Decisions to be made in the design and analysis of ...staff.bath.ac.uk/abscjkw/Paris2017/Paris2017.pdf · Decisions to be made in the design and analysis of gridshell structures Chris

Decisions to be made in the design and analysis of gridshell structures

Chris J K Williams Chalmers University, Göteborg, Sweden University of Bath, UK

Amancio Williams

1913 - 1989

Félix Candela, 1910 - 1997

Frei Otto 1925 - 2015

Ted Happold 1930 - 1996

D'Arcy Wentworth Thompson On Growth and Form 1917

Munich Olympic Stadium 1972 Frei Otto and Leonhardt, Andrä und Partner - Jörg Schlaich

Multihalle Mannheim 1974 Carlfried Mutschler + Partners, Frei Otto, Ove Arup & Partners (Ted Happold, Ian Liddell)

Portcullis House 2000 Hopkins Architects Arup

Sydney Opera House 1973 Jørn Utzon and Ove Arup - with partners Geoffrey Wood (left) and Ronald Jenkins (right)

Membrane theory of shellsCoefficients of the first fundamental form�

Coefficients of the second fundamental form

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Peterson-Mainardi-Codazzi Equations�

Gauss's Theorema Egregium

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Inextensional deformation

and write

:

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Equilibrium

�

Strain rate

�

Virtual Work

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gij = gi ⋅g j

bij = gi, j ⋅n

cij = ε imε jnbij

∇icij = ∇i ε imε jnbmn( ) = ε imε jn∇ibmn = 0

K =12ε imε jnbijbmn =

12cijbij

∂ε im

∂t= 0

χij =12∂cij

∂t

∇iχij =

12∂∂t

∇icij( ) = 0

χ ijbij =12∂∂t

ε imε jnbij( )bmn = 2 ∂K∂t = 0

gσ ijg j( ),i+ g p jg j + pn( ) = 0

∇iσij + p j = 0

σ ijbij + p = 0

σ ij = σ ji

v = ∂r∂t

= vjgj + vn

v ,i = vj ,igj − vjΓ ik

j gk + vjbijn+ v,in− vbijg

j

= vj ,i − vkΓ ijk − vbij( )g j + vjbi

j + v,i( )n= ∇iv j − vbij( )g j + vjbi

j + v,i( )n0 = γ ij =

12∂gij∂t

= 12v ,i ⋅g j + gi ⋅v , j( )

= 12

∇iv j +∇ jvi( )− vbij

σ ijγ ij dAM∫ = σ ij ∇iv j − vbij( )dA

M∫

= ∇i σijv j( ) + vj∇iσ

ij − vσ ijbij( )dAM∫

= qiσijv j ds

∂M∫ + vj p

j + vp( )dAM∫

Montreal Biosphère 1967 Richard Buckminster Fuller

British Museum 2000 Foster + Partners Buro Happold Waagner-Biro

Amsterdam Maritime Museum 2011 Ney + Partners

Gardens by the Bay glasshouses 2011 Grant Associates, Wilkinson Eyre, Atelier One

Cathédrale éphémère de Créteil 2013 T/E/S/S 

Laboratoire Navier à l’Ecole des Ponts ParisTech Viry

Trabeculae in head of femur

Markham Moor petrol station on the A1 in Nottinghamshire. Sam Scorer and Hajnal-Kónyi 1960

Decisions to be madeShape

MaterialConnection details

Erection method

Cost

Structural support

Cladding

Structural analysis technique

Geometry definition

3 x 6 x 8 x 16 x 7 = 16,128