Higher-Order Implicit Dynamic Time Integration Method

A general procedure is presented for the use of higher-order approximations of a system’s dynamic response using new time integration schemes. An implicit method is developed and presented that makes use of higher-order polynomial acceleration variations for multi-degree-of-freedom dynamic structural analyses. A variable $\theta$ is used to increase the stability and accuracy of the method. The relative merits and stability aspects of the method are described. The higher-order method is compared with two traditional implicit methods, the Wilson- $\theta$ Method and the Constant Average Acceleration Method of the Newmark family. The peak displacement percent difference and percent time difference to peak displacement are used to measure the accuracy of the methods when applied to a multi-degree-of-freedom frame problem.