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    Plane Strain

    Uploaded by

    Ariella Claresta
    The document contains a series of mathematical equations relating to plane stress. The equations include terms with variables such as x, y, v representing displacements, Poisson's ratio, and other mechanical properties. The equations are part of a stress-strain relationship for analyzing how planar surfaces deform and distribute forces under loading.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd

    Plane Strain

    Uploaded by

    Ariella Claresta
    16 views4 pages
    The document contains a series of mathematical equations relating to plane stress. The equations include terms with variables such as x, y, v representing displacements, Poisson's ratio, and other mechanical properties. The equations are part of a stress-strain relationship for analyzing how planar surfaces deform and distribute forces under loading.

    Original Description:

    Plane Strain

    Copyright

    © © All Rights Reserved

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    DOCX, PDF, TXT or read online from Scribd

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    The document contains a series of mathematical equations relating to plane stress. The equations include terms with variables such as x, y, v representing displacements, Poisson's ratio, and other mechanical properties. The equations are part of a stress-strain relationship for analyzing how planar surfaces deform and distribute forces under loading.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    16 views4 pages

    Plane Strain

    Uploaded by

    Ariella Claresta
    The document contains a series of mathematical equations relating to plane stress. The equations include terms with variables such as x, y, v representing displacements, Poisson's ratio, and other mechanical properties. The equations are part of a stress-strain relationship for analyzing how planar surfaces deform and distribute forces under loading.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    You are on page 1of 4

    Plane Stresssss

    y232 x322 v 1 v x32 y23 x32 y23


    v 1 v 1 v x13 y23 x32 y21
    v 1
    y12 y23 x21 x32
    v 1
    v x21 y23 x32 y12
    v 1
    y31 y23 x13 x32
    2 2 2 2 2 2 2 2 2 2 2 2
    v x32 y23 x32 y23 v 1 x32 y23
    2 2 v 1
    v x32 y31 x13 y23
    v 1
    x13 x32 y21 y23
    v 1
    v x32 y12 x21 y23
    v 1
    x21 x32 y12 y23
    v 1
    2 2
    2 2 2 2 2 2 2 2 2 2

    v 1
    y31 y23 x13 x32 v x32 y31 x13 y23
    v 1
    y31 x13
    2 2 v 1
    v x13 y31 x13 y21
    v 1
    y12 y31 x21 x13
    v 1
    v x21 y31 x13 y12
    v 1
    0
    2 2 2 2 2 2 2 2 2
    x21
    2 2 2
    v 1 v 1
    x13 x32 y21 y23 v x13 y31 x13 y21 x13 y21 v x13 y12 x21 y21 x21 x13 y12 y21
    v 1 v 1 2 2 v 1 v 1
    y12 v x13 y23 x32 y21 2 2 2 2 2 2 2 2 2 2 2 2

    y12 y23 x21 x32 v 1 v x32 y12 x21 y23 y12 y31 x21 x13
    v 1 v 1
    v x13 y12 x21 y21
    v 1
    y12 x21
    2 2 v 1 v 1
    v x21 y12 x21 y12
    2 2 2 2 2 2 2 2 2 2 2 2

    v x21 y23 x32 y12 x21 x32 y12 y23 v x21 y31 x13 y12 x21 x13 y12 y21 v x21 y12 x21 y12 x21 y12
    v 1 v 1 v 1 v 1 v 1 2 2 v 1

    2 2 2 2 2 2 2 2 2 2 2 2

    Masih harus di kaliin 1/a1kuadrat sama yang di belakang E


    x322 x32 y23 x13 x32 x32 y21 x21 x32 x32 y12
    y23
    2
    y31 y23 y12 y23
    2 2 2 2 2 2
    2
    x32 y23
    x32
    2 y23 x13 y23
    x13 x32
    y21 y23 x21 y23
    x21 x32
    y12 y23
    2 2 2 2 2 2
    2

    x13 x32 y31 y23 x13 y23 x13 2 x13 y21 x21 x13 x13 y12
    0 2 y31 y12 y31

    x21
    2 2 2 2 2 E E 1

    2
    A1
    2 2 2
    y12 x32 y21 y21 y23 x13 y21 2 y21 x21 y21 y12 y21 1v A1
    x13 x32 x13 x21 x13
    2 2 2 2 2 2

    x21 x32 x21 y23 x21 x13 x21 y21 x21
    2
    2 x21 y12
    2 y12 y23 y12 y31 y12
    2 2 2 2 2

    x32 y12 y12 y23 x13 y12 y12 y21 x21 y12 2 y12
    2
    x21 x32 x21 x13 x21
    2 2 2 2 2 2
    Plane strraaiinnn

    1 v x322 ( 1 v) y232 v x32 y23 x32 y23 v


    1
    y31 y23 ( v 1) x13 x32 v
    1
    v x13 y23 x32 y21 v
    1
    y12 y23 ( v 1) x21 x32 v
    1
    v x21 y23 x32 y12 v
    1
    2
    2
    2 2 2 2
    v x32 y23 x32 y23 v 1 ( 1 v ) x32 v y23
    2 1 2
    v x32 y31 x13 y23 v
    1
    x13 x32 ( v 1) y21 y23 v
    1
    v x32 y12 x21 y23 v
    1
    x21 x32 ( v 1) y12 y23 v
    1

    2 2 2 2 2 2

    2 0 y31 y23 ( v 1) x13 x32 v v x32 y31 x13 y23 v 1 v x132 ( 1 v) y312 v x13 y31 x13 y21 v y12 y31 ( v 1) x21 x13 v v x21 y31 x13 y12 v
    1 1 1 1 1

    2 2 2 2 2 2
    x21
    1 1
    x13 x32 ( v 1) y21 y23 v v x13 y31 x13 y21 v ( 1 v ) x13 v y21 v x13 y12 x21 y21 v x21 x13 ( v 1) y12 y21 v
    1 1 2 1 2 1
    1 y12 v x13 y23 x32 y21 v
    2 2 2 2 2 2

    y12 y23 ( v 1) x21 x32 v 1
    v x32 y12 x21 y23 v
    1 1
    y12 y31 ( v 1) x21 x13 v
    v x13 y12 x21 y21 v
    1 1 2
    2 v x21 ( 1 v) y12
    2
    v x21 y12 x21 y12 v
    1
    2 2 2 2 2
    2
    v x21 y23 x32 y12 v x21 x32 ( v 1) y12 y23 v v x21 y31 x13 y12 v x21 x13 ( v 1) y12 y21 v v x21 y12 x21 y12 v ( 1 v ) x21 v y12
    1 1 1 1 1 2 1

    2 2 2 2 2 2

    Masih harus di kaliin 1/a1kuadrat sama yang di belakang E


    x322 x32 y23 x13 x32 x32 y21 x21 x32 x32 y12
    y23
    2
    y31 y23 y12 y23
    2 2 2 2 2 2
    2
    x32 y23
    x32
    2 y23 x13 y23
    x13 x32
    y21 y23 x21 y23
    x21 x32
    y12 y23
    2 2 2 2 2 2
    2

    x13 x32 y31 y23 x13 y23 x13 2 x13 y21 x21 x13 x13 y12
    0 2 y31 y12 y31

    x21
    2 2 2 2 2
    E
    y12 y21
    2
    y12 x32 y21 y21 y23 x13 y21 2 y21 x21 y21 2
    x13 x32 x13 x21 x13
    A1
    2 2 2 2 2 2

    x21 x32 x21 y23 x21 x13 x21 y21 x21
    2
    2 x21 y12
    2 y12 y23 y12 y31 y12
    2 2 2 2 2

    x32 y12 y12 y23 x13 y12 y12 y21 x21 y12 2 y12
    2
    x21 x32 x21 x13 x21
    2 2 2 2 2 2

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