EXPLICIT IMPLICIT AND SEMI-IMPLICIT DIRECT TIME INTEGRATION SCHEMES FOR STRUCTURAL DYNAMIC PROBLEMS

Abstract

The study has been carried out for various direct step—by—step time integration schemes. In this thesis, the Newmark's Predictor—Corrector algorithm for explicit, implicit and combined implicit—explicit and Trijulld~s semi—implicit schemes are used for determining the dynamic response. Various numerical exampl—es are solved to iR.1ustrate the capabilities and effectiveness of these methods. The problem of spherical shell with and without the stiff element at the crown, dam reservoir foundation system are solved using finite element method and the dynamic response for various load condition are solved by Newmark's Predictor—Corrector algorithm of explicit, implicit and combined implicit—explicit schemes. Numerical experiments, are. carried out to workout the criteria of select- ing the Poisson's ratio keeping the bulk modulus constant to represent the reservoir water as an elastic solid having nearly zero shear stress. A program for evaluating the dynamic response using Trij,ullct~s semi—implicit schemes based on alternate splitt-ing has been developed which has been used to solve several problems. The response obtained by this method are compared with the closed form solution and other direct integration schemes. The numerical exas