On the berger approximation: a critical re-examination

Abstract

Since the first paper by Berger some two decades ago, the simplification known as the Berger approximation has been invoked by the authors of several score papers in spite of the fact that no rational mechanical basis for the approximation could be found. Many recent papers have raised doubts on its applicability. In this paper, using certain well known results from the two dimensional theory of elasticity, a plausible explanation for the origin of the Berger method is suggested. The arguments can be developed further to show that other specious Berger-like approximations can be developed, all of them leading to uncoupled non-linear equations yielding different overall results. Further, it is shown that such methods fail to predict the non-linear behaviour with respect to important parameters and that whatever accuracy is obtained in the solution of a particular problem can at best be attributed to fortuity.