34 Lothar Gruindig,Dieter Strobel and Peter Singer 1.To define stiffness values to all finite membrane and cable elements. 2.To calculate the unstressed link lengths by using the assigned stiffness valueses and the prestress of the membrane and the forces in the cables of the formfinding result. 3.To check if the result of the statical analysis with the loads of the formfinding procedure is identical with the formfinding result. After these three steps,the statical analysis without beam elements under ex- ternal loads can be achieved very easily. 1.To calculate the external load vectors as for example snow,wind or normal loads. 2.To perform the nonlinear statical analysis:the approximate values,which are needed in this nonlinear process,are given by the formfinding result. 3.Evaluation-and visualization tools in order to judge the result of the stati- cal analysis.The stresses and forces can be visualized and compared with the maximum possible values.Stresses,forces and layer reactions can be shown, contour-lines can be calculated and visualized,cut-lines through the structure can be made,deflection of the nodes can be calculated. If beam elements are included,the statical analysis under external loads has to be done as follows:all data for the beam-elements as cross-section areas,moments of inertia,local coordinate systems,joints,etc.have to be defined firstly.In order to set all these values in a convenient way the user is supported by a Beam-Editor in EasyBeam. Fig.2.The Easy beam editor
34 Lothar Grundig, Dieter Str¨ ¨ obel and Peter Singer 1. To define stiffness values to all finite membrane and cable elements. 2. To calculate the unstressed link lengths by using the assigned stiffness valueses and the prestress of the membrane and the forces in the cables of the formfinding result. 3. To check if the result of the statical analysis with the loads of the formfinding procedure is identical with the formfinding result. After these three steps, the statical analysis without beam elements under external loads can be achieved very easily. 1. To calculate the external load vectors as for example snow, wind or normal loads. 2. To perform the nonlinear statical analysis: the approximate values, which are needed in this nonlinear process, are given by the formfinding result. 3. Evaluation- and visualization tools in order to judge the result of the statical analysis. The stresses and forces can be visualized and compared with the maximum possible values. Stresses, forces and layer reactions can be shown, contour-lines can be calculated and visualized, cut-lines through the structure can be made, deflection of the nodes can be calculated. If beam elements are included, the statical analysis under external loads has to be done as follows: all data for the beam-elements as cross-section areas, moments of inertia, local coordinate systems, joints, etc. have to be defined firstly. In order to set all these values in a convenient way the user is supported by a Beam-Editor in EasyBeam. Fig. 2. The Easy beam editor
Recent Developments in the Analytical Design of Textile Membranes 35 Then-see above-the steps 1-3 follow.The Beam Editor is also used for checking the results as internal forces and moments,layer-reactions,flexibility-ellipsoids,etc. 7 The Complete Easy Lightweight Structure Design System The Easy system is composed of a number of program suites.These are represented schematically in Fig.3. EasyForm Formfinding of lightweight structures EasySan Nonlinear Statical Load Analysis (without Beam elements) EasyCut Cutting pattern generation EasyBeam Nonlinear hybride Membrane structures including Beam elements Easy Vol Formfinding and Load Analysis of pneumatic constructions 密国四 EasyForm EasySan EasyCut EasyBeam EasyVol Fig.3.The Easy program suites Easy Form comprises the programs used for data generation together with force density form-finding.When the EasySan programs are additionally installed stat- ical structural analysis of non-linear structures becomes possible.The EasyCut
Recent Developments in the Analytical Design of Textile Membranes 35 Then -see above- the steps 1-3 follow. The Beam Editor is also used for checking the results as internal forces and moments, layer-reactions, flexibility-ellipsoids, etc. 7 The Complete Easy Lightweight Structure Design System The Easy system is composed of a number of program suites. These are represented schematically in Fig. 3. EasyForm Formfinding of lightweight structures EasySan Nonlinear Statical Load Analysis (without Beam elements) EasyCut Cutting pattern generation EasyBeam Nonlinear hybride Membrane structures including Beam elements EasyVol Formfinding and Load Analysis of pneumatic constructions Fig. 3. The Easy program suites EasyForm comprises the programs used for data generation together with force density form-finding. When the EasySan programs are additionally installed statical structural analysis of non-linear structures becomes possible. The EasyCut EasyForm EasySan EasyCut EasyBeam EasyVol