Decisions to be made in the design and analysis of...
Transcript of Decisions to be made in the design and analysis of...
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
�
Peterson-Mainardi-Codazzi Equations�
Gauss's Theorema Egregium
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Inextensional deformation
and write
:
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Equilibrium
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Strain rate
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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