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

( 1 δ )
( 1 δ )
( 1 δ )
⎡ x1 x2 ⋅ + Ψ ⋅ 2 x3
⎤
⎢ ⎥
⎢ ⎛ Ψ ⎞ ⎛ Ψ ⎞
x1 ⋅ 1− ⋅δ1 x2 ⋅ 1+
⋅δ
2 x ⎥
3
⎢
⎜ ⎟ ⎜ ⎟
⎝ 2 ⎠ ⎝ 2 ⎠
⎥
⎢ ⎥
⎢ ⎛ Ψ ⎞ ⎛ Ψ ⎞
x1 ⋅ 1+ ⋅δ1 x2 ⋅ 1+
⋅δ
2 x ⎥
⎜ ⎟ ⎜ ⎟
3
⎢ ⎝ 2 ⎠ ⎝ 2 ⎠
⎥
⎢ ⎥
⎢ x1 ⋅ − Ψ ⋅ 1 x2 x3
⎥
⎢ x ⋅ + Ψ ⋅
x x ⎥
1 1 2 3
⎢ ⎥
⎢ ⎛ Ψ ⎞ ⎛ Ψ ⎞
⎥
⎢
x1 ⋅⎜1 − ⋅δ1 ⎟ x2 ⋅⎜1 − ⋅δ
2 ⎟ x3
⎝ 2 ⎠ ⎝ 2 ⎠
⎥
⎢ ⎥
⎢ ⎛ Ψ ⎞ ⎛ Ψ ⎞
⎥
⎢x1 ⋅ ⎜1+ ⋅δ1 ⎟ x2 ⋅⎜1 − ⋅δ
2 ⎟ x3
2 2
⎥
⎢ ⎝ ⎠ ⎝ ⎠
⎥
⎢ x1 x2 ⋅( 1−
Ψ ⋅δ
2 ) x3
⎥
⎢ ⎥
⎢
x1 x2 x3
⎥
⎢ x1 x2
⋅( 1+
Ψ ⋅δ 2 ) x3
⋅( 1−
Ψ ⋅δ
3 ) ⎥
⎢ ⎥
⎢ x1 x2 ⋅( 1− Ψ ⋅δ 2 ) x3
⋅( 1−
Ψ ⋅δ
3 ) ⎥
⎢ x1 ⋅ ( 1+ Ψ ⋅δ1 ) x2 x3
⋅( 1−
Ψ ⋅δ
3 ) ⎥
⎢ ⎥
⎢ x1 ⋅( 1− Ψ ⋅δ1 ) x2 x3
⋅( 1−
Ψ ⋅δ
3 ) ⎥
⎢
Ψ Ψ
⎥
⎢
⎛ ⎞ ⎛ ⎞
x1 ⋅ ⎜1+ ⋅δ1 ⎟ x2 ⋅ ⎜1+ ⋅δ 2 ⎟ x3
⋅ ( 1+
Ψ ⋅δ
3 ) ⎥
⎢ ⎝ 2 ⎠ ⎝ 2 ⎠
⎥
⎢ ⎥
⎢ ⎛ Ψ ⎞ ⎛ Ψ ⎞
x1 ⋅ ⎜1+ ⋅δ1 ⎟ x2 ⋅⎜1 − ⋅δ 2 ⎟ x3
⋅ ( 1+
Ψ ⋅δ
3 ) ⎥
⎢ ⎝ 2 ⎠ ⎝ 2 ⎠
⎥
⎢ ⎥
⎢ ⎛ Ψ ⎞ ⎛ Ψ ⎞
x1 ⋅⎜1 − ⋅δ1 ⎟ x2 ⋅ ⎜1+ ⋅δ 2 ⎟ x3
⋅ ( 1+
Ψ ⋅δ
3 ) ⎥
⎢ ⎝ 2 ⎠ ⎝ 2 ⎠
⎥
⎢ ⎥
⎢ ⎛ Ψ ⎞ ⎛ Ψ ⎞
x1
⋅ 1− ⋅δ1 x2 ⋅ 1− ⋅δ 2 x3
⋅ ( 1+
Ψ ⋅δ
3 ) ⎥
⎢ ⎜ ⎟ ⎜ ⎟
⎝ 2 ⎠ ⎝ 2 ⎠
⎥
⎢ ⎥
⎢⎣ x1 x2 x3
⋅( 1−
Ψ ⋅δ
3 ) ⎥⎦
Plano de Experiência 13 Pontos
Anexo G – Coeficientes Planos de Experiência____________________________________
387
(G.5)
Para o plano de experiência 13 pontos considerando duas variáveis aleatórias o
modelo mecânico deve ser consultado por meio dos termos mostrados na Eq. (G.6).