A new model for thin plates with rapidly varying thickness. II. A convergence proof

Abstract

Our recent paper [6] presented a model for thin plates with rapidly varying thickness, distinguishing between thickness variation on a length scale longer than, on the order of, or shorter than the mean thickness. We review the model here, and identify the case of long scale thickness variation as an asymptotic limit of the intermediate case, where the scales are comparable. We then present a convergence theorem for the intermediate case, showing that the model correctly represents the solution of the equations of linear elasticity on the three-dimensional plate domain, asymptotically as the mean thickness tends to zero.