Comparison between recent implicit time integration methods with frequency dissipation for nonlinear structural applications

The present paper aims to test recent (Truly self-starting two sub-step method and three-parameter single-step implicit method) and classical (Generalized-α, HHT - α, and WBZ - α methods) time integration methods using the geometrically nonlinear Positional Finite Element Method (PFEM). The numerical formulation is based on the total Lagrangian approach and uses the Hessian matrix to obtain the response. The mixed hardening inelastic model applied to PFEM is also presented. Two examples validate the time integration algorithms and the inelastic model. In the first example, the mixed hardening inelastic model is compared with the the bilinear stress-strain model and the elastic-perfectly plastic hinge model, and aspects such as amplitude decay and period elongation are discussed. In the second example, the implemented algorithms are verified in a severe geometrically nonlinear example, considering the influence of numerical dissipation, time interval, and the number of elements in the response. Results show the relevance of numerical damping for numerical stabilization and the good performance of the Generalized-α algorithm.