A new dual-explicit model-based integration method with flexible and controllable numerical dissipation for linear and nonlinear structural dynamics

The dual-explicit model-based integration schemes are unconditionally stable and explicit for both velocity and displacement. This study develops a new dual-explicit model-based integration method with flexible and controllable numerical dissipation for linear and nonlinear dynamics. The new integration method adopts straightforward explicit formulations of velocity and displacement, and does not require a supplementary weighted equation of motion. By matching the eigenvalues of the amplification matrix of the recently proposed rho infinity-Bathe integration scheme, the integration parameters of the new integration scheme are derived. The numerical properties including the stability, convergence rate, period elongation, amplitude decay, and overshooting of the new method are comprehensively analyzed. The results indicate that the new integration scheme maintains second-order accuracy and unconditional stability for linear and nonlinear stiffness softening systems. Compared with several dissipative model-based integration schemes, the proposed method has larger numerical dissipations, which are flexibly controlled by two coefficients. Finally, four numerical examples are adopted to verify the capacity of the new integration method in the numerical dissipation of suppressing the spurious high-frequency response and the computational efficiency of solving linear and nonlinear structural dynamic problems.