Linearly Implicit Algorithm with Embedded Newton Iteration of Velocity and its Application in Nonlinear Dynamic Analysis of Structures

Abstract

With the application of energy dissipation and damping techniques such as viscous dampers and viscoelastic dampers in seismic engineering, dynamic equilibrium equations of overall structures involve nonlinear damping force. Therefore, numerical integration methods with explicit velocity expressions are more favorable. Based on the average acceleration method, a novel linearly implicit algorithm with explicit expression of velocity is proposed in which once Newton iteration is embedded. The stability of the proposed algorithm in solving equations of motion containing nonlinear restoring force and nonlinear damping force is analyzed using the root locus method. The nonlinear stability of the proposed algorithm is also examined using a single-degree-of-freedom shear-type structure. The dynamic response analysis of a three-storey shear structure model equipped with viscous dampers, a three-storey shear structure equipped with metal dampers, and an eight-storey planar frame structure, are carried to investigate the accuracy and stability of the proposed method with respect to the Chang method and the CR method. The results show that the proposed algorithm exhibits higher accuracy and finer stability for nonlinear dynamic problems.