An energy conservation algorithm for numerically solving nonlinear multidegree-of-freedom\nMDOF dynamic equations is proposed. Firstly, by Taylor expansion and Duhamel integration,\nan integral iteration formula for numerically solving the nonlinear problems can be achieved.\nHowever, this formula still includes a parameter that is to be determined. Secondly, through\nsome mathematical manipulations, the original dynamical equation can be further converted into\nan energy conservation equation which can then be used to determine the unknown parameter.\nFinally, an accurate numerical result for the nonlinear problem is achieved by substituting this\nparameter into the integral iteration formula. Several examples are used to compare the current\nmethod with the well-known Runge-Kutta method. They all show that the energy conservation\nalgorithm introduced in this study can eliminate algorithm damping inherent in the Runge-Kutta\nalgorithm and also has better stability for large integral steps.
Loading....