Nonlinear analysis of elastic space cable-supported membranes

In this paper a solution method is presented for the coupled problem of elastic flat or space membranes supported by elastic flexible cables. Both membrane and cable undergo large deflections. Starting from the minimal surface the membrane is prestressed by imposed boundary displacements under the self-weight. Then an iterative procedure is employed, which consists in solving the membrane and the cable large deflection problems separately in each iteration step and checking the continuity of displacements and forces between membrane and cable. The procedure is repeated until convergence is achieved. Both membrane and cable problems are solved using the analog equation method (AEM). The displacements as well as the stress resultants are evaluated at any point of the membrane and the cable from the integral representations of the solution of the analog equations, which are used as mathematical formulae. Example problems are presented, for both flat and space membranes, which illustrate the method and demonstrate its efficiency and accuracy.