The analog equation method for large deflection analysis of membranes. A boundary-only solution

Abstract

In this paper the analog equation method (AEM) is applied to nonlinear analysis of elastic membranes with arbitrary shape. In this case the transverse deflections influence the inplane stress resultants and the three partial differential equations governing the response of the membrane are coupled and nonlinear. The present formulation, being in terms of the three displacements components, permits the application of geometrical inplane boundary conditions. The membrane is prestressed either by prescribed boundary displacements or by tractions. Using the concept of the analog equation the three coupled nonlinear equations are replaced by three uncoupled Poisson's equations with fictitious sources under the same boundary conditions. Subsequently, the fictitious sources are established using a procedure based on BEM and the displacement components as well as the stress resultants are evaluated from their integral representations at any point of the membrane. Several membranes are analyzed which illustrate the method and demonstrate its efficiency and accuracy. Moreover, useful conclusions are drawn for the nonlinear response of the membranes. The method has all the advantages of the pure BEM, since the discretization and integration is limited only to the boundary.