The goal of this thesis is to implement a finite element-based code for the geometrically non- linear structural analysis and form finding of tensile structures in MATLAB. Already existing Python and MATLAB scripts allow the import and export of geometries from or to the CAD software Rhinoceros 3D. Furthermore, a special focus of this thesis lies on the design and analysis of multi-layer ETFE cushions and the interaction of enclosed pressure loads and their surrounding membranes. Taking the slenderness of membrane structures and the resulting specific mechanical behavior into account opportune simplifications can be made to their continuum mechanical description. Based on these simplifications the governing equations for the structural analysis and form finding are derived in a variational form and are imple- mented for triangular and quadrilateral plane stress elements as well as one-dimensional cable elements. The non-linear governing equations are then linearized and solved with the Newton-Raphson method. A linearization of the external virtual work components of the en- closed gas pressure and in particular the linearization of the Poisson’s law result in a fully populated system stiffness matrix, by which all degrees of freedom of a gas chamber are linked to on another. The Poisson law is regarded the constitutive equation of an enclosed gas. The Updated Reference Strategy, which was introduced by [BR99] is classified as homotopy method in a mathematical sense, is implemented to solve the inverse problem, while its appli- cation in this thesis is restricted to a solution of the related problem formulation. Additionally, the projection scheme introduced in [WB05] is used to prescribe anisotropic pre-stress con- ditions to a geometry by employing a developable reference surface. Finally, the implemented methods are extensively tested and compared to analytical bench- mark results, results of established finite element programs and are assessed regarding their plausibility. All analytical solutions of problems in the geometrical linear and non-linear do- main, not considering the pressure-volume coupling, are matched within the range of accu- racy inherent to approximative methods like the finite element method. The verification of the form finding module is predominantly conducted using well-known (analytic) solutions of min- imal surfaces, and for all tests the correct results are obtained. The accuracy of the pressure- volume coupling is investigated in three stages. In the first stage the pressure equalization in two neighboring chambers is successfully demonstrated. Next the structural response of a three-layer cushion under wind load is assessed regarding its plausibility. The observations partially meet the expectations. While the displacements of the different layers are correct regarding the order of magnitude, the absolute displacement values of the unloaded layers seem to be too small. This questionable structure response is also seen in a third test, where a two-layer cushion under wind suction deforms notably different in a comparative simulation with an established FE software.     «

The goal of this thesis is to implement a finite element-based code for the geometrically non- linear structural analysis and form finding of tensile structures in MATLAB. Already existing Python and MATLAB scripts allow the import and export of geometries from or to the CAD software Rhinoceros 3D. Furthermore, a special focus of this thesis lies on the design and analysis of multi-layer ETFE cushions and the interaction of enclosed pressure loads and their surrounding membranes. Taking the...     »