A boundary element method for prediction of silo pressures

Abstract

Silos, as storage structures, often suffer structural failure in industrial operations. In most cases the occurrence of such failure is due to underestimating the pressure exerted by the stored materials on the silo walls. This paper presents a new numerical method for the prediction of the pressure. The method is based on the small displacement theory and the classical boundary integral equation for elastoplasticity problems. The bulk solids stored in the silos are assumed to yield according to the Drucker-Prager yield criterion, but permit no tension. Constitutive relations for such materials under different stress states are formulated. The contact boundary between the bulk material and the silo wall is classified into three different categories; within each category two out of four boundary variables are eliminated, either by specifying them in advance or relating them to the other two unknown variables. A boundary integral equation for such a problem is then deduced, and its numerical implementation is also presented. The method can be used to provide the wall pressures of a silo for the filling and the initial discharging conditions. The principal advantages of using this method over the finite element method are that the dimensionality of the problem is reduced by one, and iteration over the boundary fractional force is not required under certain conditions.