Design research in architecture & civil engineering

Chris Williams

Kagiso Jobe Low cost housing in Botswana

Philibert de l’Orme, Château d’Anet 1552

Frei Otto 1925 – 2015

Ted Happold 1930 - 1996

D'Arcy Wentworth Thompson On Growth and Form 1917

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

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

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

Trabeculae in head of femur

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

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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∫