1. TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes Surface Fitting Approach For Tensile Membranes Design IASS 2004. Montpellier, 20-24 September Javier Sánchez Miguel A. Serna Paz Morer

2. TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes University of Navarra Madrid. IESE. MBA Main Campus Pamplona (Navarra) San Sebastián. TECNUN Barcelona. IESE. MBA 2/19

3. TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 3/19 overview applied research project at mechanical & civil engineering department a new approach to tensile membrane design is given to generate and modify shapes in real time end users: designers, covering the first stages of design process hybrid method: combines structural (formfinding) & geometry (surface fitting) contents Design process Existing Software tools Proposed method (formfinding-surface fitting) Examples, results Conclusion Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004

4. TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 4/19 Tensile membrane design process lack of design tools Architects, designers Requeriments Conception FormFinding Analysis Cutting pattern generation Detailing Membrane cutting & manufacturing Construction, elevation Constructors, others Engineers (Computer based tools) Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004

5. TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 5/19 Cad attributes Parametric Featured based Flexible Easy to modify Customer-supplier Formats … Design Software, CAD/CAE Solid & Surface Modeling Catia v4,v5 ProEngineer SolidWorks SolidEdge Unigraphics I-deas Mechanical Desktop … 2D,3D Drawings Autocad Rhino 3D Studio Microstation … Membranes Technet Easy-CadEasy Tensocad-Forten Sofistik Patterner Surface … Analysis. FEA Ansys Abaqus Nastran Cosmos EOS ESI … Standard Formats dxf iges step wrml stl acis … Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004

6. TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 6/19 Membrane Design tools specifications, requirements ask the end user (designer) for the tool (requirements): easy to use easy to generate and modify shapes real time shapes regeneranation not many tech parameters model tree (objet based) Combine objets (buildings, membranes) integrated tool (exp-import) acad,3DStudio,Rhino formfinding flexible … Example of design tool scene for tensile membranes. Covering a given space (a) three membranes layout (b) four membranes layout. b a Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004

7. TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 7/19 Mesh Generation Form- finding Surface fitting Tesellation Render Proposed approach combines structural(formfinding) & geometry (surface fitting) initial mesh after formfinding Nurbs fitting Function in R 3 domain render Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004

8. TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 8/19 analysis tools: accurate models required Specialised users, structural knowledge required Example: 172 nodes, 314 elements design tools: not so accurate models required Easy and fast way to generate shapes, no experts required example:38 nodes, 62 elements, Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004

9. TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 9/19 Form Finding theory traditional methods force density method uses an analytic technique to linearize the form finding equations for a tension net. This linearization makes the method independent of the material properties of the membrane. Force density ratios (cable force divided by cable length) need to be specified for each element, and different ratios give different equilibrium shapes. The method is numerically robust, independent of the initial locations of the nodes, and the equilibrium shape is found easily. The force density solution to applied loads is non-linear, and requires iteration. dynamic relaxation method solves the geometric non-linear problem by equating it to a dynamic problem. Principles of dynamic are used to solve the analysis. Appropriate dynamic properties need to be defined, like the mass and damping characteristics of the membrane. A balance of forces is made at each node, giving a residual force that produces the movement of the node in the direction of this force, according to the dynamic behavior of the net. New positions for the nodes are calculated until the final equilibrium shape is reached. At this point the residual forces are sufficiently small can be considered as a generalization of linear force density method to the bidimensional case, and takes into account the shear stress. In this case, the surface stress density ratio is given by the stress divided by the area of the element surface stress density non-linear approach The stiffness method solves a set of equations (1) that represents the translational and rotational equilibrium at each node of the structure. where [P] is the applied nodal loads vector; [K] is the Stiffness Matrix; and [U] is the Nodal displacement vector. This method required an iterative process, until equilibrium shape compatible with the given prestress conditions is reached. At each step, a global stiffness matrix is recalculated, according to the new position of the nodes, and the material properties of the membrane. Applied loads are considered in the analysis. Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004

10. TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 10/19 Grid SizeMethodTime (seconds)NodesBars 3x3Force Density0.0331624 5x5Force Density0.0493660 7x7Force Density0.06164112 9x9Force Density0.100100180 3x3Non-Linear0.0391624 5x5Non-Linear0.0783660 7x7Non-Linear0.15264112 9x9Non-Linear0.402100180 Form Finding-computer time Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004 Computational time has decreased, a few years ago it was not possible to think in real time tools Computational times for different grid sizes and formfinding methods

11. TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 11/19 NonUniform Rational B-Splines, NURBS Advanced Surface Representation and Construction Nurbs Curve and Surface Fitting Interpolation, approximation theory Geometry. Nurbs Curve and Surface fitting Parametric surface-function obtained from a collection of given points in R 3 domain (B-Spline expression) Curve and surface construction parameters and terms Control nets, basis functions, control polygon, knot vectors, range, open, periodic, uniform, parameterization, degree, knot insertion & removal, order, tangent & twist vectors, continuity, weight factors… Application for testing algorithms Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004

12. TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 12/19 Rectangular nets Application for testing algorithms N. of sides Grid size x-y Warp-Weft angles Mesh points Internal pressure Edges forces External nodal force External dist. Force Formfinding method Mouse control (rotate,translate,scale) Real time regeneration Surface parameters Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004

13. TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 13/19 Radial nets Application for testing algorithms N. of sides Grid size radial-merid Diameter Mesh points Internal pressure Edges forces External nodal force External dist. Force Formfinding method Mouse control (rotate,translate,scale) Real time regeneration Surface parameters Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004

14. TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 14/19 some examples load Sequence, using the same boundary conditions distributed force applied - value changed modifying position of a vertex Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004

15. TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 15/19 Example: 3 edges membrane. 33 nodes. (21+11) Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004

16. TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 16/19 Example 7 edges membrane. 39 nodes (18+21) Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004

17. TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 17/19 Example: 12 edges membrane.75 nodes (32+43) Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004

18. TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 18/19 conclusions New design approach for tensile membrane design Fast method. Real-time interaction user-shape The user can fell the shape More applications. Freeform modelling Material behauviour modelling Integrate the method in commercial tools as plug-ins (Autocad, Rhino…) More Designers will try to generate these shapes as it becomes easier Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004

19. TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 19/19 Javier Sánchez Mechanical Engineering Department Tecnun - University of Navarra Manuel de Lardizábal 13 20018 San Sebastián, SPAIN Tel.: +34 943 219877 Fax: +34 943 311442 E-mail: jsanchez@tecnun.es Personal website: http://www.tecnun.es/labcad/jsanchez Membranes website: http://www.tecnun.es/labcad/membranes Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004