Efficient dynamic formulation for corotational 2D beams

摘要

The corotational finite element approach is a well known method to develop nonlinear beam elements in case of large displacements and small deformations. Many authors used this method to investigate the nonlinear dynamic analysis of planar beams. Nevertheless, concerning the derivation of the inertia terms, most of the approaches found in the literature adopted either a lumped mass matrix or linear local interpolations (which gives the classical linear and constant Timoshenko mass matrix), although local cubic interpolations were used to derive the elastic force vector and tangent stiffness matrix. In this paper, a new corotational formulation for dynamic nonlinear analysis is presented. Cubic interpolations are used to derive both the inertia and elastic terms. Several examples of elastic beam with large displacements show that the proposed approach is more efficient than using classical mass matrices found in literature.