Nonlinear Analysis Of Structures With Negative Stiffness Based On The Force Analogy Method

With the development of science and technology and the progress of building technology,the requirement of building function is increasingly higher.Especially,the use of large span structures and super high-rise structures is more and more widely used,which brings forward new requirements for the seismic resistance,anti-blast and impact resistance of building structures,but also puts forward higher requirements on the nonlinear structural analysis and design.In the nonlinear analysis,the structure usually enters the plastic state,and the cumulative damage occurs.At this time,the strength and stiffness of the structure are reduced,and the relationship between force and deformation is shown as the negative stiffness(or the decline).As the softening stage after the ultimate strength of the structure,the negative stiffness has an important influence on the bearing capacity and anti-collapse capacity of the structure,become the key process to track the cumulative damage and failure process of the structure under the environmental load,and is often used to test the performance of the numerical algorithm.At the present stage,the nonlinear analysis is the main method in the seismic analysis of building structures.However,with the increasing number of complex structures and high rise structures,it has a high demand for the existing computing methods,especially the requirements of computing hardware.The main reason is that the global stiffness matrix in the traditional calculation method becomes extremely huge and complex in the iterative solution process.In particular,when the structure enters the negative stiffness,the numerical calculation is often unstable and non convergent.However,the force analogy method(FAM)as a nonlinear calculation method,can avoid iteration and solving the global stiffness matrix of the structure,only need to update the local plastic matrix,thus,improving the computational efficiency.This paper carried out the following research work:(1)Reviews the development of the FAM,introduce the solution process of the FAM combined with a example.On the basis of the nonlinear analysis method of fiber beam in FAM,derives the nonlinear dynamic analysis of fiber beam model combining with the Newmark-? integral method.Compared with the traditional finite element method(ABAQUS),the accuracy and efficiency of the proposed method are verified by a numerical example.(2)This paper introduces the basic theory of the negative stiffness and the problems caused by it and analyzes the problem of the negative stiffness with the FAM and compares it with the traditional finite element method.(3)Introduces a constitutive model with strain softening of steel materials,by using the constitutive model,the numerical characteristics of the local plastic stiffness matrix are analyzed,and comparisons with those characteristics of the global stiffness matrix in the traditional method are done.The influence of negative stiffness on dynamic nonlinear analysis is studied by numerical examples.