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Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain

Designing Tensile Structures Using Generic CAD applications

Structural Membranes 2007– Barcelona, 17-19 September 2007Javier Sánchez, Tecnun, University of Navarra, San Sebastián, Spain

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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

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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 techniquesin generic CAD applications

Objective

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Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain

Designing Tensile Structures

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Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain Designing Tensile Structures

design proccess

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Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain

conception stage

Designing Tensile Structures

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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

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Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain

Double curvature shapes & Parametric surfaces

Integration of formfinding techniquesin generic CAD applications

Objective

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Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain

Tensile structures Double curvature shape

sinclasticanticlastic

Double curvature shapes & Parametric surfaces

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Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain

Parametric surfaces complex shapes (mathematically based)

CAD tools used for: Industrial design, 3D animation, etc

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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

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Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain

parametric surfaces

Two parameters (u,w)

Bezier Surface, control net Bij

B-Spline surfaces

NURBS surfaces

Any complex shape can be represented using a parametric surface (NURBS)

Double curvature shapes & Parametric surfaces

Integration of formfinding techniquesin generic CAD applications

Objective

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Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain

FormFinding & Surface Fitting

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Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain form-finding and surface fitting

force density methoduses 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 approachThe stiffness method solves a set of equations (1) that represents the translational and rotational equilibrium at each node of the structure.

UKP 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 relaxationmethod 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

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Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain

proposedmethod 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 techniquesin generic CAD applications

Objective

generic CAD application

add-inplug-in to CAD

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Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain

CAD Applications and examples

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Own implementation to validate the method

automatic mesh generationdinamic manipulation in real time

form-finding, force density methodforce-density values: internal, boundariesnodal & distributed forcesforces & stress visualizationsparse solver

surface fitting to equilibrium shapesparameters, net control, weight factors

visualization: wireframa, renderexport data

CAD Applications and examples

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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

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Integration of formfinding techniquesin 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

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Integration of formfinding techniques in Rhino

net generation surface fitting surface trimming visualization

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Using Rhino 3D. Plug-in

• easy interface, user friendly

• manipulate shapes in real time

• represent surroundings

• file formats, compatibilities

• useful for the designer

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Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain CAD Applications and examples

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Javier Sánchez, Tecnun, University of Navarra, San Sebastian, Spain

other applications & fields

CAD Applications and examples

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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.esPersonal website: http://www.tecnun.es/labcad/jsanchezMembranes website: http://www.tecnun.es/tensileRapid Prototyping site: http://www.tecnun.es/prototyping

Designing Tensile Structures Using Generic CAD applications

Low cost software maintenance, new releases, etc

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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 0.301Numero de nodos

Tie

mp

o

(seg

un

dos)

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

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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 vectorexponential parameterization

nonuniform nodal vectorexponential parameterization

objective: polygon control

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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

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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