The Research Of High Order Single Step Method And The Comparation Of Pseudo Dynamic Testing Methods

The high order single step method is the direct integral method for solving thedynamic equations, has the advantages of four order accuracy, unconditionally stable, and good algorithm damping properties.lt had been successfully applied in nonlinear seisimic response analysis,intelligent vibration controls and the dynamic response to analytic expression of stiffness.This thesis makes improvment to the high order single step method of linear and nonlinear dynamic equation,and makes comparative research of their application in pseudodynamic test.The main research contents and results are as follows:(1) This thesis makes two improvements on the high order single step method,derives the increment-order high order single step method integral formula and the increment-dimensional high order single step method integral formula. And makes the comparative research of the three two methods in algorithm characteristics.Research shows that:the The increment-order high order single step method has the characteristics of six order accuiacy,unconditionally stable,and good algorithm damping properties, its computational accruacy is significantly higher than the increment-dimensional high order single step method and the high order single step method.The increment-dimensional high order single step method is unconditionally stable algorithm,has the same theoretical accuracy with the high order single step method.(2) Based on the high order single step method for nonlinear dynamic equations when G=G(t),This thesis presents two solving methods for the nonlinear dynamic equations when G=G(Z,t):the prediction method and the nonlinear high order single step method.This thesis use examples to show the effectiveness of the two methods.The prediction method and the nonlinear high order single step method are all implicit method,they all need repeated correction and have the same amount of calculation,but accuracy and stability of the nonlinear high order single step method is slightly better than the prediction method They expand the scope of application of the high order single step method. (3) This thesis takes the high order single step method for the entrance,selects four another explicit numerical integration methods:the precise integration method,the central difference method,The explicit Newmark method and the double β parameter method,then makes numerical simulation analysis of pseudo dynamic test, compares the five kinds of pseudo dynamic testing method in accuracy and stability.The results show that:the high order single step method needs to calculate the shear stiffness in structural pseudo dynamic test,but the shear stiffness calculation error is too large,this causes structure happening displacement oscillation phenomenon in the nonlinear stage,so accuracy and stability of the high order single step method are not good.the accuracy and stability of precise integration method are good,so the structural system whose stiffness and free degree number are not big can choose precise integration method to meet the accuracy requirements.The double β parameter method is a unconditionally stable algorithm,it shows good stability even in nonlinear example,so the structural system whose stiffness and free degree number are big can choose double β parameter method to ensure its stablility.