Direct strain measure for large-deformation analyses of beam structures

A nonlinear kinematics called the direct strain measure is proposed for large deformation and finite rotation analyses of a two-node Timoshenko beam. The kinematics extracts pure elastic deformations without deriving any virtual frame to describe rigid body motion. Internal force and stiffness matrices are derived to constitute a Newton’s method for finding the solution. Computational results show that the present method is valid for Timoshenko beams whose relative angular displacement in an element is less than 0.5 rad.