Error growth in transient large displacement calculations

Nonlinear problems are widely acknowledged as being more difficult to solve numerically than linear problems. Various kinds of errors contribute to this difficulty and in this paper some of these errors will be described and illustrated by solving certain large displacement problems using eight-noded isoparametric brick elements in space and an explicit integration method in time. First, approximation errors in time integration are illustrated, with violation of energy conservation being used as an indicator of the increased difficulties encountered in solving large displacement problems. Next, round-off errors and order of operations are discussed and illustrated for the case of a cube that is impulsively set in rotation about its centre of mass. Simple tests of invariance with respect to translation and rotation are shown to be interesting and potentially useful. Finally, approximation errors in spatial discretization, especially those associated with incomplete or inconsistent integration over the element volume, are illustrated for a large deflection beam problem.