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# The FEM Analysis of a Gehry Cladding System

By rstroup27
Mar 5, '12 3:15 PM EST

For the next couple of days, I will be writing about Finite Element Methods (FEM).  Widely considered one of the more difficult courses at Lehigh, FEM is used by structural engineers to measure or trace stress concentrations throughout a structure subjected to loads or experiencing deformation.

The reason I am writing about this is because I am currently enrolled in a FEM course and my professor, knowing my background, has asked me to "try to bridge" an architectural concept to a term-long project in FEM.  So, given my background as an architecture student - naturally - I've gone rogue and selected something wildly complex: a Gehry cladding system.  Here is the scope of my project insofar:

Scope of Project:

This project will focus on a custom Frank Gehry designed cladding system.  In scope, the project will present (1) the computational descriptions of Gehry's architectural forms, (2) how these forms are typically fabricated, and (3) an FEM analysis of built components. In Gehry's process for realizing buildings, computation serves as an intermediary agent for the integration of design intent with the geometric logics of fabrication and construction.  By using computer-generated algorithms, a curvilinear/non-orthogonal membrane can be constructed.

For this project, four hierarchical layers of cladding will be investigated:

1. A structural rib system (wide flanges)
2. A tube/pedestal purlin system (structural tubing)
3. A panel and face sheet edge system (time permitting)
4. A finish surface (time permitting)

The drawings for each of these systems (pictorial representation can be found on page 2 of a sample Gehry cladding system) will be generated using a set of algorithms deduced by graduate students at MIT.  The curves will be first input into Matlab for mathematical analysis and then graphically approximated in Rhino.  Once drawn in Rhino, they will then be exported to CAD and then SAP.  To test the cladding system, panels in the membrane system will be loaded uniformly near nodal intersections.  To test actual weather-based considerations, the model will also be subjected to a predetermined wind load of 40 ksf.  The deflections, moments and shears will then be analyzed using SAP.

In specific, the purpose of this project is to test two things: (1) whether a simple cladding system designed by Gehry can withstand given wind loads and (2) how the system responds to a uniform distribution of point loads.  By analyzing the latter, weak structural spots in the structure may then be found.  By investigating the former, the lateral resistance of the actual performance of the cladding system can be approximated.

Robert S.

I will update what I learn on this blog and will cite sources.

• 3tk

thoughts:

1. I'm under the impression that the geometric constraints of Rhino and AutoCAD (assuming by CAD you mean to imply AutoCAD) are different - you may find that some things get "lost in translation" (eg, Copenhagen ship curves can be modeled in Rhino but not AutoCAD).  I forget if gehry's work needs NURBS.

2. Is FEM not how the SEs on his projects model this?  I remember distinctly an engineering team getting some awards from SEI or ASCE for their work (maybe part of CATIA?).

3. CATIA may be better suited for this than SAP.

4. I would imagine you are also modeling dynamic loading?  I would imagine that would be more instructional (potential for analysis of weatherproofing performance, fatigue stress, etc).

rstroup27

After reading my references, it's my interpretation that Gehry's work uses NURBS, but doesn't require them.  I could be wrong on that score, but it seems that continuous curves can be generated using predefined analog inputs.

FEM is very much how many of his projects are modeled for structural analysis.  To some extent, Gehry pioneered advances in FEM, so this comes as no surprise.

CATIA is better suited.  There's no comparison.  But since I don't have access to CATIA, SAP2000 - which does model closely, but not perfectly paper surfaces - has to do.

I didn't, but it is possible to add modal loads in SAP2000.  And you are right about how instructional it can be.  Currently, I'm also researching wireless sensors and modal properties in suspension bridges for another class.  I've already analyzed dynamic loadings for loft structures (see a previous blog entry) as well.  There is one drawback: dynamic loads are one of the more difficult loads to define in SAP2000.  Many rely on cyclic loadings, such as cars driving over a bridge.  Not all can accurately represent blast or hazardous impact forces (which most buildings are defined for).  For most purposes, digital interfaces (such as Cygwin and Matlab) are used to appropriately measure the natural frequencies and periods for structures subjected to dynamic loads.

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