Finite element formulation of spatially curved and twisted rods
For spatially curved and twisted rods a set of governing equations consisting of equilibrium equations and strain displacement and constitutive relations are derived in terms of three translational and three rotational degrees of freedom. By solving the strain displacement relations for constant and zero states of strain the rigid body and constant strain modes of the rod are obtained. These displacement modes are then used as basis functions for development of a finite element model. To verify the formulation and the elemental matrices, three examples are analyzed and in each case the computed results are compared with those obtained from a discrete model representation, using prismatic Timoshenko rod elements. It is found that the curved element, which is geometrically exact, yields more accurate results and it eliminates the jumps in some force quantities, caused by the indeterminacy of the normal (and or tangent, binormal), at the nodes.
three translational and three rotational degrees of freedom
scientific article; zbMATH DE number 4035328