Modelling Complex Geometry Structures

Valerio Stuart

Modelling Complex Geometry Structures

Contents:

• Complex geometries

• Applications

• SAP2000 & API

• Case study

• Rhinoceros & Grasshopper

• Architects & Competitors

• Case studies

• Shells

• Helicoids

• Catenoids

• Gaussian surfaces

• Hyperboloids

• Surfaces of revolution

• Other weird stuff

Complex geometries

From math to the real world

Yas Viceroy, Abu Dhabi - Asymptote Architecture

From math to the real world

Aliyev Centre, Baku Azerbaijan - Zaha Hadid

From math to the real world

Walt Disney Concert Hall - Frank Gehry

From math to the real world (UK)

Aquatic Centre, London UK - Zaha Hadid(Ove Arup & Partners)

From math to the real world (UK)

Savilll Garden Visitor Centre - Glen Howells Architects (Buro Happold)

From math to the real world (UK)

Olympic Velodrome, London UK - Hopkins Architects (Expedition Engineering)

SAP2000

Conventional modelling approach using SAP2000

• Draw the geometry in CAD

• Export the geometry in .dxf format

• Import the .dxf into SAP2000

• Mesh the geometry using the SAP2000 mesh generator(or manually!)

Other approaches are possible, and there are other tools available in the market to mesh complex geometries (other than the built-in SAP2000 mesh generator).However, each program is different and might or might not be able to communicate with SAP2000 or any other structural analysis software you intend to use.

SAP2000 Application Programming Interface (API)

• Software library that offers access to a collection of objects and functions capable of remotely controlling the way that SAP2000 behaves.

• Programming tool which allows to bind any third-party application to the analysis software.

• Allows the user to develop plug-ins which can communicate with SAP2000 and carry out routine tasks or other time consuming exercises.

Alternative approach using SAP2000 API

• Identify a surface that can reproduce the desired shape

• Define the type of coordinate system, depending on the type of surface(e.g.: Cartesian, Polar, etc)

• Algebraically define the domain of the surface

• Discretise the surface into a finite number of nodes and define their position in the 3D space

• Define others properties of the structure (e.g.: materials, loads, etc)

• Create a text file in .s2k format that can be imported into SAP2000

The API can also be used to run multiple analysis, export and manipulate results to carry out different studies.

Case study

Kresge Auditorium, MIT Boston, USA - Eero Saarinen (Amman & Whitney)

The Kresge Auditorium

• Thin shell RC structure • The structure can be reproduced as a portion

of a sphere cut by 4 planes • The thickness of the shell varies:

• 90mm at the centre • 130mm at the centre of the arches • 540mm at the supports

• Radius of the sphere: 34.29m • Maximum height of the shell: 14.5m • Maximum height of the edges: 8.0m • Distance between supports: 48.5m

Several models with different levels of mesh density were required to carry out mesh sensibility studies.

Initial discretisations

• Discretisation of the surface carried out using the AutoCAD meshing tool

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• Manual discretisation of the surface

Initial discretisations

• Poor quality mesh, with excessively deformed elements, mix of triangular and quadrilateral elements

• Highly time consuming procedure

• If a mesh with different density is needed (e.g. coarse, fine, etc) the procedure has to be repeated.

• Thickness of the elements to be applied manually or approximated with loss of accuracy.

Discretisation using the API

• Definition of the geometry of the structure on plan, using the shape functions of the ISO 6 element.

Nodes

Plan view

Modelling procedure

• Transformation of the coordinates into x,y

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• Definition of the coordinate z for each node using the definition of a sphere:

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• Definition of the nodes and triangular shapes.

Elevation

Numbering of the Area elements

Modelling procedure

• Once the coordinates of the joints are known, it is possible to define them in the .s2k SAP2000 file:

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• Define the Areas. Triangular elements were used in this study:

Modelling procedure

• Using the SAP2000 language it was also possible to define:

• concrete grade

• type of supports

• element thickness

• load cases (wind, snow)

• load combinations

• other elements (i.e. frames) and their thickness

Modelling procedure

Shell element thickness:

• The position of the centre of mass of each element is known

• It’s possible to define the thickness of each shell element in relation to the position of its centre of mass

Modelling procedure

Wind load:

• The position of the centre of mass of each element is known

• It’s possible to define the wind load for each shell element in relation to the position of its centre of mass

Modelling procedure

Snow load: • The position of the centre of mass of each shell element is known and so is its

inclination

• As per the wind load, the snow load on each element can be defined in relation to the position of its centre of mass

• It’s also possible to define different load situation, where the snow it’s on a portion of the structure only.

Modelling procedure

• The Matlab script outputs an .s2k which can be imported into SAP2000, containing all the parameters describing the structure and loads.

Results

Once the program to define all the parameters required in the .s2k file has been set up, a different mesh, material properties, loads, etc. can be selected in virtually no time.

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Results

• The .s2k files are text files which can be easily saved, stored, exchanged between users thanks to their small size

• Different models can be easily created for the desired purpose (e.g.: mesh studies, influence of the elements’ stiffness on the behaviour of the structure, etc)

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Kresge Auditorium

SAP2000 Application Programming Interface (API)

• Compat ib i l i t y w i th mos t ma jo r programming languages

• Full control of element connectivity

• Ability to develop both pre- and post-processing procedures tailored to the user’s needs

• No need of using intermediate files, which reduces significantly the time needed for data exchange when working on large models

• Once the procedures have been set up it’s possible to use them for routine operations, minimising time and human errors

Advantages & Disadvantages

• Programming background/skills required

• Learning curve

• Code robustness

• Routines designed for a specific model might not be applicable to others

Thank you