1. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain Designing Tensile Structures Using Generic CAD applications Structural Membranes 2007– Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastián, Spain

2. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain Main Campus, Pamplona (Navarra) San Sebastián. TECNUN. Mechanical Engineering Department. Barcelona. IESE. MBA Madrid. IESE. MBA Technological Campus of the University of Navarra

3. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain Designing Tensile Structures Double curvature shapes & Parametric surfaces CAD Applications and examples Conclusions FormFinding & Surface Fitting Presentation Index Integration of formfinding techniques in generic CAD applications Objective

4. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain Designing Tensile Structures

5. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain Designing Tensile Structures design proccess

6. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain conception stage Designing Tensile Structures

7. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain computer tools for Tensile Structures Design easy interface, user friendly manipulate shapes in real time surroundings file formats, compatibilities structural parameters useful for the designer Comercial CAD applications required functionalities Formfinding techniques Incorporate formfinding techniques in commercial CAD applications Designing Tensile Structures

8. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain Double curvature shapes & Parametric surfaces Integration of formfinding techniques in generic CAD applications Objective

9. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain Tensile structures  Double curvature shape sinclastic anticlastic Double curvature shapes & Parametric surfaces

10. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain Parametric surfaces  complex shapes (mathematically based) CAD tools used for: Industrial design, 3D animation, etc

11. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain parametric curves parametric curve, x = f(t) Bezier curve, control polygon cuadratic cubic b-splines curves NURBS curves (Non Uniform Rational B-Splines) Double curvature shapes & Parametric surfaces

12. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain parametric surfaces Two parameters (u,w) Bezier Surface, control net B ij B-Spline surfaces NURBS surfaces Any complex shape can be represented using a parametric surface (NURBS) Double curvature shapes & Parametric surfaces Integration of formfinding techniques in generic CAD applications Objective

13. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain FormFinding & Surface Fitting

14. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain form-finding and surface fitting 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. 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. 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 Formfinding Techniques

15. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain proposed method structural net, nodes & elements structural analysis,form-finding surface fitting to obtained equilibrium shape surface trimming, curve fitting to boundaries visualizatión (render, wireframe) net generation form finding surface fitting surface trimming visualization geometric structural structural net with not many nodes good quality of fitted surface real time calculation, manipulation & visualization form-finding and surface fitting Integration of formfinding techniques in generic CAD applications Objective generic CAD application add-in plug-in to CAD

16. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain CAD Applications and examples

17. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain Own implementation to validate the method automatic mesh generation dinamic manipulation in real time form-finding, force density method force-density values: internal, boundaries nodal & distributed forces forces & stress visualization sparse solver surface fitting to equilibrium shapes parameters, net control, weight factors visualization: wireframa, render export data CAD Applications and examples

18. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain 32 nodos (21+11) 0.037 segundos examples 39 nodes (18+21) 0.044 seconds 75 nodes (43+32) 0.120 seconds CAD Applications and examples

19. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain Integration of formfinding techniques in generic CAD applications Objective 3D modeling tool Industrial design, architecture, etc Plug-in.The Rhino Software Development Kit (SDK) provides C++ developers the tools needed to develop plug-ins for Rhino. formfinding algorithms can be integrated in Rhino www.rhino3d.com

20. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain CAD Applications and examples Integration of formfinding techniques in Rhino net generation surface fitting surface trimming visualization

21. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain Using Rhino 3D. Plug-in easy interface, user friendly manipulate shapes in real time represent surroundings file formats, compatibilities useful for the designer

22. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain CAD Applications and examples

23. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain other applications & fields CAD Applications and examples

24. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain Conclusions Combines structural (formfinding) & geometry (surface fitting) techniques Required functionalities in a computer aplications for Tensile Structure Design: Own application implemented for validating the method, multiple examples Integration of formfinding techniques in Rhino. Plugin. conclusions Any complex shape can be represented using a parametric surface (NURBS) user friendly, flexible, integrate model with surroundings, file formats 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/tensile Rapid Prototyping site: http://www.tecnun.es/prototyping Designing Tensile Structures Using Generic CAD applications Low cost software maintenance, new releases, etc

25. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain

26. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain

27. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain computational times 30 nodes 38 52 68 87 103 nodes 111 132 157 187 0.016sec 0.019 0.028 0.041 0.066 0.093sec 0.114 0.177 0.261 0.301 Numero de nodos Tiempo (segundos) net generation form-finding surface fitting surface trimming visualization number of nodes mesh form-finding surface fitting surface trimming total time (seconds) (seconds) (seconds) (seconds) (seconds) equilibrium shape of model “a” is obtained 18 times faster that equilibrium shape of model “j” both shapes are equally adequated for the design stage

28. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain surface fitting to equilibrium shapes of tensile structures curve fitting aproximation - interpolation -parameterization -nodal vector(uniform-non uniform) uniform nodal vector exponential parameterization nonuniform nodal vector exponential parameterization objective: polygon control

29. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain surface fitting aproximation - interpolation -parametrization (estimate u,w) -nodal vector (uniform-non uniform) -shape equations no fitting points in this area find net control surface fitting to equilibrium shapes of tensile structures

30. Designing Tensile Structures Using Generic CAD Applications. Structural membranes 2007, Barcelona, 17-19 September 2007 Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain surface fitting to tensile structures adequate control net size surface trimming net generation form-finding surface fitting surface trimming visualization surface fitting to equilibrium shapes of tensile structures net generation form-finding surface fitting surface trimming visualization