Dispersion and Time Integration Schemes in Finite-Element Analysis — A Practical Pictorial Manual

Abstract

Using a simple physical model, i.e. propagation of stress waves in a thin elastic rod, we can show how the equivalent finite-element (FE) model can be treated by various methods (the central difference method, and the Newmark and Houbolt methods) to secure numerical integration in time and what differences, with respect to an ideal continuum model, can be expected. The FE histories of displacements, velocities, accelerations and strains, presented in pictorial form, are compared with those in an idealized elastic continuum. Differences due to time and space discretizations are shown and explained. Matlab programs are available at http://www.it.cas.cz/files/u1784/mtl.zip . Readers (especially novice finite-element users) are urged to modify the input parameters, observe the invoked changes and try to understand why and how they arise.