Equilibrium Consistent Anisotropic Stress Fields in Membrane Design Kai-Uwe Bletzingerl,Roland Wiichner2 and Fernass Daoud3 1 Lehrstuhl fuir Statik Technische Universitat Miinchen 80290 Miinchen,Germany kub@bv.tum.de 2 Lehrstuhl fiir Statik Technische Universitat Miinchen 80290 Miinchen,Germany wuechner@bv.tum.de 3 Lehrstuhl fuir Statik Technische Universitat Miinchen 80290 Miinchen,Germany daoud@bv.tum.de Key words:form finding,anisotropic surface stress,minimal surface,mesh control. Abstract.This paper deals with the control of mesh distortions which may appear during the form finding procedure of membrane design.The reason is the unbalance of surface stresses either due to the interaction of edge and sur- face or incompatibilities along the sewing lines of adjacent membrane patches. An approach is presented which is based on a rational modification of the surface tension field.The criterion is based on the control of the element dis- tortion and derived from differential geometry.Several examples demonstrate the success of the method. 1 Introduction Two different lines of research have developed which deal with the generation of structural shapes:the fields of "form finding"and "structural optimiza- tion",respectively.The methods of form finding are usually restricted to tensile structures(cables and membranes)whereas the methods of structural optimization are far more general and can usually be applied to any kind of structure.So far,The differences of the two approaches are not only the level 143 E.Onate and B.Kroplin (eds.).Textile Composites and Inflatable Structures,143-151. C 2005 Springer.Printed in the Netherlands.Equilibrium Consistent Anisotropic Stress Fields in Membrane Design Kai-Uwe Bletzinger1, Roland W¨uchner ¨ 2 and Fernass Daoud3 1 Lehrstuhl fur Statik ¨ Technische Universit¨at M¨unchen ¨ 80290 Munchen, Germany ¨ kub@bv.tum.de 2 Lehrstuhl fur Statik ¨ Technische Universit¨at M¨unchen ¨ 80290 Munchen, Germany ¨ wuechner@bv.tum.de 3 Lehrstuhl fur Statik ¨ Technische Universit¨at M¨unchen ¨ 80290 Munchen, Germany ¨ daoud@bv.tum.de Key words: form finding, anisotropic surface stress, minimal surface, mesh control. Abstract. This paper deals with the control of mesh distortions which may appear during the form finding procedure of membrane design. The reason is the unbalance of surface stresses either due to the interaction of edge and sur￾face or incompatibilities along the sewing lines of adjacent membrane patches. An approach is presented which is based on a rational modification of the surface tension field. The criterion is based on the control of the element dis￾tortion and derived from differential geometry. Several examples demonstrate the success of the method. 1 Introduction Two different lines of research have developed which deal with the generation of structural shapes: the fields of ”form finding” and ”structural optimiza￾tion” , respectively. The methods of form finding are usually restricted to tensile structures (cables and membranes) whereas the methods of structural optimization are far more general and can usually be applied to any kind of structure. So far, The differences of the two approaches are not only the level 143 E. Oñate and B. Kröplin (eds.), Textile Composites and Inflatable Structures, 143–151. © 2005 Springer. Printed in the Netherlands