Finite Difference Solution for Plate on Elastic Solid

Abstract

A new adaptation of an existing finite difference solution to the problem of a plate resting on an elastic solid foundation is introduced (program FIDIES). Square elements are employed throughout the slab, and external distributed loads are converted to point forces applied at the center of corresponding grid squares. Responses are calculated at the center of each plate element. Numerous convergence studies establish user guidelines with respect to required grid fineness. The accuracy of FIDIES is confirmed by comparison with closed‐form solutions, when available, an earlier finite difference solution, as well as these convergence studies. The effect of slab size is investigated for each of the three fundamental loading conditions, i.e., interior, edge, and corner. Predictive equations are derived for the latter two cases. These formulas, which were previously unavailable, highlight differences in behavior exhibited by the elastic solid and dense liquid subgrade idealizations.