An Energy-Conserving Time Integration Method for Co-Rotational Formulation Force-Based Beam Elements

In this paper, we develop an energy-conserving time integration method for the co-rotational formulation force-based beam elements, aiming to achieve unconditional stability in nonlinear dynamic analysis. The proposed method incorporates material and geometric nonlinearities, with geometric nonlinearity addressed through the co-rotational technique. To ensure energy conservation in the time-discrete system, restoring force corrections are applied to the material stress and geometric configuration. It is proved that the method achieves energy conservation for discrete systems, thereby ensuring unconditional stability in nonlinear analyses. Also, the proposed method is second-order in accuracy. Finally, the effectiveness of the proposed method is verified through three numerical examples. In particular, the simulations demonstrate that the iterations converge well at both the global structural and element levels, and the computation effort can be significantly reduced by selecting appropriate initial correction parameters. While the restoring force correction procedure increases computational costs, the method’s capacity for larger time integration steps maintains total computational cost at acceptable levels.