Contribution to new numerical integration in dynamics

Abstract

The problem of time integration in the dynamics of building structures is primarily a mathematical problem of the accuracy of the numerical integration of the acceleration time course. All existing methods are trying more or less successfully to master this problem. The best known and most widely used is the Newmark method, which by its very nature is only a trapezoidal rule applied to both acceleration and speed. The most effective method of numerical integration of repeated integrals was introduced mathematically [1], namely the modification of numerical integration methods of the Gaussian type for use on repeated integrals. In this work is introduced their simple use in problem solution of mechanics and dynamics of structures and consequently comparison of the results with the traditional Newmark Direct Time Integration method is presented.