A generalized Timoshenko beam with embedded rotation discontinuity

A novel generalized Timoshenko beam finite element with higher order shape functions is proposed to simulate structural failure. An embedded rotation discontinuity is adopted at the element level to describe the development of plastic hinges and crack opening. The material behaviour at the discontinuity is characterized by a discrete linear law linking the bending moment and the rotational jump, which allows capturing the released fracture energy. Outside the discontinuity, the behaviour is reproduced within the framework of elasto-plastic generalized standard materials. The generalized enhanced Timoshenko beam finite element, the variational formulation and the specific computational procedures are detailed. Numerical examples of a cantilever beam submitted to a rotation, to a transversal displacement and a two-storey reinforced concrete frame illustrate the capacity of the new beam formulation to regularize the results and to reproduce the structural behaviour up to failure.