Time-step constraints in transient coupled finite element analysis

In transient finite element analysis, reducing the time-step size improves the accuracy of the solution. However, a lower bound to the time-step size exists, below which the solution may exhibit spatial oscillations at the initial stages of the analysis. This numerical 'shock' problem may lead to accumulated errors in coupled analyses. To satisfy the non-oscillatory criterion, a novel analytical approach is presented in this paper to obtain the time-step constraints using the θ-method for the transient coupled analysis, including both heat conduction-convection and coupled consolidation analyses. The expressions of the minimum time-step size for heat conduction-convection problems with both linear and quadratic elements reduce to those applicable to heat conduction problems if the effect of heat convection is not taken into account. For coupled consolidation analysis, time-step constraints are obtained for three different types of elements, and the one for composite elements matches that in the literature. Finally, recommendations on how to handle the numerical 'shock' issues are suggested.