Space Time Finite Elements and Dynamics

Abstract

<p>Variational methods using the least action principle are used to set up equations for the vibration of systems. Using variational methods, finite elements of structures can be formulated on the space time domain to allow calculation of transient vibratory response to initial conditions and forcing functions. This work attempts to systematize such formulations, discuss limitations in the methods, and compare the accuracy of the two simplest methods to conventional finite difference techniques. Examples are given for single degree of freedom systems, the stretched string, simply supported beam, and plate. No method superior to the Newmark ß method has been developed.</p>