Evaluation of high order single-step integrators for structural response calculation

Abstract

Implicit, single-step integration methods which are absolutely stable and have fourth and sixth order accuracy are applied to linear structural dynamics equations. Test cases for which the discretized problems are solvable exactly are employed to determine the number of floating point operations needed to achieve specified accuracy levels. Examples involving longitudinal vibration of a bar and flexural vibration of a simply supported beam subjected to harmonic and impact loading are analyzed. The central concern in this paper is efficiently to integrate a discretized system which may have been derived by using finite element or finite difference methods. It is found that high order methods may permit sufficiently increased integration step size to reduce by a factor as high as six the total computation effort needed to achieve similar accuracy from traditional lower order methods.