SINGLE STEP ALGORITHMS FOR DIRECT INTEGRATION OF EQUATIONS OF MOTION - A COMPARISON

Abstract

Dynamic analysis of structures for the evaluation of the timewise response can be conducted using direct integration of equations of motion or using mode superposition technique. A large "number of methods have been proposed in the past for direct, integration of equations of motion. In this thesis two general families of single step algorithms for direct integration are studied. In these algorithms the response at the end of the following time step (n+l) is related to the response evaluated at the end of the previous time step •(n). These differ from multistep algorithms in which in order to evaluate response at step n+l, response at steps n, n-1, n-2, etc., Is required. The two families studied are (a) Generalized Newmark algorithm (GN) emanating from the generalization of the Newmark method (b) Single Step algorithm due to Zienkiewicz, Wood and their coworkers. From these generalized forms a number of new and existing algorithms can be simulated. Stepwise procedure for SS and GN family of algorithms are developed in the predictor-corrector form. From these procedures Newmark's unconditionally stable algorithm, Houbolt .-(originally multistep) algorithm and Wilson 6 are simulated. It is seen that these general single step procedures offer possibilities of time step changes during the analysis. The predictor corrector form can be used with advantage in linear as well. as in nonlinear problems. Each family is seen to have advantages as well as • disadvantages over the other.