEOMETRICALLY-EXACT ROD MODEL INCORPORATING SHEAR AND TORSION-WARPING DEFORMATION

A fully nonlinear, three-dimensional rod model is developed that incorporates transverse shear and torsion-warping deformation. The geometric setting is that of a constrained body model with configuration space modeled on R(3) x SO(3) x R: a differentiable manifold. The proposed model incorporates the classical notion of bi-moment (and bi-shear) in a fully nonlinear, geometrically exact context. Explicit. properly invariant. constitutive equations that generalize those of the linearized theory are developed. The underlying variational formulation of the model is discussed, and computational procedures employing a Galerkin projection arc addressed. Numerical examples are presented that illustrate the performance of the formulation.