Surface Fitting Approach For Tensile Membranes Design Javier Sánchez Miguel A. Serna Paz Morer IASS 2004.
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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 University of Navarra Main Campus San Sebastián. TECNUN Pamplona (Navarra) Barcelona. IESE. MBA Madrid. IESE. MBA 2/19 TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes • • • • • 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 3/19 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. Javier Sánchez. Montpellier. IASS 2004 overview Architects, designers Requeriments Construction, elevation lack of design tools Conception FormFinding Membrane cutting & manufacturing Analysis Detailing Cutting pattern generation Constructors, others 4/19 TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes Engineers (Computer based tools) Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004 Tensile membrane design process Design Software, CAD/CAE 2D,3D Drawings Membranes Technet Easy-CadEasy Tensocad-Forten Sofistik Patterner Surface … Standard Formats Analysis. FEA Ansys Abaqus Nastran Cosmos EOS ESI … 5/19 Catia v4,v5 ProEngineer SolidWorks SolidEdge Unigraphics I-deas Mechanical Desktop … dxf iges step wrml stl acis … TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes Cad attributes • Parametric • Featured based • Flexible • Easy to modify • Customer-supplier • Formats … Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004 Autocad Rhino 3D Studio Microstation … Solid & Surface Modeling Membrane Design tools 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 … a b Example of design tool scene for tensile membranes. Covering a given space (a) three membranes layout (b) four membranes layout. 6/19 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. Javier Sánchez. Montpellier. IASS 2004 specifications, requirements Proposed approach Mesh Generation initial mesh 7/19 Formfinding after formfinding Surface fitting Tesellation Render Nurbs fitting Function in R3 domain TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes render Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004 combines structural(formfinding) & geometry (surface fitting) 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, 8/19 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. Javier Sánchez. Montpellier. IASS 2004 analysis tools: accurate models required Form Finding theory 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. P K U 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. 9/19 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. Javier Sánchez. Montpellier. IASS 2004 traditional methods Grid Size Method Time (seconds) Nodes Bars 3x3 Force Density 0.033 16 24 5x5 Force Density 0.049 36 60 7x7 Force Density 0.061 64 112 9x9 Force Density 0.100 100 180 3x3 Non-Linear 0.039 16 24 5x5 Non-Linear 0.078 36 60 7x7 Non-Linear 0.152 64 112 9x9 Non-Linear 0.402 100 180 Computational times for different grid sizes and formfinding methods 10/19 TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes 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 Form Finding-computer time Parametric surface-function obtained from a collection of given points in R3 domain (B-Spline expression) n 1 m 1 Qu, w Bih, j Ni , k (u)M j , l (w) i 1 j 1 NonUniform Rational B-Splines, NURBS Advanced Surface Representation and Construction Nurbs Curve and Surface Fitting Interpolation, approximation theory Curve and surface construction parameters and terms Application for testing algorithms 11/19 Control nets, basis functions, control polygon, knot vectors, range, open, periodic, uniform, parameterization, degree, knot insertion & removal, order, tangent & twist vectors, continuity, weight factors… 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. Javier Sánchez. Montpellier. IASS 2004 Geometry. Nurbs Curve and Surface fitting • • • • • • • • • • 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 Application for testing algorithms 12/19 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. Javier Sánchez. Montpellier. IASS 2004 Rectangular 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 Application for testing algorithms 13/19 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. Javier Sánchez. Montpellier. IASS 2004 Radial nets load Sequence, using the same boundary conditions modifying position of a vertex 14/19 TECNOLOGICAL CAMPUS OF THE UNIVERSITY OF NAVARRA School of Engineering. San Sebastián. Spain www.tecnun.es/labcad/membranes distributed force applied - value changed Surface Fitting Approach For Tensile Membranes Design. Javier Sánchez. Montpellier. IASS 2004 some examples 15/19 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. Javier Sánchez. Montpellier. IASS 2004 Example: 3 edges membrane. 33 nodes. (21+11) 16/19 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. Javier Sánchez. Montpellier. IASS 2004 Example 7 edges membrane. 39 nodes (18+21) 17/19 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. Javier Sánchez. Montpellier. IASS 2004 Example: 12 edges membrane.75 nodes (32+43) • • • • • • • 18/19 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 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. Javier Sánchez. Montpellier. IASS 2004 conclusions 19/19 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. Javier Sánchez. Montpellier. IASS 2004 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: [email protected] Personal website: http://www.tecnun.es/labcad/jsanchez Membranes website: http://www.tecnun.es/labcad/membranes