Stress-adapted numerical form finding of pre-stressed surfaces by the updatedreference strategy

In this paper we present the updated reference strategy for numerical formfinding of pre-stressed membranes, which is based on standard finite elementdiscretization. The singularities of the inverse problem are regularizedby a homotopy mapping. A projection scheme is proposed where anisotropicpre-stress is defined with respect to an additional reference plane, whichreflects the initially developable surface of membrane strips in the productionprocess. Physically problematic combinations of edge geometry and surfacestress are solved by a self-adaptive stress correction scheme. The algorithmis based on a local criterion derived from differential geometry. Severalexamples illustrate the success of each idea and implementation.     «

In this paper we present the updated reference strategy for numerical formfinding of pre-stressed membranes, which is based on standard finite elementdiscretization. The singularities of the inverse problem are regularizedby a homotopy mapping. A projection scheme is proposed where anisotropicpre-stress is defined with respect to an additional reference plane, whichreflects the initially developable surface of membrane strips in the productionprocess. Physically problematic combinations of edge...     »