Development of Direct Integration Algorithms for Structural Dynamics Using Discrete Control Theory

Abstract

In structural dynamics, integration algorithms are often used to obtain the solution of temporally discretized equations of motion at selected time steps. Various time integration algorithms have been developed in the time domain using different methods. In order for an integration algorithm to be reliable it must be stable and accurate. A discrete transfer function is used to study the properties of integration algorithms. A pole mapping rule from control theory in conjunction with a discrete transfer function is used to develop new integration algorithms for obtaining solutions to structural dynamics problems. A new explicit integration algorithm, called the CR (Chen and Ricles) algorithm, is subsequently developed based on the proposed method. The properties of the algorithm are investigated and compared with other well established algorithms such as the Newmark family of integration algorithms. By assigning proper stable poles to the discrete transfer function the newly developed CR explicit algorithm is unconditionally stable and has the same accuracy as the Newmark method with constant acceleration. In addition, the CR algorithm is based on expressions for displacement and velocity that are both explicit in form, making it an appealing integration algorithm for solving structural dynamics problems.