An efficient hybrid implicit time integration method with high accuracy for linear and nonlinear dynamics

Abstract

In this work, an effective hybrid implicit method is proposed to analyze linear and nonlinear dynamic problems. The proposed hybrid method is a type of three sub-step method and is unconditionally stable. New method has multiple free parameters which can be employed to control accuracy and numerical dissipation. The new method can obtain controllable numerical dissipation which ranges from the non-dissipative case to the asymptotic annihilating case. Meanwhile, high computation accuracy than classical sub-step methods can be obtained. The new method can obtain the identical effective stiffness matrix for three sub-steps to save computational cost and internal storage for linear cases. Verified by numerical examples, the new method has simple calculation procedure, and is efficient for linear dynamics. Especially for nonlinear dynamics, the new method shows high solution accuracy and excellent energy conservation performance when compared with other methods.