Method

Surface-based design have become used in architecture through B-Spline-modeling software. A surface can serve as a repre-sentation for many different aspects of a design beyond its initial function. It is a two-dimensional object unfolded into the three-dimensional space. However, instead of being surfaces as border conditions, they are often perceived as the objects themselves. This represents a physical building component that is developed when the surface is translated into a building with structural requirements and materialproperties. The strategy of the structural analysis optimization introduced into the design permits a minimum number of con-straints, minimum stress and deformation-displacement.

4. ConclusionsIntegrating the generative means of form-finding into a design process witha broader range of parameters proved suc-cessful. Altering local areas of theglobal geometry while simultaneously main-tain the architectural expression

Abstract

This is a method for designing intercon-nected surface structures, a common and complex component of architecture, using an optimized analysis.Structures are omnipresent in the industri-alized world and architecture appearing as roof supports, slabs or building exoskel-etons, yet are complex enough that modeling them by conventional software is time con-suming and tedious. This method represents structures as a set of rigid bars connectedby pin joints and supported by minimum amount of colums, which may change location during optimization. By including the loca-tion of the joints as well as the strength (stress, displacement, deformation) of in-dividual beams in the design variables, the method can simultaneously optimizethe geometry.

CR Categories:[Computer Graphics]: 3d-NURBS-Modeler (Rhinoceros™-Grasshopper) and Object Modeling—Physically based modeling;[Numerical Analysis]: SolidWorksKeywords: Performance Design, constrainedoptimization, nonlinear optimization

Figure 1: Rhino-Grasshopper mesh design and design generated by structural analysis optimization in SolidWorks

INTERCONNECTED SURFACE DESIGN APPROACHES BY STRUCTURAL ANALYSIS OPTIMIZATION

Goi Artetxega2238@columbia.eduAAD, 2009Columbia University, GSAPP

Strategies to optimize interconnected structures by analysis data. Design, analysis, synthesis, evaluation.

Figure 2: Iterations from Rhino-Grasshopper. Case studies.

The method used in this research gener-ates a mesh of structural elements along the initial surface. As shown in Figure 1 the developed design process starts with a flexible grid on a surface. The different iterations are summarized in three. Figure 2. One initial surface is translated into SolidWorks software, which then is exposed to gravity with perimetric constraints. Figure 3-4. The resulting mesh deflection with appropiate reactions towards the lo-cal stresses and deformations is fed back into Rhino-Grasshopper and translated to SolidWorks to its dead load using minimum amount of constraints. Figure 5

The geometry of the initial mesh is altered to reduce bending. This process negotiates the form-driving ‘forces’, the structural and the architectural. The new, altered mesh then is transformed back into either a single surface in the 3d-modeling software. In the latter case the in-between space now describes a volume for space frame con-struction. Figure 6

Figure 3: Case study 1. Gravitational forces.

Figure 4: Case study 1. Stress-displacement.

Figure 5: Minimum constraint.

Figure 8: Rhino-Grasshopper evoluted mesh design

From this new starting point a Grasshop-per definition is used to find a solution of a space frame which deals with closest points. In Figure 7-8-9 these factors arerepresented by spaces which should be free of structural elements, a minimal number of structural members, and a minimum of over-all deviation.The structural analysis data, which result from that next feedback loops, Figure 10finally are used to generate in a simpli-fied, but parametrically driven manner, all structural members of the developed space frame system. The project uses a 3d-NURBS-Modeler (Rhinoceros™) for surface genera-tion, surface modification and the visual-ization of geometry. Structural analysis is done in SolidWorks.

Figure 6: Rhino-Grasshopper altered mesh design

Figure 7:Rhino-Grasshopper evoluted mesh design

Figure 10: Model comparison

Conclusions

Integrating form-finding into a design pro-cess with parameters proved successful. Altering the geometry while maintaining the architectural expression led to less deformation in the shape. At the same time the formal collection is not limited to shapes that are force-driven. Being able to transfer the data from a surface model to a structural mesh and back again pro-vides a fast and easy way to improve the model. The design process is driven by architectural and structural parameters simultaneously.The negotiation between different aspects gives solutions which are improved during the generative process. The procedure is seen as an approximation for the early de-sign stage that offers architects the pos-sibility to integrate structural aspects into their work and use them as design tool. The use of Rhino-Grasshopper defini-tions within the design process is a pow-erful method to generate variation and at the same time search a solution space.Especially when searching for a balance of multiple or even conflicting interests this approach is beneficial.

Feedback loops in SolidWorks

References

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ARUP,Ove: Candela / The Shell Builder. New York: Reinhold PublishingCorporation, 196338 Markus

Software

Rhinoceros Nurbs Modeling

Grasshopper Generative Modeling for Rhino

SolidWorks

AutoDesk Maya 2009