CAD-Integrated Form-Finding of Structural Membranes Using Extended Catmull–Clark Subdivision Surfaces

Abstract

Extended Catmull–Clark subdivision surfaces are implemented within a CAD-integrated analysis workflow for form-finding by using the updated reference strategy. In this context, form-finding determines the shape of a structure that is in equilibrium for a predefined stress state. Following the principles of isogeometric analysis, the geometry for the form-finding is described by the control mesh of the subdivision surface. Using the subdivision scheme, the coarse control mesh is recursively refined to a smooth limit surface. The shape functions are obtained from the refinement process by applying algorithmic differentiation to the subdivision algorithm. This approach also supports sharp features like creases and corners. In this way, the modeling functionalities of common CAD environments are covered which allows seamless integration of the analysis into the CAD system. A core-congruential element formulation enables the efficient combination of mechanical properties with different geometric discretizations. This allows an existing framework to be extended easily with subdivision surfaces. Within this work, form-finding is applied to prestressed cable and membrane structures. Weak boundary conditions allow the modeling of oriented edge supports. The CAD-integrated implementation within the framework of a visual programming language is outlined. Using selected numerical examples, the method is demonstrated and verified. • Form-finding of tensile structures based on extended Catmull–Clark surfaces. • FEM-based form-finding using the updated reference strategy. • Modular implementation within an interactive CAD-integrated IGA environment.