3D-Membrantheorie

3D Membrane Theory.

For the force equilibrium of membrane structures only inner tensile normal stresses and shear stresses tangential to the membrane surface can be considered. For load that acts in out-of-membrane-plane direction membranes with small curvature appropriately show only small stiffness. By application of the principle of virtual displacement a consistent finite element discretization is presented that allows an approximate determination of membrane displacement and membrane stress state. The presented computational approach is analyzed for the applied element type and is applied to a hypar membrane exposed to work load as well as to a spinnaker membrane exposed to horizontal load.