Large deflection analysis of elastic space membranes

In this paper a solution to the problem of elastic space (initially non-flat) membranes is presented. A new formulation of the governing differential equations is presented in terms of the displacements in the Cartesian co-ordinates. The reference surface of the membrane is the minimal surface. The problem is solved by direct integration of the differential equations using the analogue equation method (AEM). According to this method the three coupled non-linear partial differential equations with variable coefficients are replaced with three uncoupled equivalent linear flat membrane equations (Poisson’s equations) subjected to unknown sources under the same boundary conditions. Subsequently, the unknown sources are established using a procedure based on the BEM. The displacements as well as the stress resultants are evaluated at any point of the membrane from their integral representations of the solution of the substitute problems, which are used as mathematical formulae. Several membranes are analysed which illustrate the method and demonstrate its efficiency and accuracy as compared with analytical and existing numerical methods