Carregamento Mef
8
> > > > > > (1.1) (1.1) > > > > (1.2) (1.2) > > DEFINIÇÃO DO VETOR DE CARREGAMENTO DOS ELEMENTOS Q8 E Q9 MÉTODO DOS ELEMENTOS FINITOS Prof.: Sylvia Almeida - Aluno: Mayco Velasco de Sousa ESFORÇOS EQUIVALENTES ELEMENTO Q8 restart : with linalg : with plots : with LinearAlgebra : EQUAÇÃO DE DESLOCAMENTO PARA ELEMENTO Q8 u d c0 C c1$x C c2$y C c3$x 2 Cc4$ y 2 Cc5$x$y C c6$x 2 $y Cc7$x$y 2 u := c6 x 2 y Cc7 x y 2 C c3 x 2 Cc4 y 2 Cc5 x y Cc1 x Cc2 y C c0 APLICAÇÃO DAS CONDIÇÕES DE CONTORNO E MANIPULAÇÃO DA EQUAÇÃO DE DESLOCAMENTO A1 d subs x = K a, y = K b, u Ku1 : A2 d subs x = a, y = K b, u Ku2 : A3 d subs x = a, y = b, u K u3 : A4 d subs x = K a, y = b, u Ku4 : A5 d subs x = 0, y = K b, u Ku5 : A6 d subs x = a, y = 0, u K u6 : A7 d subs x = 0, y = b, u K u7 : A8 d subs x = K a, y = 0, u Ku8 : solve A1, A2, A3, A4, A5, A6, A7, A8 , c0, c1, c2, c3, c4, c5, c6, c7 c0 = K 1 4 u1 K 1 4 u2 K 1 4 u3 K 1 4 u4 C 1 2 u5 C 1 2 u7 C 1 2 u6 C 1 2 u8, c1
-
Upload
mayco-velasco -
Category
Documents
-
view
217 -
download
0
description
KJ
Transcript of Carregamento Mef
> >
> >
> >
(1.1)(1.1)
> >
> >
(1.2)(1.2)
> >
DEFINIÇÃO DO VETOR DE CARREGAMENTO DOS ELEMENTOS Q8 E Q9
MÉTODO DOS ELEMENTOS FINITOSProf.: Sylvia Almeida - Aluno: Mayco Velasco de Sousa
ESFORÇOS EQUIVALENTES ELEMENTO Q8
restart : with linalg : with plots : with LinearAlgebra :EQUAÇÃO DE DESLOCAMENTO PARA ELEMENTO Q8
ud c0Cc1$xCc2$yCc3$x2Cc4$y
2Cc5$x$yCc6$x
2$yCc7$x$y
2
u := c6 x2 yCc7 x y2Cc3 x2
Cc4 y2Cc5 x yCc1 xCc2 yCc0
APLICAÇÃO DAS CONDIÇÕES DE CONTORNO E MANIPULAÇÃO DA EQUAÇÃO DE DESLOCAMENTO
A1d subs x =Ka, y =Kb, uKu1 :A2d subs x = a, y =Kb, uKu2 :A3d subs x = a, y = b, uKu3 : A4d subs x =Ka, y = b, uKu4 : A5d subs x = 0, y =Kb, uKu5 : A6d subs x = a, y = 0, uKu6 : A7d subs x = 0, y = b, uKu7 : A8d subs x =Ka, y = 0, uKu8 :solve A1, A2, A3, A4, A5, A6, A7, A8 , c0, c1, c2, c3, c4, c5, c6, c7
c0 =K14
u1K14
u2K14
u3K14
u4C12
u5C12
u7C12
u6C12
u8, c1
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
(1.3)(1.3)
> >
> >
> >
> >
> >
=12
u6Ku8
a, c2 =K
12
u5Ku7
b, c3 =
14
u1Cu2Cu3Cu4K2 u5K2 u7
a2
, c4
=14
u1Cu2Cu3Cu4K2 u6K2 u8
b2
, c5 =14
u1Ku2Cu3Ku4
a b, c6 =
K14
u1Cu2Ku3Ku4K2 u5C2 u7
a2 b
, c7 =
K14
u1Ku2Ku3Cu4C2 u6K2 u8
a b2
assign %
ud collect u, u1, u2, u3, u4, u5, u6, u7, u8 :
FUNÇÕES DE INTERPOLAÇÃO
N 1 d factor coeff u, u1 : N 2 d factor coeff u, u2 : N 3 d factor coeff u, u3 : N 4 d factor coeff u, u4 : N 5 d factor coeff u, u5 : N 6 d factor coeff u, u6 : N 7 d factor coeff u, u7 : N 8 d factor coeff u, u8 :NdMatrix N 1 , 0, N 2 , 0, N 3 , 0, N 4 , 0 , N 5 , 0, N 6 , 0 , N 7 , 0, N 8 , 0 ,
0, N 1 , 0, N 2 , 0, N 3 , 0, N 4 , 0 , N 5 , 0, N 6 , 0 , N 7 , 0, N 8
N :=
2 x 16 Matrix
Data Type: anything
Storage: rectangular
Order: Fortran_order
ESFORÇOS NO LADO 1-2
q12dMatrix qx12 , qy12 :
eq1d evalm subs y =Kb, Transpose N &*q12 :
fe12d t$map eq1/int eq1, x =Ka ..a , eq1 :
ESFORÇOS NO LADO 2-3
q23dMatrix qx23 , qy23 :
eq2d evalm subs x = a, Transpose N &*q23 :
fe23d t$map eq2/int eq2, y =Kb ..b , eq2 :
> >
> >
> >
> >
> >
(1.4)(1.4)
> >
> >
> >
> >
> >
> >
> >
> >
ESFORÇOS NO LADO 3-4
q34dMatrix qx34 , qy34 :
eq3d evalm subs y = b, Transpose N &*q34 :
fe34d t$map eq3/int eq3, x =Ka ..a , eq3 :
ESFORÇOS NO LADO 4-1
q41dMatrix qx41 , qy41 :
eq4d evalm subs x =Ka, Transpose N &*q41 :
fe41d t$map eq4/int eq4, y =Kb ..b , eq4 :
ESFORÇOS EQUIVALENTES TOTAL DO ELEMENTO Q8
feq8d evalm fe12Cfe23Cfe34C fe41
> >
> >
> >
(1.4)(1.4)feq8 :=
13
t a qx12C13
t b qx41
13
t a qy12C13
t b qy41
13
t a qx12C13
t b qx23
13
t a qy12C13
t b qy23
13
t b qx23C13
t a qx34
13
t b qy23C13
t a qy34
13
t a qx34C13
t b qx41
13
t a qy34C13
t b qy41
43
t a qx12
43
t a qy12
43
t b qx23
43
t b qy23
43
t a qx34
43
t a qy34
43
t b qx41
43
t b qy41
ESFORÇOS EQUIVALENTES ELEMENTO Q9
restart : with linalg : with plots : with LinearAlgebra :
EQUAÇÃO DE DESLOCAMENTO PARA ELEMENTO Q9
> >
> >
(2.2)(2.2)
(2.1)(2.1)
> >
> >
> >
ud c0Cc1$xCc2$yCc3$x2Cc4$y
2Cc5$x$yCc6$x
2$yCc7$x$y
2Cc8$x
2$y
2
u := c8 x2 y2Cc6 x2 yCc7 x y2
Cc3 x2Cc4 y2
Cc5 x yCc1 xCc2 yCc0
APLICAÇÃO DAS CONDIÇÕES DE CONTORNO E MANIPULAÇÃO DA EQUAÇÃO DE DESLOCAMENTO
A1d subs x =Ka, y =Kb, uKu1 :A2d subs x = a, y =Kb, uKu2 :A3d subs x = a, y = b, uKu3 : A4d subs x =Ka, y = b, uKu4 : A5d subs x = 0, y =Kb, uKu5 : A6d subs x = a, y = 0, uKu6 : A7d subs x = 0, y = b, uKu7 : A8d subs x =Ka, y = 0, uKu8 : A9d subs x = 0, y = 0, uKu9 :solve A1, A2, A3, A4, A5, A6, A7, A8, A9 , c0, c1, c2, c3, c4, c5, c6, c7, c8
c0 = u9, c1 =12
u6Ku8
a, c2 =K
12
u5Ku7
b, c3 =
12
u6Cu8K2 u9
a2
, c4
=12
u5Cu7K2 u9
b2 , c5 =
14
u1Ku2Cu3Ku4
a b, c6 =
K14
u1Cu2Ku3Ku4K2 u5C2 u7
a2 b
, c7 =
K14
u1Ku2Ku3Cu4C2 u6K2 u8
a b2, c8
=14
u1Cu2Cu3Cu4K2 u5K2 u6K2 u7K2 u8C4 u9
a2 b2
assign %
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
(2.3)(2.3)
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
ud collect u, u1, u2, u3, u4, u5, u6, u7, u8 :
FUNÇÕES DE INTERPOLAÇÃO
N 1 d factor coeff u, u1 : N 2 d factor coeff u, u2 : N 3 d factor coeff u, u3 : N 4 d factor coeff u, u4 : N 5 d factor coeff u, u5 : N 6 d factor coeff u, u6 : N 7 d factor coeff u, u7 : N 8 d factor coeff u, u8 : N 9 d factor coeff u, u9 :
NdMatrix N 1 , 0, N 2 , 0, N 3 , 0, N 4 , 0 , N 5 , 0, N 6 , 0 , N 7 , 0, N 8 , 0,N 9 , 0 , 0, N 1 , 0, N 2 , 0, N 3 , 0, N 4 , 0 , N 5 , 0, N 6 , 0 , N 7 , 0, N 8 , 0,N 9
N :=
2 x 18 Matrix
Data Type: anything
Storage: rectangular
Order: Fortran_order
ESFORÇOS NO LADO 1-2
q12dMatrix qx12 , qy12 :
eq1d evalm subs y =Kb, Transpose N &*q12 :
fe12d t$map eq1/int eq1, x =Ka ..a , eq1 :ESFORÇOS NO LADO 2-3
q23dMatrix qx23 , qy23 :
eq2d evalm subs x = a, Transpose N &*q23 :
fe23d t$map eq2/int eq2, y =Kb ..b , eq2 :
ESFORÇOS NO LADO 3-4
q34dMatrix qx34 , qy34 :
eq3d evalm subs y = b, Transpose N &*q34 :
fe34d t$map eq3/int eq3, x =Ka ..a , eq3 :
ESFORÇOS NO LADO 4-1
q41dMatrix qx41 , qy41 :
(2.4)(2.4)
> >
> >
> >
> >
> >
eq4d evalm subs x =Ka, Transpose N &*q41 :
fe41d t$map eq4/int eq4, y =Kb ..b , eq4 :
ESFORÇOS EQUIVALENTES TOTAL DO ELEMENTO Q9
feq9d evalm fe12Cfe23Cfe34C fe41
> >
(2.4)(2.4)feq9 :=
13
t a qx12C13
t b qx41
13
t a qy12C13
t b qy41
13
t a qx12C13
t b qx23
13
t a qy12C13
t b qy23
13
t b qx23C13
t a qx34
13
t b qy23C13
t a qy34
13
t a qx34C13
t b qx41
13
t a qy34C13
t b qy41
43
t a qx12
43
t a qy12
43
t b qx23
43
t b qy23
43
t a qx34
43
t a qy34
43
t b qx41
43
t b qy41
0
0
