Modelos Não Lineares do Método dos Elementos de Contorno para ...

( 1 δ ) ( 1 δ )
( 1 δ ) ( 1 δ )
⎡ x1 ⋅ + Ψ ⋅ 1 x2 ⋅ + Ψ ⋅ 2 x3
⎤
⎢
⎥
⎢
x1 ⋅ − Ψ ⋅ 1 x2 ⋅ + Ψ ⋅ 2 x3
⎥
⎢
⎛ Ψ ⎞
⎥
⎢ x1 x2 ⋅ ⎜1+ ⋅δ
2 ⎟ x3
⎥
⎢
⎝ 2 ⎠
⎥
⎢ ⎛ Ψ ⎞
⎥
⎢x1
⋅ ⎜1+ ⋅δ1
⎟ x2 x3
⎥
⎢ ⎝ 2 ⎠
⎥
⎢
⎛ Ψ ⎞
⎥
⎢x1
⋅⎜1 − ⋅δ1
⎟ x2 x3
⎥
⎢ ⎝ 2 ⎠
⎥
⎢
⎛ Ψ ⎞
⎥
⎢ x1 x2 ⋅⎜1 − ⋅δ
2 ⎟ x ⎥
3
⎢
⎝ 2 ⎠
⎥
⎢
x1 ⋅ ( 1+ Ψ ⋅δ1 ) x2 ⋅( 1−
Ψ ⋅δ
2 ) x
⎥
⎢
3 ⎥
⎢ x1 ⋅( 1− Ψ ⋅δ1 ) x2 ⋅( 1−
Ψ ⋅δ
2 ) x3
⎥
⎢
⎥
⎢
x1 ⋅ ( 1+ Ψ ⋅δ1 ) x2 ⋅ ( 1+ Ψ ⋅δ 2 ) x3
⋅ ( 1+
Ψ ⋅δ
3 ) ⎥
⎢ x1 ⋅( 1− Ψ ⋅δ1 ) x2
⋅( 1+
Ψ ⋅δ 2 ) x3
⋅ ( 1+
Ψ ⋅δ
3 ) ⎥
⎢
⎥
⎢
⎛ Ψ ⎞
x1 x2 ⋅ 1+ ⋅δ 2 x3
⋅( 1−
Ψ ⋅δ
3 ) ⎥
⎢ ⎜ ⎟
⎝ 2 ⎠
⎥
⎢ ⎥
⎢ ⎛ Ψ ⎞
x1 ⋅ 1+ ⋅δ1 x2 x3
⋅( 1−
Ψ ⋅δ
⎥
⎢ ⎜ ⎟
3 )
⎝ 2 ⎠
⎥
⎢ ⎥
⎢ ⎛ Ψ ⎞
⎥
⎢
x1 ⋅⎜1 − ⋅δ1 ⎟ x2 x3
⋅( 1−
Ψ ⋅δ
3 )
⎝ 2 ⎠
⎥
⎢ ⎥
⎢ ⎛ Ψ ⎞
⎥
⎢ x1 x2 ⋅⎜1 − ⋅δ 2 ⎟ x3
⋅( 1−
Ψ ⋅δ
3 )
⎝ 2
⎥
⎢ ⎠
⎥
⎢ x1 ⋅ ( 1+ Ψ ⋅δ1 ) x2 ⋅( 1− Ψ ⋅δ 2 ) x3
⋅ ( 1+
Ψ ⋅δ
3 ) ⎥
⎢ ⎥
⎣ x1 ⋅( 1− Ψ ⋅δ1 ) x2 ⋅( 1− Ψ ⋅δ 2 ) x3
⋅ ( 1+
Ψ ⋅δ
3 ) ⎦
Plano de Experiência Hiper-Cubo
Anexo G – Coeficientes Planos de Experiência____________________________________
391
(G.9)
Para o plano de experiência Hiper-Cubo contendo duas variáveis aleatórias o
modelo mecânico deve ser consultado com os valores indicados na Eq. (G.10).
⎡ x1 x2
⎤
⎢
x ⋅ + Ψ ⋅ x ⋅ + Ψ ⋅
⎥
( 1 δ ) ( 1 δ )
( 1 δ ) ( 1 δ )
( 1 δ ) ( 1 δ )
( 1 δ ) ( 1 δ )
⎢ 1 1 2 2 ⎥
⎢x1 ⋅ + Ψ ⋅ 1 x2
⋅ − Ψ ⋅ ⎥ 2
⎢ ⎥
⎢x1 ⋅ − Ψ ⋅ 1 x2
⋅ + Ψ ⋅ 2 ⎥
⎢x ⋅ − Ψ ⋅ x ⋅ − Ψ ⋅ ⎥
⎣ 1 1 2 2 ⎦
Considerando três variáveis aleatórias a Eq. (G.10) deve ser reescrita como:
(G.10)