Advanced approaches for analysis and form finding of membrane structures with finite elements

Part I deals with material modelling of woven fabric membranes. Due to their structure of crossed yarns embedded in coating, woven fabric membranes are characterised by a highly nonlinear stress-strain behaviour. In order to determine an accurate structural response of membrane structures, a suitable description of the material behaviour is required. A linear elastic orthotropic model approach, which is current practice, only allows a relative coarse approximation of the material behaviour. The present work focuses on two different material approaches: A first approach becomes evident by focusing on the meso-scale. The inhomogeneous, however periodic structure of woven fabrics motivates for microstructural modelling. An established microstructural model is considered and enhanced with regard to the coating stiffness. Secondly, an anisotropic hyperelastic material model for woven fabric membranes is considered. By performing inverse processes of parameter identification, fits of the two different material models w.r.t. measured data from a common biaxial test are shown. The results of the inversely parametrised material models are compared and discussed. Part II presents an extended approach for a simultaneous form finding and cutting patterning computation of membrane structures. The approach is formulated as an optimisation problem in which both the geometries of the equilibrium and cutting patterning configuration are initially unknown. The design objectives are minimum deviations from prescribed stresses in warp and fill direction along with minimum shear deformation. The equilibrium equations are introduced into the optimisation problem as constraints. Additional design criteria can be formulated (for the geometry of seam lines etc.). Similar to the motivation for the Updated Reference Strategy [4] the described problem is singular in the tangent plane. In both the equilibrium and the cutting patterning configuration finite element nodes can move without changing stresses. Therefore, several approaches are presented to stabilise the algorithm. The overall result of the computation is a stressed equilibrium and an unstressed cutting patterning geometry. The interaction of both configurations is described in Total Lagrangian formulation. The microstructural model, which is focused in Part I, is applied. Based on this approach, information about fibre orientation as well as the ending of fibres at cutting edges are available. As a result, more accurate results can be computed compared to simpler approaches commonly used in practice