Inelasticity-Separated Finite Element Method And Its Application In Seismic Response Analysis Of RC Structures

Engineering structures may undergo various kind of extreme environmental loads in the service period,and the earthquake generally causes severe damage and enormous losses.The nonlinear analysis method which is known as the most important way for investigating the disaster mechanism of structures has received increasing attention in recent years.With the development of the computer technique,the nonlinear analysis theory has made progress greatly and the refined simulation method which requires the use of microscopic models is becoming more and more popular.However,with the increase of the scale of the structures and the degree of the refinement,the degree of freedoms and the number of elements of the structural model increase rapidly such that the computational cost required for solving the linear system of equations in analysis can be increased significantly.Although there are many novel methods that have been developed for improving the computational efficiency in recent year,the lower efficiency of nonlinear analysis still limits its application.Therefore,the advanced nonlinear analysis theory that has the ability of both high speed computation and refined simulation is still needed in the field of structure engineering.In this paper,a new and efficient analysis method for material nonlinearity,which is called inelasticity-separated finite element method(IS-FEM),is proposed by separating the material strain and resorting to finite element theory.Then,the numerical characteristic of this method is investigated and some measures aiming to improve its computational performance are developed.Furthermore,an efficient seismic response analysis method for engineering structures and a novel inelasticity-separated modeling stratege for reinforced concrete(RC)frame structures are proposed successively within the framework of IS-FEM.Based on the above researches,this paper finally implements efficient seismic response analysis of RC frame structure and investigate the structural seismic performance.The detailed contexts of this paper are as follows:(1)By separating the material strain according to its initial elastic moduls,two new variables,linear elastic strain and inelastic strain,can be obtained and the separation is achieved in material level.The inelastic strain field of element is constructed through interpolation method.Then,the inelasticity-separated governing equation is constructed by using the principle of virtual work.The Woodbury formula is adopted to solve the governing equation efficiently and the corresponding iterative solution procedure is established to implement nonlinear analysis.In the proposed method,the use of the Woodbury formula can avoid the updating and factorization of global stiffness matrix in each iteration,which is the the most time consuming process in traditional method,and only require factorizing the Schur complement matrix with small dimension representing local nonlinearity.Thus,the computational efficiency can be improved greatly.Moreover,because the proposed method is developed on the basis of the fundamental theory of finite element method,it does not require using special type of element and thus have wide applicability.(2)The limitation of Woodbury formula is investigated by analyzing its numerical characteristic.It is indicated that the Schur complement matrix in Woodbury formula generally has no characteristic of sparseness and this results in the proposed IS-FEM only suitable for the case where the material nonlinearity only occur in some very local regions.When the scale of the nonlinearity regions is large,the IS-FEM may loses its advantage in efficiency.To overcome these limitations and extend the application of the proposed method,a series of improvement measures are developed.Firstly,the method for approximating the Schur complement matrix is proposed,thus reducing the computational cost requied for Woodbury formula remarkably.Subsequently,to minimize the error caused by the approximation,a method for modifying the approximate displacement which is helpful for accelerating the rate of iteration convergence and enhancing the stability of iteration is proposed and an adaptive iteration strategy is developed through evaluating the approximation error.The above improvements can make the IS-FEM being used for more-general situations where the nonlinearity may be not confined within local regions.(3)The Newmark-(3 method is adopted to integrate the equation of motion.Then,by considering the basic concept of inelasticity separation,the inelasticity-separated structural govering equation for dynamic problem,of which the matrix expression form is the same with that of the govering equation for static analysis,is established.To overcome the limitations in the selection of damping matrix and time step and improve the applicability of the proposed IS-FEM in dynamic response analysis,the methods that consider the initial elastic stiffness based Rayleigh damping and tangent stiffness based Rayleigh damping within the framework of IS-FEM respectively are developed,and the strategy for updating the time step adaptively during analysis is established by investigating the characteristic of earthquake waves.Based on these mearsures,a complete theoretical framework for implementing efficient seismic response analysis of engineering structures using IS-FEM is constructed.(4)An inelasticity-separated fiber beam-column element is proposed by investigating the relationship between the inelastic material stain and the inelastic section deformation and modeling the inelastic section deformation field using interpolation scheme.Meanwhile,an improve section inelastic state judgment process and a modified Kent-Park concrete material consititutive model are developed to reduce the number of inelastic degree of freedom(IDOF)when applying this type of element to implementing the seismic response analysis of RC frame structures.Moreover,to consider the effect of beam-column joints in analysis,the local plastic mechanism for depicting the concentrated rotational deformation in the beam ends caused by the bond slip of longitudinal bars is established and an inelasticity-separated shear panel element for modeling the shear deformation of joint core is developed,respectively.Based on the above elements,the inelasticity-separated analystical model of RC frame structures that consider the effect of joint can be constructed.The proposed analystical model can be used to implement accurate and efficient seismic response analysis of RC frame structures and to perform comprehensive and reliable seismic performance evaluation for such kind of structrual system.