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TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain

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

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TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain

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

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

  3. 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 TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 3/19

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

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

  6. a b Example of design tool scene for tensile membranes. Covering a given space (a) three membranes layout (b) four membranes layout. 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 • … Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004 TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 6/19

  7. Mesh Generation Form-finding Surface fitting Tesellation Render Nurbs fitting Function in R3 domain after formfinding initial mesh render Proposed approach combines structural(formfinding) & geometry (surface fitting) Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004 TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 7/19

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

  9. force density method surface stress density 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 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 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. Form Finding theory traditional methods Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004 TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 9/19

  10. Form Finding-computer time Computational time has decreased, a few years ago it was not possible to think in real time tools Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004 Computational times for different grid sizes and formfinding methods TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 10/19

  11. Parametric surface-function obtained from a collection of given points in R3 domain (B-Spline expression) Geometry. Nurbs Curve and Surface fitting NonUniform Rational B-Splines, NURBS Advanced Surface Representation and Construction Nurbs Curve and Surface Fitting Interpolation, approximation theory Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004 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 TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 11/19

  12. Rectangular nets • 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 Application for testing algorithms TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 12/19

  13. Application for testing algorithms Radial nets • 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 TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 13/19

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

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

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

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

  18. conclusions • Newdesign 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 TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 18/19

  19. Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004 TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 19/19

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