A High Precision Direct Integration Scheme Based on Variational Principle and Its Applications

Abstract

Dynamics response of systems to impact or loading may be effectively treated by direct integration. However, it is often difficult to select the time-step of integration properly, especially in the case which the system is badly stiff. High Precision Direct integration based on variational principle is given (HPD-VP) for homogeneous systems and HHPD-VP method for the nonhomogeneous systems are given. This method not only takes the advantage of variational principle formula, which is much precise and is stiff A-stable, but also can avoid the truncation error of the computer. For the large systems, especially, the systems with different frequency or the stiff systems, our methods are stable, accurate and efficient. Numerical experiments show the convergence order of the scheme derived from the variational principle, and is much precise and is effective in engineering.