Nonlinear Absolute Nodal Coordinate Formulation of a Flexible Beam Considering Shear Effect

Nonlinear modeling of a flexible beam with large deformation was investigated. Absolute nodal cooridnate formulation is employed to describe the motion, and Lagrange equations of motion of a flexible beam are derived based on the geometric nonlinear theory. Different from the previous nonlinear formulation with Euler-Bernoulli assumption, the shear strain and transverse normal strain are taken into account. Computational example of a flexible pendulum with a tip mass is given to show the effects of the shear strain and transverse normal strain. The constant total energy verifies the correctness of the present formulation.