Finite Displacement Theory of Naturally Curved and Twisted Beams with Finite Rotations

Abstract

A finite rotation is not a quantity in a vector space. Various approaches, therefore, exist for evaluating the finite rotation. Euler angles [1–4], finite rotation tensors [5] and finite rotation vectors [6–8] have been employed as a measure for finite rotations. The exact finite displacement functions of beams have been derived in terms of the three translation and three rotation parameters. It is widely accepted, however, that four parameters are necessary and sufficient for formulating a beam theory under the Bernoulli-Euler hypotheses. When the number of parameters decreases from six to four, some approximations are introduced in the most of existing literature. Consequently, the most of existing equations are available only for the analyis of geometrically nonlinear behavior of beams with moderate rotations.