Newmark-based Linearly Implicit Numerical Integration Methods And Applications To Dynamic Analysis Of Structures With Damper

With the development of novel viscous liquid,viscoelastic materials and metal materials,new dampers with greater energy consumption and deformation capacity appear.This induces local nonlinear problems for structures with those types of dampers.For this kind of nonlinear problems,how to effectively improve the efficiency of numerical integration method without losing their accuracies and stabilities has become a problem that needs to be solved urgently.In order to improve computational efficiency,this paper proposes three linearly implicit numerical integration methods based on the strategy of Newton iteration,and studied their accuracies and stabilities,as well as their reliability for nonlinear problems.This paper mainly includes the following aspects:(1)Based on the average acceleration method in Newmark method,the strategy of Newton iteration is introduced.The acceleration term,velocity term and displacement term are used as iteration variables in the equation for one Newton iteration and three novel linearly implicit numerical integration methods are derived.The explicit schemes of velocity and displacement of the three algorithms are more practical and convenient for solving nonlinear equations of motion.(2)The essential differences and relations of the three new algorithms are explained by using Taylor expansion.Then,the stability of the three algorithms in solving the equations of motion with nonlinear restoring force and nonlinear damping force is compared and analyzed by using the root locus method.The stability criteria of the new algorithm of Newton iteration embedded in acceleration term in two kinds of common nonlinear problems are given,and the unconditional stability of the other two algorithms for nonlinear problems is proved.(3)Through the dynamic response analysis of the three-layer shear structure model with viscous damper,the stability and accuracy of the three algorithms are compared.The results show that compared with Chang method and CR method,the two algorithms based on Newton iteration embedded in acceleration term and velocity term show higher accuracy,while the algorithm based on Newton iteration embedded in displacement term has lower accuracy.(4)Through the dynamic response analysis of three-layer shear structure model and eight-layer plane frame structure with hysteretic damper,the stability and accuracy of the three algorithms are compared and analyzed.The results show that the three algorithms have good accuracy and stability,while the accuracy of Chang method and CR method are low.And the Chang method and CR method are occasionally unstable.(5)Through the dynamic response analysis of four-layer shear structure model with suspended mass pendulums,the stability and accuracy of the three algorithms are compared and analyzed.The results show that the two algorithms based on Newton iteration embedded in acceleration term and velocity term show higher accuracy.The accuracy of the algorithm based on Newton iteration embedded in displacement term is low,and the computation deviation of Chang method and CR method is larger.