ENERGY-CONSERVING TIME INTEGRATION METHOD FOR TIMOSHENKO BEAMS

An energy-conserving time integration method is proposed for the nonlinear dynamic analysis of Timoshenko beams. Co-rotational techniques are used to consider its structural geometric nonlinearity, and a linked interpolation form is adopted in the spatial discretization to avoid shear-locking phenomenon of a beam. The multi-parameter correction method is used to modify the equivalent nodal dynamic equations in the time discretization, which results in the energy conservation of the discrete system under conservative loading. The method has second-order local accuracy and shows better numerical stability, compared to the average acceleration method and the implicit midpoint method. The proposed method is compared to the Simo's method in two-dimensional cases and it is found that the Simo's method does not conserve system energy under a conservative external moment. Finally, the excellent performance and energy-conserving characteristic of the algorithm are verified by three numerical simulations.