Análise dinâmica de estruturas: propriedades numéricas e comparação de métodos de integração direta no tempo

Abstract

This work describes in an extensive and grouped way the main numerical properties of direct time integration algorithms and their evaluation methods: convergence, consistency, stability, overshoot and computacional cost. It also presents and compares two direct time integration methods developed in the last decade. Both methods chosen have second-order accuracy, unconditional stability, control of spurious high frequencies with the definition of only one parameter by the user, are easy to implement and have a similar computacional cost per time step. The main differences between the methods lies in the fact that the first uses two sub-steps per time step, while the second does not use sub-steps, in addition to the differences in the accuracy of each methodology. The comparison of the methods under study is carried out through the implementation and application of three numerical examples of structural dynamics, where the numerical results obtained can be evaluated and compared according to the selected control parameter.