A NEW FORMULATION OF FINITE DISPLACEMENT THEORY OF CURVED AND TWISTED RODS

The governing equations for the finite displacement beam theory are often formulated through the principle of virtual work by introducing the pertinent kinematic field with displacement components defined in terms of the coordinates fixed in space. However, this formulation can hardly be applied for the theory of space beam without any restrictions on the magnitude of displacements, since the kinematic field becomes highly nonlinear largely due to the finite rotations in space.This paper presents a new formulation which considerably simplifies the derivations through the principle of virtual work. By the formulation, the governing equations can be easily obtained even for the exact theory under beam assumptions.