The Analog Equation Method (AEM) is applied to non-linear analysis of heterogeneous anisotropic membranes with arbitrary shape. In this case, the response of the membrane is described by three coupled non-linear differential equations with variable coefficients. The present formulation, being in terms of the three displacements components, permits the application of geometrical in-plane boundary conditions. The membrane is prestressed either by prescribed boundary displacements or by tractions. Using the concept of the analog equation, the three coupled non-linear equations are replaced by three uncoupled Poisson's equations with fictitious sources under the same boundary conditions. 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 capabilities. Moreover, useful conclusions are drawn for the non-linear response of heterogeneous anisotropic membranes. The method has all the advantages of the pure BEM, since the discretization and integration are limited only to the boundary.
展开▼
