Form finding with dynamic relaxation and isogeometric membrane elements

A method for form finding with dynamic relaxation and Non-Uniform Rational B-Splines (NURBS) based isogeometric membrane elements has been implemented and studied regarding the influence of the discretization and element shape on the form finding. The procedure allows for rapid form finding since NURBS describe the curved geometry well and it is shown that the form-finding can be performed using a coarse mesh. However, to minimize the bending strain energy a fine mesh is needed. Using smaller elements is more advantageous than increasing the degree of the basis functions, keeping the number of integration points few and converging at a lesser number of iterations. Using isogeometric analysis (IGA) simplifies further studies since the form-found shape can be exactly represented with a shell element formulation. The method is suitable to be used in computer aided design environments such as Rhinoceros 3D during design stages, where the form finding can be evaluated together with other studies in a design context.