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σ ⁽⁻¹⁾ = ε ⁽⁻¹⁾ = ε _y (u ⁽⁰⁾ ) = 0

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u ⁽⁰⁾ = u ⁽⁰⁾ (x)

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(0)

div y σ ⁽⁰⁾ = 0 et σ ⁽⁰⁾ = K(y) e ε ⁽⁰⁾ = K(y)( e ε _x (u ⁽⁰⁾ ) + ε _y (u ⁽¹⁾ ))

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x

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ε _x (u ⁽⁰⁾ )

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Θ

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u ¹ ∈ U ^Y _per =

H _per ¹ (Θ) d

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Z

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Θ

ε _y (v) : K e ε _x (u ⁽⁰⁾ ) dy , ∀v ∈ U ^Y _per

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ε _y (u ⁽¹⁾ ) = H ε _x (u ⁽⁰⁾ )

= ⇒ ε ⁽⁰⁾ = ε _x (u ⁽⁰⁾ ) + H ε _x (u ⁽⁰⁾ )

= ⇒ σ ⁽⁰⁾ = ( K e + KH e ) ε _x (u ⁽⁰⁾ )

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(1)

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∀v ∈ U ^Y _per Z

Θ

ε _y (v) : K e ε _y (u ⁽²⁾ ) dy = − Z

Θ

ε _y (v) : K e ε _x (u ⁽¹⁾ ) dy + Z

Θ

v · (f

d + div _x σ ⁽⁰⁾ ) dy

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h.i _Θ = R

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Θ

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div x

σ ⁽⁰⁾

Θ

+ D f d

E

Θ = 0 σ ⁽⁰⁾

Θ = D

K e + KH e E

Θ

ε ⁽⁰⁾

Θ

V(“E\Za

ε ⁽⁰⁾

Θ = ε _x (u ⁽⁰⁾ )

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σ ^M = σ ⁽⁰⁾

Θ

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ε ^M = ε ⁽⁰⁾

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u ^M = u ⁽⁰⁾

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σ (x) = σ ^M + σ ^m (x)

^V(“E\Za

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^V(“E\Za

ε ^M = h ε i _Θ

ƒ

x

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Θ

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