A convex optimization approach for moderately large deflection problem in circular membranes

Membranes are a limiting case of the plates where the bending stiffness of the plate goes to zero. A variational formulation is obtained for the problem of moderately large deflections in circular membranes subjected to axisymmetric transverse loads and axisymmetric boundary conditions. For this variational formulation, unique stresses and displacements are shown to exist under quite general loading conditions. And, the variational formulation is cast as a constrained convex optimization problem. Furthermore, an algorithm for computing the stresses and a procedure for obtaining the displacements from the stresses is given.