Reply to comments by Robert P. Comer

Abstract

In his letter, Comer (1986) addresses three different points whch bear on three related publications on load-induced flexure of elastic plates (Comer 1983; Ward 1984; Wolf 1985a). As his first point is primarily an annotation to his own publication on the subject (Comer 1983), I will restrict my reply to the remaining two points. Comer’s (1986) second criticism refers to my statement on similarity (Wolf 1985a, p. 27 1). If the sentence under discussion has been construed to state that geometrical similarity between two otherwise identical plate models implies their physicaZ similarity, this represents a misinterpretation. Clearly, non-dimensional analysis of elastic-plate flexure cannot be formulated in terms of a geometrical scale-length (see, e.g. Wolf 1984). My statement therefore purports to draw attention to something different: I expect the accuracy of thin-plate theory to be comparable for two models provided that the ratios between horizontal load dimension and plate thickness are comparable. This is obviously not completely supported by Comer’s (1983) results (see his fig. 3). Inspection of fig. 2 in Wolf (1 985a), however, illustrates that neglecting pre-stress in thick-plate theory overestimates the response. More specifically, the figure shows that the differences increase with horizontal load dimension and with plate thickness. As the linear scale of the model in Comer’s (1983) fig. 3(c) is larger than the scale of the model in fig. 3(a), I therefore conclude that including pre-stress in his thick-plate theory would reduce the relative discrepancies in fig. 3(c) by more than in fig. 3(a) so that they would become comparable. For further clarification, I calculate peak deflections for two geometrically similar models. In the first model, disc-load radius and elastic-plate thickness are 200 km; the second model is scaled down by a factor of four (the other parameters are as in Wolf 1985a). Compared with the response according to my thick-plate theory, the thin-plate deflection is reduced by 15 and 10 per cent, respectively. I am therefore entitled to denote the relative discrepancies as ‘similar’. Whereas this is a minor subtlety, Comer’s (1986) final comment on the relation between special and general solutions is of greater import. It is certainly legitimate to point out that