Thick‐plate flexure re‐examined

Abstract

Summary. The flexure of an incompressible, thick elastic plate floating on an inviscid substratum and subject to an external gravity field is re‐analysed. The solution is derived from momentum equations which account for the advection of hydrostatic pre‐stress. This is contrasted with a recently published thick‐plate solution derived from momentum equations without a pre‐stress term. It is demonstrated that neglecting pre‐stress advection renders the solution singular when the model degenerates into an inviscid half‐space. If pre‐stress advection is included, the solution remains correct in this limit. A numerical comparison of both types of thick‐plate solution with results based on conventional thin‐plate theory further shows that, for geophysically relevant models, the difference in the momentum balance entails discrepancies between the thick‐plate solutions which are comparable to the errors introduced by the thin‐plate approximation. Copyright © 1985, Wiley Blackwell. All rights reserved