PERFORMANCE OF THE HHT-α METHOD FOR THE SOLUTION OF NONLINEAR SYSTEMS

The HHT-α method previously developed shows favorable numerical dissipation, in addition to unconditional stability, in the solution of linear elastic systems. However, its performance in the solution of nonlinear systems has not been studied yet. In this paper, the numerical properties of a subfamily of this integration method with -⅓ ≤ α ≤ 0, β = ¼(1 - α)² and γ = ½-α for the solution of nonlinear systems are analytically explored using a linearized analysis, where the stiffness term in total form is used to determine the restoring force. A theoretical proof of unconditional stability for nonlinear systems is presented. The subfamily of the integration method is verified to possess favorable numerical dissipation for both linear and nonlinear systems. Period distortion affected by the step degree of either nonlinearity or convergence is studied. Although the analysis is conducted for a single-degree-of-freedom nonlinear system, the application to a multiple-degree-of-freedom nonlinear system is also illustrated. It is confirmed that the performance of the HHT-α method for nonlinear systems is generally the same as that for linear elastic systems, except for the high dependence on the step degree of nonlinearity.