3
E e 1 := I e 1 := K e E e I e , x i , x f , ( 29 L x f x i - K 12 E e I e L 3 6 E e I e L 2 12 E e I e L 3 - 6 E e I e L 2 6 E e I e L 2 4 E e I e L 6 E e I e L 2 - 2 E e I e L 12 E e I e L 3 - 6 E e I e L 2 - 12 E e I e L 3 6 E e I e L 2 - 6 E e I e L 2 2 E e I e L 6 E e I e L 2 - 4 E e I e L := K 1 K e E e I e , 0 , 18 , ( 29 2.058 10 3 - × 0.019 2.058 - 10 3 - × 0.019 0.019 0.222 0.019 - 0.111 2.058 - 10 3 - × 0.019 - 2.058 10 3 - × 0.019 - 0.019 0.111 0.019 - 0.222 = := K 2 K e E e I e , 0 , 18 , ( 29 2.058 10 3 - × 0.019 2.058 - 10 3 - × 0.019 0.019 0.222 0.019 - 0.111 2.058 - 10 3 - × 0.019 - 2.058 10 3 - × 0.019 - 0.019 0.111 0.019 - 0.222 = := K 3 K e E e I e , 0 , 18 , ( 29 2.058 10 3 - × 0.019 2.058 - 10 3 - × 0.019 0.019 0.222 0.019 - 0.111 2.058 - 10 3 - × 0.019 - 2.058 10 3 - × 0.019 - 0.019 0.111 0.019 - 0.222 = :=

Ejemplo matricial Mathcad

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Matrices de rigidez de una estructura en mathcad

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  • Ee 1:= Ie 1:= Ke Ee Ie, xi, xf, ( ) L xf xi

    K

    12Ee Ie

    L3

    6Ee Ie

    L2

    12Ee Ie

    L3

    6Ee Ie

    L2

    6Ee Ie

    L2

    4Ee Ie

    L

    6Ee Ie

    L2

    2Ee Ie

    L

    12Ee Ie

    L3

    6Ee Ie

    L2

    12Ee Ie

    L3

    6Ee Ie

    L2

    6Ee Ie

    L2

    2Ee Ie

    L

    6Ee Ie

    L2

    4Ee Ie

    L

    :=

    K1 Ke Ee Ie, 0, 18, ( )2.058 10 3

    0.019

    2.058 10 30.019

    0.0190.222

    0.0190.111

    2.058 10 30.019

    2.058 10 30.019

    0.0190.111

    0.0190.222

    =:=

    K2 Ke Ee Ie, 0, 18, ( )2.058 10 3

    0.019

    2.058 10 30.019

    0.0190.222

    0.0190.111

    2.058 10 30.019

    2.058 10 30.019

    0.0190.111

    0.0190.222

    =:=

    K3 Ke Ee Ie, 0, 18, ( )2.058 10 3

    0.019

    2.058 10 30.019

    0.0190.222

    0.0190.111

    2.058 10 30.019

    2.058 10 30.019

    0.0190.111

    0.0190.222

    =:=

  • E1

    1

    234

    := E2

    3456

    := E3

    567

    8

    :=

    n 1 4..:= p 1 4..:=

    K3G 0 identity 8( ):= K2G 0 identity 8( ):=K1G 0 identity 8( ):=

    K1GE1n

    E1p,

    K1n p,

    := K2GE2n

    E2p,

    K2n p,

    := K3GE3n

    E3p,

    K3n p,

    :=

    KG K1G K2G+ K3G+:=

    KG

    2.058 10 30.019

    2.058 10 30.019

    00

    00

    0.0190.222

    0.0190.111

    00

    00

    2.058 10 30.019

    4.115 10 30

    2.058 10 30.019

    00

    0.0190.111

    00.444

    0.0190.111

    00

    00

    2.058 10 30.019

    4.115 10 30

    2.058 10 30.019

    00

    0.0190.111

    00.444

    0.0190.111

    00

    00

    2.058 10 30.019

    2.058 10 30.019

    00

    00

    0.0190.111

    0.0190.222

    =

    f stack augment submatrix KG 4, 4, 4, 4, ( ) submatrix KG 4, 4, 6, 6, ( ), ( ) augment submatrix KG 6, 6, 4, 4, ( ) submatrix KG 6, 6, 6, 6, ( ), ( ), ( ):= fem 8140.5

    :=

  • f0.4440.111

    0.1110.444

    =

    2

    3

    f 1 fem218.7145.8

    =:=

    v23m2

    v32m3

    K2

    02

    03

    1.3532.41.358.1

    =:=

    v12

    m1

    v21m2

    K1

    0002

    27812781

    +

    31.05105.322.95

    32.4

    =:=

    v34m3v43m4

    K3

    0300

    13.540.513.540.5

    +

    10.88.1

    16.256.7

    =:=