Cours Mecanique Du Solide

download Cours Mecanique Du Solide

of 59

Transcript of Cours Mecanique Du Solide

  • 8/6/2019 Cours Mecanique Du Solide

    1/59

    " !$ #& %& ( '0 )2 14 36 57 )2 9 8A @B 8C %E D" !$ 14 !$ #& %E " FG 1" H

    I( PR QT SV UX W` Yb ad c` SV eg fi hp W` qs rt hv uw c` ai e YR xy cb WE e w e r d " a Yb a hp W r e " U r qi S hv ad v e

    I( Pp I( P R ( SV e ad c` S fi hp W` qs rt hv uw c` a as r r ( SV e ad c` S Y ` W` UX hv uw c` a

    I( Pp I( Pp I( P X rt hv W Yb a r ( SV e ad c` S

    X y jl kn mo X l o n 7 z X X kC jl C {} |~ i o V o kn m y n y jl o o

    o o d zn y X A zo ( i X |~ i X l s zn o n l m i l ` |~ n l A n mo o s zn o n l mA d o o o ( o s zn o n l m z z kn y kn m V y

    l i ( V i o k jl l s n n i A y s zn o n l m mo z V X i X n w w o l g y l n o z

    z s zn o n l mo C l o o d zn y l o mo o n l m jl i y kn y kn n i o jl mo k j X zn y n l |~ i l o i

    mo k l V i o

    6 0

    y n i A n B

    0

    6

    iA ( p

    ad " Ul SV uw c` a `

    |~ n l i mo n m 7 zn y n n i y ` z V m zn o kn m y y i X jl n i o A j l o mo o n l mC

    A

    B b w " p t w ` v s w ` d

    I( Pp I( P ~ P R ( SV e ad c` S fi hp W` qs rt hv uw c` a

    jl k X l b y o mo o n l m zn X kn y i X j o n A 7 jl R o o

    0

    X n b jl R z n i mo j X n m y g jX V X b l mo k kn mo n i y n

    |( V m

    T

    g

    o X

    o i C y o y

    v 7

    C

    g i y o y

    6

    A X p

    E

    i mo n mA i X g

    y

    A 0

    B b w " p t w ` v s w ` d

    I( Pp I( Py P R ( SV e ad c` S Y ` W` UX hv uw c` a

  • 8/6/2019 Cours Mecanique Du Solide

    2/59

    jl k X l y T o mo o n l m j d ( V g y i X j o n " 7 jl T o o T

    }

    n jl z n i mo j X n m y g jX V X g l

    mo k kn mo n i y n

    |( V m

    g

    o X

    o i X y

    2 0

    v 7

    g i X y

    0

    6

    A X p

    E

    i mo n mA i X g

    yA 0

    B b w " p t w ` v s w ` d

    I( Pp I( P w P

    ad v U rt hv W ad W r SV a v a r ( SV e ad c` S fi hp W` qs rt hv uw c` a as r v a r ( SV e ad c` S Y ` W` UX hv uw c` a

    n V y n i mo C mo k l V i o j d ( V g y i X

    n mo k l V i o zn X kn y i X

    2

    n V y n i mo C y n i A j d ( V g y i X g

    n y n i zn X kn y i X

    p G l |~ i A |l m y m w l y C jX V X y

    mo k kn mo n i y n b j kn X jl

    " !

    #

    iA ( % $

    #

    iA

    $

    iA ( p

    ' &

    ) (

    s z 0 l |~ i i X n y z X i X 2 1

    a

    jX V X

    j 3

    w

    T

    jl X z

    T

    C

    4n

    6 5z |( V m y zn l y n mo i o kn mo o V i o

    n m z l w 0 5l jX V X

    7

    n C z C l w 9 80 @ 7 |~ n l n mo l y C jX V X

    " !

    I( P ~ PB A W` ai SD C hv a fi hp W` qs rt hv uw c` a

    E

    kn X n mG F y zn X kn y i X C j o n 7 jX V X l mo k kn mo n i y n

    C

    H

    0

    P IR Q

    S

    2 T

    U

    7 V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    3/59

    I( Py P ` qi ( SV d " ai e Yb a dR h

    I( Py Pp I( P

    q qi SV ad W rt hv ad b Ul St w fs ad W r S hv uw c` a

    Emo k kn mo n i y n ( V m z n i m y i X

    j o n R 7

    !mo n V s n n i V C mo k kn mo n i y n d j kn X jl

    y mo k kn mo n i y n d j m F X

    n n m V X V y |( V m m V |l |~ m A

    ( C i l g |l y i X C i X y s zn o n l m mo V y jl

    |( V m m V |l |~ m A

    C

    !

    W e qi uw c` ad W` fs ai e

    C

    I( Py P ~ P ` qi ( SV d " a Yb a dR h

    c S v a " " ad W rg fi hp W` qs rt hv uw c` a

    iA ( p

    "

    d $ #

    v

    6

    d X p

    mC

    p 7

    C

    C

    jl X z

    C

    6

    X

    6

    p

    C

    mC

    6

    X

    6

    d p

    j 3 y X k mo n jl %' &) (1 03 2 5 4 |~ l m y n i A zn X kn y i X C n l |~ i jX V X y mo k kn mo n i y n b j kn X jl

    C

    ad " Ul SV uw c` a

    y X k mo n jl 6 %' &) (1 03 2 5 4 |~ l m y n i zn X kn y i X A kn V i d m V ~ i X n y i X A o y mo k kn mo n i y n j kn X jl

    l n |( V m y zn l y n m |~ l m

    8

    3

    X jl X z

    j 3 y n i A zn X kn y i X C jX V X

    X jl kn |~ n X jX V i A j |~ i 3 y z V y zn l y

    I( Py Py P ` qi ( SV d " a Yb a dR h

    c S v a " " ad W rg Y` ` W` UX hv uw c` a

    iA (

    "

    d $ # p

    v

    6

    d X p

    mC

    p 7

    jl X z

    6

    X

    6

    p

    7 V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    4/59

    mC

    6

    X

    6

    d p

    j 3 y X k mo n jl %' &) (1 03 2 5 4 |~ l m y n i A j d ( V g y i X C n l |~ i jX V X y mo k kn mo n i y n ` j kn X jl

    ad " Ul SV uw c` a

    y R X k mo n jl%' &) (1 03 2 5 4

    |~ l mb y R n i j d ( V g y i X kn V i d m V i X n y i X o b y R mo k kn mo n i y n l j kn X jl

    l n |( V m y zn l y n m |~ l m

    8

    3

    X jl X z

    j 3 y n i A j d ( V g y i X C jX V X

    X jl kn |~ n X jX V i j |~ i 3 y C z V y zn l y

    I( Py P w P ` qi ( SV d " a Yb a dR h

    c S x qd W` ai SD C hv a fi hp W` qs rt hv uw c` a

    E

    kn X n mG F y zn X kn y i X C j o n jX V X y mo k kn mo n i y n

    C

    H

    P IR Q

    S

    2 T

    U

    IR Q

    S

    "

    C

    #

    T

    U

    IR Q

    S

    T

    U

    Q

    S

    T

    v

    C

    mC

    P IQ

    S

    T

    U

    H

    v

    6

    p

    j 3 y X k mo n jl %' &) (1 03 2 5 4

    |~ l m 7 kn X n mG F y C zn X kn y i X

    H

    H

    Q

    S

    2 T

    ~ P

    !

    hp W` qd " U rt hv uw c` a YR xy cb W e p hv Yb a

    ~ Pp I( PR QT SV UX W` Yb ad c` SV e fi hp W` qs rt hv uw c` ai e YR xy cb W e p hv Yb a

    X y jl kn mo X l o y jl

    w jl o o B n jl z n i mo j X n m y n l |~ i i X n y z X i X jl

    jl R o o "

    R ( SV e ad c` S fi hp W` qs rt hv uw c` a Yb UX W` e cb W SV q qi SV ad W rt hv ad YR x qs rt c Yb a

    g

    o X

    o i C y o y

    p

    g i y o y

    A p

    ad " Ul SV uw c` a

    yA 0

    C

    s zC n B jl n 6 5T |~ i o

    uw c` ad v fs W uw c` ai e

    R ( SV e ad c` S Y` ` W` UX hv uw c` a Yb UX W` e cb W SV q qi SV ad W rt hv ad YR x qs rt c Yb a

    g

    o X

    o i X y

    2

    p

    g i X y

    A

    A p

    V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    5/59

    ad " Ul SV uw c` a

    yA 0

    s zC n B jl n 6 5T |~ i o

    uw c` ad v fs W uw c` ai e

    ad v U rt hv W ad W r SV a

    as r

    kn V i l |~ i i X n y z X i X |l m y m w l y C jX V X

    T

    C

    fs Ul e b Ul St rt hv fi cb p hv ai SV eT

    ` 0 5l jX V X

    ` 80 7 |~ n l n mo l y C jX V X

    " !

    ~ P ~ P R ( SV e ad c` S fi hp W` qd " U rt hv uw c` a c r ( SV e ad c` S Yb ai e ` h r ai e e ai e

    X y jl kn mo X l o y jl

    R l y C jX V X y mo k kn mo n i y n b j kn X jl

    n

    l mo k kn mo n i y n y k

    g j m F X l |~ i T i X n

    z X i X

    j o y jl

    E

    y jl z g |~ y jl d o o o j l |~ i i X n y z X i X

    j o y jl X jl l X

    " !$ #

    m kn V i l |~ i 5l jX V X

    j 3

    n

    s z

    & %( '0 ) 1 2 4 3

    5

    V m z X o k i X n i l y d o o o jl |~ i o j l o y jl s kn m ( n i y w z V m zn o kn m y y i X jl n i o A j l o mo o n l m

    yA 0

    j 3 7 |~ n l jl k X l m y A o mo o n l m zn X kn V y i X C j l o y jl jX V X l mo k kn mo n i y n

    |( V m o kn y kn n i o jl mo k j X zn y

    n

    4 6C 8 7

    n

    o o

    s

    l

    @ 9B A" C

    E D

    n

    FH G

    P I

    b w " p t

    y

    X

    o X n

    G

    I& n

    ~ Py PB A W` ai SD C hv a fi hp W` qs rt hv uw c` a YR xy cb WE e p hv Yb a Yb UX W` e

    H

    Q

    S

    T

    p

    Q V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    6/59

    ~ P w P ` qi ( SV d " ai e Yb a dR h

    ~ P w Pp I( P A c S v a " " ad W rg fi hp W` qs rt hv uw c` a Yb UX W` e

    C

    s z

    n i A zn X kn y i X n jX V X y mo k kn mo n i y n ( V m z n i m y i X

    ~ P w P ~ P A c S v a " " ad W rg Y` ` W` UX hv uw c` a Yb UX W` e

    s zg

    n i A j d ( V g y i X C n jX V X

    ~ P w Py P A c S x qd W` ai SD C hv a fi hp W` qs rt hv uw c` a Yb UX W` e

    H

    H

    Q

    S

    2 T

    s zH'

    kn X n mG F

    y C zn X kn y i X j o y jl C jX V X

    ~ P ~ P " ad W r YR xy hp W` ai St rt hv a YR xy cb W0 e p hv Yb a b Ul S SV Ul b ( St r cb W

    U

    a

    T

    s z j y V X z n i mo

    n |~ i

    uw c` ad v fs W uw c` a

    j o y jl

    ~ P!

    P

    ` qi ( SV d " a YR x " b$ # d& %

    E

    n i j X n m y j l o y jl |( V m m V |l |~ m R A l 5l

    T

    s z( '

    |l mo0 )

    zn y m XF

    s ( V y j l |~ i

    i X n y z X i X

    j o y jl

    2 1

    |l mo 0 ) zn y m X Fs ( V jl l m 7 5l

    1

    R 5l

    b Ul SV UX p v d v a2 3 as r b Ul e e UX W r b Ul S

    g

    4

    4$ 5

    6

    7

    8

    7

    5

    j 3

    9

    1

    l

    1

    T

    l

    9

    1

    T

    7 X

    1

    T

    B

    S

    l

    9

    1

    l

    1

    mC

    9

    1

    T T

    X

    o X n i o

    1

    l

    1

    T

    A @

    jl X z

    A @

    T

    S

    9

    1

    X

    1

    B V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    7/59

    V y zn l y X

    9

    1

    l

    1

    9

    1

    1

    n G

    mC

    9

    1

    V

    1

    9

    1

    9

    1

    X o

    l

    jl X z

    9

    1

    X

    1

    j 3 y X k mo n j 4 (1 0

    A @

    T

    ~ P P p hv Yb a" ad WG SV X r U rt hv W0 UX cw r c S YR xy cb W U

    a

    1

    a Yb UX W` e

    cb W SV q qi SV ad W rt hv ad

    ~ P Pp I( P " ad W r fi hp W` qs rt hv uw c` a ad W cb W hp W r Yb a x U

    a

    A

    m l |~ i C jl

    x U

    a Yb a SV X r U rt hv W

    j " o y jl jl X z

    j y V X z n i mo n z X V i o p kn V i l |~ i

    i X n y z X i X C j o y jl

    ! 4

    X z

    T E

    |l X l

    1

    a

    jX V X y mo k kn mo n i y n b j kn X jl

    l j 3

    !

    "

    #

    jl X z

    A

    A

    A

    A

    A B

    A

    A

    y n i |l mo0 )

    zn y m X Fs ( V y jl l m 7 5l

    n

    $

    y s zn o n l m l l V mo C |~ m o k |( V m

    4X z

    A

    % $

    $

    ' &

    s

    j 3

    T

    T

    I

    T

    U

    jl X z

    ) (

    s z

    ) (

    1 02 03 0

    z g |~ V i o C j n i A zn X kn y i X n G |~ n m |~ n X j y zn l V mo 7 5l jl mo

    y

    j o y jl

    fs Ul e b Ul St rt hv fi cb p hv ai SV e hp W r qi SV ai e e UX W r e

    4V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    8/59

    Id ai S fs Ul e

    y o y jl

    v UX W ai SV ad W` Y hv fi cb v UX hv SV a

    n

    b Ul e e UX W r b Ul S

    V y mo 9 8 |l mo 0 ) zn y m X Fs ( V y

    jl

    r cw r hp W r

    j o y jl n |( V m l o g

    ) (

    l d " a fs Ul e

    l 5l jl

    e " qs r S hv a

    V o kn m y n ~ j o y jl z j mo o l |~ i j o y jl s z m mo |~ X j

    l |~ i

    1

    j o y jl o n y i X C o o j jl 4 A k Fi V y g g o o j jl

    1

    n

    V l

    2 1 1

    s z

    n

    2 1

    mo |~ zn s n n i y |l mo 0 ) zn y X m X Fs ( V y A jl C n

    1

    l m

    j 3 z i m l l y jl n

    1

    jX V X y C z V y zn l ` jl

    ( C

    s B

    1

    V X

    1 1 1

    jl X z

    ) (

    ~ P P ~ PB A W` ai SD C hv a fi hp W` qs rt hv uw c` a

    E kn X n mG F y zn X kn y i X C j l o y jl

    ad W SV X r U rt hv W UX cw r c S YR xy cb WE U

    a

    1

    a

    jX V X l mo k kn mo n i y n b j kn X jl

    C

    H

    Q

    S

    T

    p

    mC

    E

    n i mo d j l y V i |l mo 0 ) zn y m X Fs ( V y jl C l m 7 5l jl mo V y

    l V l m

    H

    Q

    S

    7 A

    T

    T

    S

    T

    7

    j 3

    H

    Q

    S

    T

    ~ P P p hv Yb a ad W SV X r U rt hv W UX cw r c S YR xy cb W U

    a Yb a Y hv SV ai f rt hv W

    1

    a

    5l n g |l y z n mo z V X Fs n X C mo l V i A l m l 5l

    ! "

    $ #

    %

    V y zn l y X y n i A zn X kn y i X C j z n mo z V n l |~ i jX V X y mo k kn mo n i y n

    &

    ( ' 0 )

    1

    5

    l m z n X V |l |l y i X n m y X k mo n jl %' &) (1 03 2 5 4 |~ l m y n i A zn X kn y i X

    C

    m l |~ i jl A 7 5l jl A mo V y

    )

    5l jX V X y mo k kn mo n i y n ( V m z n i m y i X

    |l X A

    )

    l 5l

    jl d kn m y V o kn m y n ` j z n mo z V w ( z i l w jl l X C j V |l mo y |( V m D F m V |l X

    ~ P Pp I

    $ 2

    3 V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    9/59

    n |( V m l o g

    $ 2

    C

    V y zn l y X X j V l mo C |( V m l 7 kn X n mG F y C zn X kn y i X C j z n mo z V 1

    4

    V |l mo y X k mo n jl %' &) (1 03 2 5 4

    H

    H

    Q

    S

    s T

    mA

    )

    cb W U

    a Yb a SV X r U rt hv W

    1

    a Yb UX W` e

    jl X z X j V |l mo y |( V m D F m V |l X

    ~ P P ~ P

    H

    Q

    S

    $ 2 T

    Q

    S

    s T

    V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    10/59

    !" #% $' &( 0 )2 13 $ #

    I( P R ( SV e ad c` S fi hp W` qs rt hv uw c` a as rg r ( SV e ad c` S Y ` W` UX hv uw c` a

    I( Pp I( P5 4 q

    1

    Wb h rt hv W e

    X y jl kn mo X l o y jl

    w jl o o B n jl z n i mo j X n m y n l |~ i i X n y z X i X jl

    jl R o o "

    R ( SV e ad c` S fi hp W` qs rt hv uw c` a Yb UX W` e cb W SV q qi SV ad W rt hv ad

    g

    o X

    o i C y o y

    p

    C

    g i y o y

    A p

    ad " Ul SV uw c` a

    y

    A 0

    C

    s zC n B jl n 6 5T |~ i o

    uw c` ad v fs W uw c` ai e

    R ( SV e ad c` S Y ` W` UX hv uw c` a Yb UX W` e

    g

    o X

    o i X y

    2

    p

    g i X y

    A

    A p

    ad " Ul SV uw c` a

    y

    A 0

    s zC n B jl n 6 5T |~ i o

    uw c` ad v fs W uw c` ai e

    I( P ~ P

    ad v U rt hv W ad W r SV a

    as r

    kn V i l |~ i i X n y z X i X |l m y m w l y C jX V X

    2

    T

    C

    fs Ul e b Ul St rt hv fi cb p hv ai SV eT

    ` 0 5l jX V X

    ` 80 7 |~ n l n mo l y C jX V X

    " !

    ~ P R ( SV e ad c` S fi hp W` qd " U rt hv uw c` a cE r ( SV e ad c` S Yb ai e ` h r ai e e ai e

    4 6C 7

    n

    o o

    s

    l

    9B A" C

    E D

    n

    F G

    P I

    b w " p t p v b

    PB A W` ai SD C hv a fi hp W` qs rt hv uw c` a YR xy cb W e p hv Yb a Yb UX W` e

    H

    Q

    S

    2 T

    p

    7 6 V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    11/59

    w P ` qi ( SV d " ai e Yb a dR h

    w Pp I( P A c S v a " " ad W rg fi hp W` qs rt hv uw c` a Yb UX W` e

    C

    s z

    n i zn X kn y i X C n jX V X y mo k kn mo n i y n ( V m z n i m y i X

    v mo k kn mo n i y n b j m F X n m V X V y

    jX V X

    " !

    w P ~ P A c S v a " " ad W rg Y` ` W` UX hv uw c` a Yb UX W` e

    s zg

    n i A j d ( V g y i X C n jX V X

    w Py P A c S x qd W` ai SD C hv a fi hp W` qs rt hv uw c` a Yb UX W` e

    H

    H

    Q

    S

    2 T

    s z

    H'

    kn X n mG F y C zn X kn y i X j o y jl C jX V X

    ~ P " ad W r YR xy hp W` ai St rt hv a YR xy cb WE e p hv Yb a b Ul S SV Ul b ( St r " cb W U

    a

    T

    s z j y V X z C n i mo

    n |~ i

    uw c` ad v fs W uw c` a

    j o y jl

    P ` qi ( SV d " a YR x "b$ # d& %

    A @

    T

    s z

    1

    5l |( V m V y n y

    n |( o V i |( V m g

    j y V X z C n i mo

    n

    1

    P p hv Yb a ad W SV X r U rt hv W UX cw r c S YR xy cb W U

    a

    1

    a Yb UX W` e

    Pp I( P " ad W r fi hp W` qs rt hv uw c` a ad W cb W hp W r Yb a

    ) (

    fs Ul e b Ul St rt hv fi cb p hv ai SV e hp W r qi SV ai e e UX W r e

    A l 5l jl

    e " qs r S hv a

    j o y jl ` y o y jl

    v UX W ai SV ad W` Y hv fi cb v UX hv SV a

    n

    b Ul e e UX W r b Ul S

    V y mo

    ) (i l 7

    P ~ PB A W` ai SD C hv a fi hp W` qs rt hv uw c` a

    H

    Q

    S

    T

    V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    12/59

    # # $' &( 13 3 ) $ # 1 !" # $' &(

    # 3 # 1

    ai SV fi hv fs a I " ad W r fi hp W` qs rt hv uw c` a YR xy cb W ad W` e ad v a

    Yb a Yb ad c

    hp W r e

    4

    n 6 5 |~ i o V o kn m y n y y jl n i y i X n T jl o o

    " ( o i mo n y k A |( V m l X Fs jl C o o C X k F Fs D l y n A jl

    y F X n l m V o jl kn |l z l m l z n mo zn y g jl z n i mo n

    jl m s V d n R C Fs A A |~ n l o zn y n m V l o l m j l 5l

    |( o V i |( V m n |~ n m |~ n X j y zn l V mo V |l V j z n mo zn y

    !

    "

    #% $' &) (1 02 &) 31 46 58 72 3 72 31 0@ 9 AB $' C2 D) E1 4F 3H GI 7@ DQ PS R1 4F 31 CU TF 3H G6 5V &W $ 4F RH GX 02 &Y T` $' CU TF 3a (1 DY C R1 TX D) bU 0 3 31 Tc &) 3d Af eg Af 31 CU Th (1 DY C R1 TX D) bU 0 3 31 Cp i 7@ 0q GX r@ GX TF E1 Af 3d sI t

    31 Cv uw eg C (1 TX D) eg C 72 3H GI $' C2 xy &) 3H G 52 31 T &) 31 02 4F G 72 R1 4X DY RH 3H G6

    c U ' U q k jm lo n jo 8 lk m n

    Cf 31 C 7@ 02 &) 3c 72 eg 02 2 &) 3c 3H GX T (H eg C GX TX DY TX 0 Rc 72 3 72 31 0@ 9f V $' 4X 4F 3H G% ih s 31 T

    sI t D) 72 31 CU TX D) bU 0 3H G eg Af eg x E1 C 3H G6 5 72 3v AB $g GF GF 3{ z| 5 72 3{ &) eg C2 xy 0 31 02 4

    }y ~

    31 Td $' 4X TX D) (1 02 &) RH 3H G 31 C| s 3H Gd 72 31 0@ 9 V $' 4X 4F 3H Gd GF eg CU T $g GX TX 4F 31 DY CU TF 3H G

    GF 3c 72 R1 2 &W $g (H 31 4% 7 $' C G &) 3 2 &W $' C{ 31 4X TX D) (6 $' & i V 31 T &) 31 02 4F G DY C (1 &Y DQ

    CV $' D) GF eg C G GF eg CU T 72 R C2 D) 3H G V $' 4% &) 3H G $' C2 xy &) 3H G 31 T% p V $' 4 4` $' 2 eg 4X T

    &W $a 31 4X TX D) (6 $' &) 3B i S % 72 3H GF (H 31 C 7 $' CU TF 3y

    #% $' &) (1 02 &) 31 4 &) 3 Af eg Af 31 CU T (1 DY C R1 TX D) bU 0 3 31 Cv i 31 T & R1 C 31 4X xy D) 3 (1 DY C R1 TX D) bU 0 3 72 3 (H 3 31 C 7@ 02 &) 3 72 eg 02 2 &) 3y c Cf 4` $' 2 31 &Y &) 3 &) 3 Af eg Af 31 CU T 7S DY C 31 4

    TX D) 3h 7S 02 C 3h V $' 4X 4F 3 72 3 &) eg C2 xy 0 31 02 4

    }y ~

    V $' 4 4 $' 2 eg 4X T G $ Af RH 7@ DW $' TX 4X D) (H 3 z

    ~

    c U ' U q m n | 8 6 f U k lk U f j ) lo k jm lo n

    c C (H eg C GX D) 72 E1 4F 3v 02 C 31 C 7@ 02 &) 3v GX 0 GX 31 C 7@ 0 31 C 02 C eg DY CU Ta 2 92 3y 5

    (H eg C GX TX DY TX 0 R 7S 02 C 3 TX DY x 3| ih s 72 3q AB $g GF GF 3 C R1 xy &Y DY x 36 $' 2 &) 3| 31 Tv 72 3

    &) eg C2 xy 0 31 02 4B &W $g bU 0 31 &Y &) 3 3H GX T GF eg 0 72 Rv 02 C & eg Af eg x E1 C 3y 5 72 3

    AB $g GF GF 3 z| 5@ 31 C uw eg 4X Af 3h 72 3h 72 31 A DQ (H 31 4F (1 &) 3 72 3 4` $H r eg C 52 72 3 AB $

    C2 D) E1 4F 3 bU 0 3I &W $ TX DY x 3d ih s (H eg C GX TX DY TX 0 3 &) 3I 4` $H r eg C 7@ 0 72 31 A DQ (H 31 4F (1 &) 3

    s 3H GX Ta $' 0 (H 31 CU TX 4F 3{ 72 3f & $' 4F (B tf k c C 4F 31 E1 4F 3f &W $v ey GX DY TX D) eg C

    7@ 0 31 C 7@ 02 &) 3B V $' 4 & $' C2 xy &) 3{ bU 0 3 u $' DY T &W $ TX DY x 3v ih s $H 3H (B &W $

    31 4X TX D) (6 $' &) 3d 72 3H GF (H 31 C 7 $' CU TF 3y

    1 F 1 X Y 1 W F H X 2 Y ` ' U F 1 Y 1 X ) U y 2 ) f g f 1 U c 1 Y 1 X ) U d 1 q @ ) f g f 1 U c @ V ' ) U d 1 q 1 1 1 X y ) d 1 Y

    X ) U h @ 1 @ 2 ) d 1 v w g 1 X ) g 2 d 1 2 d F H 2 1 X Y H H 6

    6 % g

  • 8/6/2019 Cours Mecanique Du Solide

    13/59

    3 @2 # ! ( '0 )2 1 36 57 )2 9 8A @B 8C %E D" !$ 14 !$ #& %E " FG 1" H

    I( P5 4T ` W` UX hv uw c` a YR xy cb W ~ w e r d " a Yb a hp W r e " U r qi S hv ad v e

    I( Pp I( P R ( SV e ad c` SV eg Yb ai e Ul f rt hv W e " qi fs UX Wb hv uw c` ai e

    I( Pp I( Pp I( P5 4 q

    1

    Wb h rt hv W

    7 R l o n jl {} |~ i o V o kn m y n y jl o o n o l g y l X A mo z

    D

    s z

    D

    s zn o n l m mo z V |l |l y i X k g |( V m 7 5 o kn m y n l m l mC n

    s zn o n l m mo z V |l |l y i X k g |( V m l m

    T jl k X l y o mo o n l m jl zn y X k z V l y i X 5l n mo z k l m y A o n 7 |( V m o kn y kn n i o jl mo k j X zn y n l

    |~ i

    T

    0

    D

    0

    iA X

    D

    6

    iA (

    4

    V |l mo y |l m X zn |~ C j zn y n jl mo k zn y

    i mo X i X

    iA X

    V l i l y C jl n 6 5 jl n 6 5 1

    5

    l m z n X z X y jl kn mo X A jl n 6 5T |~ i o n

    T

    j o n 7 n z V y zn l y X

    v lA

    T! "

    v lA

    T

    # "2 T

    lA lA

    T

    T! # "

    o

    "2 T T! "

    X l

    T

    T! "

    7 X l

    T

    T! # "

    jl X z

    D

    0

    D

    $

    D

    0

    6

    iA (

    D

    I( Pp I( P ~ P R ( SV e ad c` SV eg b Ul St rt hv fi cb p hv ai SV e

    7

  • 8/6/2019 Cours Mecanique Du Solide

    14/59

    Q p hv e e ad c` S

    l l o mo o n l m jl i mo k l V i o jl mo z

    0

    D

    n jl i y n i n l |~ i

    i l 7

    ad " Ul SV uw c` a

    y |~ i w |( l l y i X n l y ` z V m zn o kn m y y i X jl n i o j l o mo o n l m X jl l X

    T y E

    E

    s

    s

    y i

    y

    !

    c v a

    l l o mo o n l m jl i mo k l V i o jl mo z

    4

    V X z z C

    T E

    E

    n i A j l z l |l y l X jl kn |~ n X jX V i j |~ i 3 y z V y zn l y

    I( P ~ P C S hp W` fi hv a W Yb UX " ad W r UX R Yb a v U Y` ` W` UX hv uw c` a Yb UX W` e cb W SV q qi SV ad W rt hv ad e C( UX p hp v qi ad W

    I( P ~ Pp I( PB A W` W fs q

    4V X l mo k kn mo n i y n

    C( UX p hp v qi ad W

    d y o mo o n l m j d ( V g y i X

    k Fi V ` V o mo o n l m jl zn y X k z V l y i X V |l |l y i X k

    l m y o n 7

    7

    7

    D

    $

    D

    I( P ~ P ~ P

    !

    W e qi uw c` ad W` fs ai e

    4 V |l mo y |l m X zn |~ X jX V n i V b jl j d ( V g y i X C jX V X l mo k kn mo n i y n

    C( UX p hp v qi ad W

    w n mo k l o g

    y T X k mo n jl T mo k l V i o zn X kn y i X v n kn V i mo |~ zn s n n i o o n g y z n i mo j X n m y j

    o n 7

    !

    D

    0

    D

    y X k mo n j n i A zn X kn y i X C n l |~ i B

    T

    C

    $

    D

    6

    iA (

    D

    I( Py P ` qi ( SV d " a Y c " " ad W rg fi hp W` qs rt hv uw c` a ad W

    Yb UX W` e v a SV q qi SV ad W rt hv ad b Ul St w fs ad W r S hv uw c` a

    E

    X k mo n C j n i A zn X kn y i X C n jX V X y mo k kn mo n i y n b j kn X jl

    C( UX p hp v qi ad W

    X C

    D

    m j V |l mo y X k mo n C jl ' %' &) (1 03 2 5 4 |~ l m y n i A zn X kn y i X

    j 3

    4

    V |l mo y ` jl jl kn m V y j l s zn o n l m

    V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    15/59

    kn V i A n m V X V y |( V m m V |l |~ m A

    5

    V m z X o k i X n i X y X k mo n j n i A zn X kn y i X C n jX V X y mo k kn mo n i y n ( V m z n i m y i X k zn m

    D

    ad " Ul SV uw c` a"

    mo k l V ( kn V i A d m V ` i X y C mo k kn mo n i y n ( V m z n i m y i X

    o R Fi V y k n X w ( z C i l w i mo

    i X y n i o

    ad W

    jl mo z j n i m y X n n i n jl 6 & 2 5 & 2 C jX V X

    o i i l y n C

    D

    d X

    D

    p

    d X

    D

    p

    s z

    D

    p R 7 z z kn y kn m V y j n i m y X n n i j |~ i jX V X

    D

    p

    X

    j 3

    D

    #

    d % $

    1

    &

    X o

    n i o

    1

    y l o o

    4

    n

    X

    p 7

    X

    S

    "

    #

    I( P w P C S hp W` fi hv a W Yb UX " ad W r UX R Yb a v U Y` ` W` UX hv uw c` a Yb UX W` e cb W SV q qi SV ad W rt hv ad W W C( UX p hp v qi ad W

    4

    V X l T mo k kn mo n i y n X Fi V y k n

    1

    &

    1v 1p ( ' 1v 0 ) 1

    d y A o mo o n l m j d ( V g y i X

    1

    o g j T o mo o n l m jl mo z

    V |l |l y i X k

    1

    l jl C z n l ` jl mo z j n i m y X n n i

    n jl z n l ` jl mo z jl 6 &

    25 &

    2

    1

    1

    s z

    1

    1 1

    1

    1

    1

    F

    D

    0

    D

    $

    D

    0

    6

    iA (

    D

    T

    D

    0

    D

    p

    $

    D

    0

    6

    iA (

    D

    p

    0

    p

    $

    0

    6

    iA (

    p 7

    V y zn l ` jl

    D D

    p

    @

    @

    "

    l

    1

    X

    @

    "

    @

    "

    l

    1

    p

    Q V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    16/59

    mC

    0

    X

    1

    1

    jl X z

    D

    @

    @

    "

    1

    @

    "

    @

    "

    1

    D

    7

    s z

    D

    7 z z kn y kn m V y j n i m y X n n i j z n i mo j X n m y j o n kn X j y k

    4

    n X i mo i X mo z C jl 6 & 2 5 & 2 C j o n C

    7

    7 z z kn y kn m V y jl 6 &

    2 5 &

    2

    C jl g

    ad " Ul SV uw c` a

    $

    D

    n $

    X 5 |l m n i |( s n Fs kn X kn m V 7 s mo |~ zn s n n i n X zn y jl

    D

    7 n

    7

    ~ P5 4T ` W` UX hv uw c` a YR xy cb WE e p hv Yb a

    X y jl kn mo X l o y jl

    jl o o n jl C z n i mo C j X n m y g

    l |~ i i X n y z X i X j o y jl X jl o o n o l g y A mo z C jl p

    ~ Pp I( P ` qi ( SV d " a Yb a v U SV qi et cb r UX W r a fi hp W` qs rt hv uw c` a YR xy cb WE e p hv Yb a Yb UX W` e cb W SV q qi SV ad W rt hv ad C( UX p hp v qi ad W

    D

    p

    ~ P ~ P

    ` qi ( SV d " a Y c " " ad W rg fi hp W` qs rt hv uw c` a YR xy cb W e p hv Yb a ad W cb W hp W r Yb UX W` e cb W SV q

    qi SV ad W rt hv ad C( UX p hp v qi ad W

    T

    C

    $

    D

    A p

    ad " Ul SV uw c` a

    E n i n j l X mo z C y d z V y o k z j mo V |l |l y i ( V i n l |~ i j o y jl i A

    A 0

    ~ Py P ` qi ( SV d " a Yb a v U SV qi et cb r UX W r a fi hp W` qs rt hv uw c` a YR xy cb WE e p hv Yb a Yb UX W` e cb W SV q qi SV ad W rt hv ad W` W C( UX p hp v qi ad W

    1

    1

    D

    D

    s zg

    D

    mo z C j n i m y X n n i

    D

    D

    p

    D

    p

    D

    7

    D

    p n

    D

    7 o i mo |~ zn s n n i 7 z z kn y kn m V y j n i m y X n n i jl C n jX V X

    1

    n

    mo z C jl 6 & 25 & 2

    p

    p

    7

    s z

    p n

    7 R mo |~ zn s n n i 7 z z kn y kn m V y jl 6 & 25 & 2 C jl C n jl jX V X

    1

    ~ P w P` ` qi ( SV d " a Y c& " " ad W r fi hp W` qs rt hv uw c` aT YR xy cb W e p hv Yb aT ad W& cb W hp W r Yb UX W` e cb W SV q qi SV ad W rt hv ad W W C( UX p hp v qi ad W

    1

    1

    1

    1

    $

    D

    $

    D

    $

    B V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    17/59

    s zg $

    D

    n i A n jl mo z j n i m y X n n i j o y jl

    $

    D

    A

    D

    p

    A

    D

    p

    $

    n i A n jl mo z C jl 6 & 25 & 2

    $

    A

    p

    A

    p

    ~ P ~ P ` qi ( SV d " a Y c " " ad W r fi hp W` qs rt hv uw c` a ad W

    YR xy cb W& e p hv Yb a Yb UX W` e e WE SV q qi SV ad W rt hv ad b Ul St w fs ad W r S hv uw c` a C( UX p h

    v qi ad W c W` W

    D

    4

    V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    18/59

    2 !" #% $' &( 0 )2 13 $ #

    I( P ` qi ( SV d " a Yb a v U SV qi et cb r UX W r a fi hp W` qs rt hv uw c` a YR xy cb WE e p hv Yb a Yb UX W` e cb W SV q qi SV ad W rt hv ad C( UX p hp v qi ad W

    D

    p

    s z p R mo z C 5 o kn m y n l mo V |l |l y i X k l m l |~ i i X n y z X i X C j o y jl

    ~ P~ ` qi ( SV d " a Y c" " " ad W r fi hp W` qs rt hv uw c` a YR xy cb W e p hv Yb a ad W" cb W hp W r UT b S hv ( S hw " hp v ag Yb UX W` e cb W SV q qi SV ad W rt hv ad

    C( UX p hp v qi ad W

    $

    D

    T

    C

    $

    D

    P ` qi ( SV d " a Yb a v U SV qi et cb r UX W r a fi hp W` qs rt hv uw c` a YR xy cb WE e p hv Yb a Yb UX W` e cb W SV q qi SV ad W rt hv ad W` W C( UX p hp v qi ad W

    1

    l |~ i i X n y z X i X A j T o y jl d jl o o " d j z z kn y kn m V y j n i m y X n n i

    D

    p R n j z z kn y kn m V y

    jl 6 & 2 5 & 2

    p

    1

    D

    D

    s z

    D

    mo z C j n i m y X n n i j o y jl

    D

    D

    p

    D

    p

    D

    7

    n

    mo z C jl 6 &

    25 &

    2

    C j o y jl

    p

    p

    7

    w P~ ` qi ( SV d " a Y c" " " ad W r fi hp W` qs rt hv uw c` a YR xy cb W e p hv Yb a ad W" cb W hp W r UT b S hv ( S hw " hp v ag Yb UX W` e cb W SV q qi SV ad W rt hv ad

    W W C( UX p hp v qi ad W

    1

    1

    1

    1

    $

    D

    $

    $

    s zg $

    D

    n i A n jl mo z 5 o kn m y n l mo A V |l |l y i X k l m y C o y jl g

    $

    D

    A p

    s zg$

    n i A n jl mo z C j n i m y X n n i g

    $

    A

    D

    p

    A

    D

    p

    $ n i A n jl mo z C jl 6 & 2 5 & 2

    $

    A

    p

    A

    p

    ~ P~ ` qi ( SV d " ag Y c" " " ad W r fi hp W` qs rt hv uw c` ag ad W

    YR xy cb W e p hv Yb ag Yb UX W` e e W SV q qi SV ad W rt hv ad b Ul St w fs ad W r S hv uw c` a C( UX p hp v qi ad W

    c W` W

    D

    3 V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    19/59

    # # $' &( 13 3 ) $ # 1 $ 2 !" #% $' &(

    # 3 # 1

    ai SV fi hv fs a" I R Q p hv e e ad " ad W r Yb a e p hv Yb ai e

    |l m y jl o o jl i o zn y j mo o " "

    m j l m V F y 0 y o d z n y j V F y g |~ n l F y o o n m

    V X g p mo o n n i l m y o X m i V 7

    l m z |l m y

    |~ n l s n i F y o o n m V X b p mo o n n i jl n 6 5g zn ~ jl o o

    S

    n jl o o " mo n y k |( V m l X C X 5 o n X l y

    |( o V i |( V m l X |~ n o |~ l y

    y X w n |~ l y C i

    l X o o X k F Fs D l y g n y jl n 6 5 l m X C jl X o i n

    |~ n m V X n X z A |( V m V y n y V 6 5 F X jl |l X F m V X jl A |~ n i o

    j |l m y

    V y zn l y n m 7 z z kn y kn m V y j |l m y

    ai SV fi hv fs a

    c ` rt c SV a YR xy cb W` a rt h) C( a uw cb h r a et c S

    v a e

    X Fs A T X Fs n X ` jl g o o " jl y F X n l ma V

    |~ o k l mg y o n o ~ |( V m m jl |~ y

    s n m y z V y A X l |l |~ o X i X |~ n X jX V i & zo i l o y

    |~ i A mo o 5l C n Fs C mo o C jX V X y C |l V s n m y z V

    p

    '

    A 5l

    E

    o R 5l n mo z l mC Fs n B l X zn y

    k z V l y i X mo k j X zn l y A l X g |l y mo z i l X V |l |l y i X

    n

    5

    n X jX V i zo i l o C |~ m y jl E Fs

    5l n mo z l m |~ m y

    jl zn y X C k z V l y i X i l

    o m j l y o n i |( V m l X mo k l V i o T n l n i g n

    X o k mo |~ zn s n n i

    6

    { p z g R 7 X j y i X R y o zo X kn zn z i mo d {

    z X k V mo C A n jX V X R y |l V s n m y z V p

    '

    !

    !"

    ! #

    $

    %

    ! &

    '

    I( P

    I( Pp I( P

    5 |l m n m n ( X n T X zn y jl 7 V F y 0 )g n jl y F X n l m

    I( P ~ P~

    |~ o

    2 1

    n (

    1

    (

    m z n m 7 V l mo jl

    3 1

    n jl A (

    1

    n X zn y jl b i |~ l m l X V y n l m

    jl 4 ) jl l X k

    ~ P

    Fs kn X kn m V 7 X l X C zo X n g X k j X X C i l ` D ( V o l m y o V i A jl o X zo X n mA y o 7 j n V i A V y j o kC j

    d jl n y |l mo k z k jl n i X |l mo k zn y o n m n i X n |~ i |~ n l |l mo kn s m z n o C z o l mo

    E n i A j X n m y C j l X Fs jl o o n jl y F X n l mI |( V m m V |l |~ m l 5l |( o V i |( V m o z n i mo

    n |~ n m |~ n X j y zn l V mo Fs C

    T

    T

    V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    20/59

    %E )2 32 1 " 1" F %& ( '0 )2 1 36 57 )2 9 8A @B 8C %E D" !$ 14 !$ #& %E " FG 1" H

    I( PB A rt c Yb a qd W` ai SD C( qs rt hv uw c` a YR xy cb W ~ w e r d " a Yb a hp W r e " U r qi S hv ad v e

    7 R l o n jl {} |~ i o V o kn m y n y jl o o

    I( Pp I( P ` qi ( SV d " a Yb a v U cb hv e e UX W` fs a fi hp W` qs rt hv uw c` a Yb UX W` e cb W SV q qi SV ad W rt hv ad C( UX p hp v qi ad W

    E

    kn X n mG F y zn X kn y i X C jl 7 jX V X

    C

    H

    0

    Q

    S

    T

    H

    0

    m y X k mo n C jl mo k l V i o zn X kn y i X j |~ i jX V X y mo k kn mo n i y n

    C( UX p hp v qi ad W

    D

    jl X z

    H

    D

    s z

    D

    0

    D

    |l l y o V X z C jl mo z 5 o kn m y n l mo A V |l |l y i X k l m y C o n 7

    0

    p |l l y o V X z C jl mo z i o kn m y n l mo V |l |l y i X k l m 7

    ad " Ul SV uw c` ai e

    !g E

    o g jl

    ( SV fs ai eT hp W r qi S hv ad c` SV ai e

    V |l |l y i X k l m l o n ( n o g jl C y n l mo

    n i o n l |~ i X o i i l y

    5

    V mA z i mo X o g C jl y n l mo |l l y o V X z w |( o ) l mo i l y

    7!

    X jl kn |~ n X jX V i o j mo k kn mo n i y n b j kn X jl n C

    4

    V X l mo k kn mo n i y n

    &

    ( ' 0 )

    0

    p

    4

    V X l mo k kn mo n i y n

    1

    &

    1

    1( '

    10 )

    1

    1

    0

    1

    m j V |l mo y w jl C z g |~ y jl d o o o C

    1

    @

    @

    X

    1

    7 6

  • 8/6/2019 Cours Mecanique Du Solide

    21/59

    jl X z

    6

    1

    #

    $

    @

    6

    l

    1

    X

    mC

    l

    1

    (

    @

    j 3

    1

    I( P ~ P ` qi ( SV d " a Yb a v U cb hv e e UX W` fs a fi hp W` qs rt hv uw c` a YR xy cb W e p hv Yb a Yb UX W` e cb W SV q qi SV ad W rt hv ad W` W C( UX p hp v qi ad W

    E kn X n mG F y zn X kn y i X C j o n 7 jX V X l mo k kn mo n i y n

    W W C( UX p hp v qi ad W

    1

    C

    H

    1

    0

    Ig Q

    S

    1

    % U

    H

    1

    0

    v

    1

    1

    m y X k mo n C jl mo k l V i o zn X kn y i X j |~ i jX V X

    1

    W W C( UX p hp v qi ad W

    l

    1

    D

    D

    p w

    p

    s z

    D

    p n

    p o i mo |~ zn s n n i mo z C j X n m y C j n i m y X n n i n jl 6 & 2 5 & 2 C j |~ i

    j 3

    H

    1

    1

    D

    1

    D

    s z

    1

    D

    0

    D

    1

    |l l y o V X z C jl mo z 5 o kn m y n l mo

    1

    0

    1

    |l l y o V X z C jl mo z i o kn m y n l mo

    D

    0

    D

    p

    1

    v

    D

    p

    1

    |l l y o V X z C jl mo z j n i m y X n n i

    p 7

    1

    S

    @

    1

    1

    |l l y o V X z C jl mo z jl 6 & 2 5 & 2 g

    j 3

    H

    1

    1

    D

    1

    D

    I( Py P ` qi ( SV d " a Yb a v U cb hv e e UX W` fs a fi hp W` qs rt hv uw c` a Yb UX W` e v a SV q qi SV ad W rt hv ad b Ul St w fs ad W r S hv uw c` a

    4

    V X

    |l m y m w X Fi V y k n

    H'

    D

    D

    s z

    D

    D

    p

    "

    D

    p

    #

    mC

    D

    p 7

    X

    7

    j 3

    D

    d

    R X o

    n i o

    1

    y l o o

    7 V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    22/59

    5

    V m z X o k i X n i

    H'

    D

    I( P w PB A W` ai SD C hv a " qi fs UX Wb hv uw c` a YR xy cb WE e w e r d " a Yb a hp W r e " U r qi S hv ad v e

    I( P w Pp I( PB A W` ai SD C hv a X r ad W rt hv ad p v a

    4

    V X l mo k kn mo n i y n

    7 kn X n mG F y |~ o n i y n y jl i C jl kn m s mo z V |l |l y i X k g l m l |~ i V o kn m y n

    o n y C i X g

    H

    j i X mo z l X A mo z C z X o n m V s

    E

    kn X n mG F y C |~ o n i y n y j o n 7 z X X k |( V m y |~ i o l C

    H H

    I( P w P ~ PB A W` ai SD C hv a " qi fs UX Wb hv uw c` a

    E

    kn X n mG F y C k z V l y i X C j o n 7 jX V X

    C

    H H

    H

    P I Q

    S

    T

    U

    H

    j 3

    H H

    H

    mC

    H

    H

    s z

    n

    o i mo |~ zn s n n i R y m V 6 5g kn y kn n i V mo jl mo z z X o n m V s n X z X o n m V s

    j 3

    H

    I( P w Py P

    !

    W e ai S l U rt hv W Yb a x qd W` ai SD C hv a " qi fs UX Wb hv uw c` a

    b o l o y A mo z V |l |l y i X k l mA y o n T 7 jl kn m s n i C j l X kn X n mG F y |~ o n i y n y g n y X m V y n i

    |( X V y mo

    H

    n

    H H

    H

    n

    j o

    hp W r q C( SV UX v a b SV ad hv i SV a Y c " c ad " ad W r

    n y o n j

    fs W e ai S l U rt h5

    ~ PB A rt c Yb a qd W` ai SD C( qs rt hv uw c` a YR xy cb WE e p hv Yb a

    ~ Pp I( P ` qi ( SV d " a Yb a v U cb hv e e UX W` fs a fi hp W` qs rt hv uw c` a YR xy cb W e p hv Yb a Yb UX W` e cb W SV q qi SV ad W rt hv ad C( UX p hp v qi ad W

    4

    V X

    C( UX p hp v qi ad W

    H

    D

    s z

    D

    |l l y o V X z C jl mo z 5 o kn m y n l mo

    D

    p

    p R mo z kn y kn n i V mo 5l n mo z k C l m l |~ i i X n y z X i X C j o y jl

    7 7 V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    23/59

    G l |~ i j o y jl ( V y mo C

    T

    9B A" C

    E D

    j 3

    D D

    T $

    D

    9B A" C

    E D

    4

    n

    T $

    9B A" C

    E D

    mC

    $

    jl X z |l l y o V X z C jl mo z

    hp W r qi S hv ad c` SV ai e

    V |l |l y i X k l m

    cb W e p hv Yb a

    i l y

    j 3

    H

    D D

    T $

    D

    9B A" C

    E D

    ad " Ul SV uw c` ai e

    !R E

    |l l y o V X z jl mo z A i o kn m y n l mo C j l o y jl A i l y V y mo i X |l l y o V X z jl mo z

    i o kn m y n l mo j l o n T jl T |~ i o g V o kn m y n y n V jl o y jl w g |( |l m y m i l y n g X jl kn |~ n X jX V i o j

    mo k kn mo n i y n b 3 z V y zn l y

    7! E

    |l l y o V X z C j l X mo z y d z V y o k g z A j mo C V |l |l y i ( V i l m l |~ i B j o y jl C

    ~ P ~ P

    ` qi ( SV d " a Yb a v U cb hv e e UX W` fs a fi hp W` qs rt hv uw c` a YR xy cb W e p hv Yb a Yb UX W` e cb W SV q

    qi SV ad W rt hv ad W` W C( UX p hp v qi ad W

    4

    V X

    1

    W W C( UX p hp v qi ad W

    H

    1

    1

    D

    D

    s z

    D

    |l l y o V X z C jl mo z j n i m y X n n i

    D

    D

    p

    1

    p

    D

    p

    1

    p

    n

    |l l y o V X z C jl mo z jl 6 & 2 5 & 2

    p

    1

    p

    p

    1

    p

    S

    @

    1

    p

    1

    p

    j 3

    H

    1

    1

    D

    D

    ~ Py P ` qi ( SV d " a Yb a v U cb hv e e UX W` fs a fi hp W` qs rt hv uw c` a YR xy cb W e p hv Yb a Yb UX W` e cb W e W SV q qi SV ad W rt hv ad b Ul St w fs ad W r S hv uw c` a

    4

    V X

    |l m y m

    W W C( UX p hp v qi ad W

    H'

    D

    D

    s z

    D

    D

    p

    1

    p

    n

    j 3

    H'

    D

    7 7 V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    24/59

    $ # # 2 !" # $' &( 0 )2 13 $ #

    I( P ` qi ( SV d " a Yb a v U cb hv e e UX W` fs a fi hp W` qs rt hv uw c` a YR xy cb WE e p hv Yb a Yb UX W` e cb W SV q qi SV ad W rt hv ad C( UX p hp v qi ad W

    p mo k l V i o jl mo z

    a

    r qi S hv ad c` SV a

    V |l |l y i X k C l m l |~ i j l o y jl g

    H

    D

    p

    p

    s z

    D

    |l l y o V X z C jl mo z 5 o kn m y n l mo

    D D

    T $

    D

    9B A" C

    E D

    kn V i l |~ i i X n y z X i X C j o y jl

    ad " Ul SV uw c` a

    E

    |l l y o V X z jl mo z i o kn m y n l mo A j l o y jl i l y ( V y mo i X A |l l y o V X z jl mo z i o k

    m y n l mo j l g o n jl R |~ i o V o kn m y n y n V g jl o y jl b w |( |l m y m i l y n b X jl kn |~ n X jX V i o j mo k kn mo n i y n

    3 z V y zn l y

    ~ P ` qi ( SV d " a Yb a v U cb hv e e UX W` fs a fi hp W` qs rt hv uw c` a YR xy cb WE e p hv Yb a Yb UX W` e cb W SV q qi SV ad W rt hv ad W` W C( UX p hp v qi ad W

    1

    H

    1

    D

    D

    s z

    D

    |l l y o V X z C jl mo z j n i m y X n n i

    D

    D

    p

    1

    p

    D

    p

    1

    p

    n

    |l l y o V X z C jl mo z jl 6 & 2 5 & 2

    p

    1

    p

    p

    1

    p

    P ` qi ( SV d " a Yb a v U cb hv e e UX W` fs a fi hp W` qs rt hv uw c` a YR xy cb WE e p hv Yb a Yb UX W` e cb W e W SV q qi SV ad W rt hv ad b Ul St w fs ad W r S hv uw c` a

    H'

    D

    w PB A W` ai SD C hv a " qi fs UX Wb hv uw c` a YR xy cb WE e p hv Yb a Yb UX W` e cb W SV q qi SV ad W rt hv ad

    H H

    H

    Q

    S

    2 T

    p

    p

    p

    H

    l

    v

    n

    o o

    7 V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    25/59

    # # $' &( 13 3 ) $ # 1 &7 $ # # 2 !" # $' &(

    # 3 # 1

    ai SV fi hv fs a I g e fi hp p v U rt hv W e YR xy cb W` a} rt h) C( a et c S cb W

    Yb ad h fs ai SV fi v a

    X Fs X Fs n X A T l jl C z n i mo g l jl y F X n l m

    S

    jl C n i C j X n m y

    T

    |( V m m V |l |~ m l 5l

    |~ n m |~ n X j y zn l V mo g g Fs n |( o V i A |( V m g F y o o V X

    p mo o n n i 7 i o kn m y n l m j l & jl n g z n mo zn y T jl z n i mo

    n jl m s

    G

    T

    jl n g z n mo zn y X k jX V X y |l V s n m y z V &

    '

    j l mo k kn mo n i y n Fi V y k n w

    I( P

    V |l |l y i ( V i y X k mo n jl 7 kn X n mG F y zn X kn y i X

    jl kn o n m g X n m 7 k i ( V y j kn mo n i y n y s kn m ( k |( V m 7 V F y

    )

    ~ P

    V y zn l y n m |~ kn m y d jl jl |~ n o o zn V y X jl Fs V l o l m jl |~ y j k i l l mo

    ai SV fi hv fs a c ad " ad W r" YR xy cb W` a b Ul SV SV a Ul b cw qi a

    fs W r SV a cb W c S

    E

    A mo k kn mo n i y n o n m mo mo l |l |~ o k Fi V y k n w X ( V m mo

    A G X Fs n X jl o o " jl y F X n l m

    S

    n jl z n i mo

    g g y n jl C A T X |~ o k l m y C o w X m i V n mo

    |~ o R z i mo l l m s n m y z V 7

    |~ y jl kn o n m g X k

    |( V m 7 V F y

    E

    z i zn o n n R o i

    l |l |~ o k V X p mo o n n i o

    " !

    #

    $

    %

    &

    '

    (

    )1 0

    )1 02 )1 04 3

    R1 TF 31 4X A DY C 31 4 7@ DY 4F 3H (1 TF 31 Af 31 CU T &) 3H G (H eg A ey G` $' CU TF 3H G 72 3% &W $ DY TF 3H GF GF 36 5

    7 8

    @ 9 o 7@ 0f eg DY CU TA 9 31 Ca uw eg C (1 TX D) eg CB 72 3 31 T 72 3 &W $h 72 R1 4X DY RH 3

    72 3h

    )1 0 0C B

    C 72 RH 7@ 02 DY 4F 3d &) 3 3H (1 TF 31 02 4c 4F eg T` $' TX D) eg C

    5

    7 D

    72 3h &W $ TX DY x 3y

    0

    02 )1 0F E

    (1 4X DY 4F 3B & DY CU TF R1 xy 4` $' &) 3{ 2 4F 31 A D) E1 4F 3{ 72 3B & R1 C 31 4X xy D) 3{ 31 C GX 02 2 ey G` $' CU Ta bU 0 & DY C GX T` $' CU T DY C2 DY TX DW $' & 5k &W $ V $' 4X 4F 3B 3H GX T DY A Af eg 2 DY &) 3 $H 3H (

    02 C 3h DY C (1 &Y DY CV $' D) GF eg C H Gy

    0 0

    #% $' &) (1 02 &) 31 4I &W $ 4F R6 $g (1 TX D) eg C

    5

    7

    P I 5 7@ 0 A 02 4 GX 02 4c &W $ V $' 4X 4F 3y 5V 31 TI 31 Cq 72 RH 7@ 02 DY 4F 3 eg 02 4I bU 0 31 &Y &) 3d DY C (1 &Y DY CV $' D) GF eg C 5 &W $ V $' 4X 4F 3 bU 02 DY TX TF 3

    &) 3 A 02 46 c C 72 eg C2 C 3h &) 3h Af eg Af 31 CU TI 7S DY C 31 4X TX D) 3 72 3 &W $a V $' 4X 4F 3h V $' 4 4` $' 2 eg 4X T G $ Af RH 7@ DW $' TX 4X D) (H 3 q z

    ~

    QS R TV UX WY Ta F bA ce d fh g

  • 8/6/2019 Cours Mecanique Du Solide

    26/59

    0 B %T # % 1" B %E F 1 32 1" ) 8 0 H 32 1& 8 g H ( 8 32 ) F G % %E 1" !$ 1" B %

    I( P h r ai e e a Yb a C p hv e e ad " ad W r

    X y jl kn mo X jl n 6 5 o y jl

    n

    T

    n z i zn l mA l X

    |~ n o l m 7 z |l V X g 7 R n n l s n n i |( V m m V |l |~ m

    l mo k kn mo n i y n

    l n R l |~ i i X n y z X i X C jl 7

    E V |l |~ n y s zn o n l m d o o o jl F y o o n n i n ( b jl

    T

    l m

    C

    ! # "

    % $

    ! # "

    ' &

    ( )

    (1 0

    2 35 47 69 8A @ BC 69 85 DF EC 8F BH GP IR QS ET BH IV U

    W{ Y X2 ' lk U v

    )R `

    5

    7 8 a

    3H GX T DY C 72 R1 31 C 7 $' CU TI 7@ 0 4F R uw R1 4F 31 CU TX D) 31 &c bq

    B

    C 3 PS 31 T6 5 7S $' 2 4F EH G &W $ &) eg Dk 72 3h (H eg A ey GX DY TX D) eg Cq 72 3H G DY TF 3H GF GF 3H G! d

    5

    7 8! e# f' g% hT iq p

    5

    7 8r e# f' g% hC iq pt sv u

    5

    7 8r wx sy iq p u

    5

    7 pt sy iq p

    5 54 5

    7

    i y

    g% h

    5

    7 8! e# f' g' iq p

    5

    7 8! e# f' g' iq pt sR u

    5

    7 8r wx sy iq p u

    5

    7 pt s7 iq p

    5 5 5

    7

    i y

    g'

    eg 4 & DY C GX T` $' CU T 1 5v

    g% h g'

    52 72 eg C ( d

    5

    7 8 a

    @ 5

    7 8! e# f' g% hC iq p

    5

    5

    7 8! e# f' g' iq p

    5

    7 8! e# f' g% hC iq pt s

    5

    5

    7 8! e# f' g' q iq pt s

    3H GX T DY C 72 R1 31 C 7 $' CU TI 7@ 0 4F R uw R1 4F 31 CU TX D) 31 &o 7S R1 TX 0 72 3y 5 31 C V $' 4X TX D) (1 02 &Y D) 31 4c eg 02 4 b b

    g'

    4F R uw R1 4F 31 CU TX D) 31 &k &Y D) R

    d

    5

    78 a

    @5

    78

    e# f' g% hC iq pH

    `

    5

    7 8 a

    $' 2 V $' 4X TX D) 31 CU Th $' 0 2 &W $' C p T` $' C2 x 31 CU T 31 T 31 C V 5 (y 3H GX T 7@ DY 4F 3d $' 0 2 &W $' C V $g GF G` $' CU T V $' 4

    `

    c C 7@ DY Tc bU 0 3 C 3h xy &Y D) GF GF 3 V $g G GX 02 4 31 C B GX D 5

    7 8 a

    @

    5

    7

    0t

    V ' 6 lk { jo U X2 y 8 k B | U X o lk U f jo 8 8 j X2 y B jo lk

    km l

    $a 4F RH GX 02 &Y T` $' CU TF 3 3H GX Tr d

    5

    7

    o n1 nt n

    5

    7

    B

    5

    7

    u5

    7

    5

    7

    f uw eg 4F (H 3h R1 &) R1 Af 31 CU T` $' DY 4F 3 3 92 31 4F (H RH 3h V $' 4 GX 02 4 31 C 02 C eg DY CU T 72 3 &W $ GX 02 4 u $g (H 3f % 7@ 0 (H eg CU T` $g (1 T6

    5

    7

    uw eg 4F (H 3h 72 3 u 4F eg TX TF 31 Af 31 CU TI 72 3 xy &Y D) GF GF 31 Af 31 CU T6

    B

    &Y &) 3 $' 2 V $' 4X TX D) 31 CU T $' 0 2 &W $' C T` $' C2 x 31 CU TP

    5

    7

    4F R6 $g (1 TX D) eg C C eg 4X AB $' &) 3

    Q'

  • 8/6/2019 Cours Mecanique Du Solide

    27/59

    o n i A n C

    A

    i p

    s zg

    n i A jl p mo o n n i A jl mo l y n n i w

    V |l V V Fs n i

    n i A jl p mo o n n i A jl |l s o n n i

    P v hv eg Yb a c b

    Y c SV X r r ad " ad W r Yb a C p hv e e ad " ad W r

    X V y mo C n o i z X k V mo A n jl C o n X |l |~ o k C

    !

    |l X l T

    {

    s z z d zn y n i A jl A p mo o n n i A jl 2 F y o o n n i

    X V y mo {

    w P

    cb hv e e UX W` fs a Yb ai e Ul f rt hv W e " qi fs UX Wb hv uw c` ai e Yb a fs W r Ul f r

    E|l l y o V X z jl mo k zn y jl

    l m

    T

    l jX V X l mo k kn mo n i y n

    C

    p

    "

    % $

    ! # "

    % $

    % $

    s zC |~ i jl l m 7 z 7 j z i zn

    E|l l y o V X z jl mo k zn y jl

    T

    l m

    l jX V X

    jl X z

    T

    p

    "

    ' &

    r # "

    ' &

    ' &

    R y o n kn X j y kT T

    T

    V y mo |l l y o V X z jl g zn y X k z V l y i X jl z i zn g |l l y o V X z jl

    i o n m" m o A n i mo

    n

    T

    l C

    b

    T

    w

    % $ ' &

    w

    % $ ' &

    ad " Ul SV uw c` a

    V l m

    jX V X y z l V i o

    T

    n m V X V y |( V m m V |l |~ m A

    C

    % $ ' &

    i zn |~ X zn X n b n

    i zn n i mo

    T

    n

    o 7 V l m l X F X mo zn F X

    5l n g |l y mo l y n n i j l zn d X j mo C l m l |l V

    % $ ' &

    i

    % $ ' &

    i

    $ 2

    % $ ' &

    "

    D!

    "

    #

    $

    74

    V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    28/59

    4

    3"

    i l y y mo o i X g

    v |( jl p mo o n n i

    !

    v |( jl 2 F y o o n n i

    !

    ~ P

    X r U rt hv W e UX W` e SV X r r ad " ad W r YR xy cb W e p hv Yb a UX cw r c S YR xy cb W U

    a

    1

    a

    X y jl kn mo X l o y jl n E mo V y

    e UX W` e SV X r r ad " ad W r

    V l o l mR j l T 5l

    )

    5l jX V X l mo k kn mo n i y n

    X D F

    jl X zC j l X

    p hv UX hv e W h X r c SV X r Yb a b Ul S UX h r a

    % $ 2

    A

    % $ 2

    s z mo z 5l n mo z k |( V m 7 5l

    )

    l m y o y jl n

    A

    n i A jl mo z n g

    3h TX RH eg 4F E1 Af 3d 7@ 0 Af eg Af 31 CU TI (1 DY C R1 TX D) bU 0 3 $' 2 2 &Y D) bU 0 R $' 0 GF eg &Y D) 72 3d $' 0 eg DY CU T i 72 3h & $ 92 3 i f 72 eg C2 C 3 d

    4 5

    7 !# "H u

    5

    7 $

    w& %

    5

    7

    '

    w

    u5

    7

    '

    w

    ( )1 03 2 4 56 )7 4

    $H 3H ( d

    k

    | Af eg Af 31 CU TI 7S DY C 31 4X TX D) 3d 7@ 0 GF eg &Y D) 72 3 V $' 4 4 $' 2 eg 4X T i

    k

    5

    7 $

    w& %

    &W $a (H eg A ey G` $' CU TF 3 7@ 0 Af eg Af 31 CU TI (1 DY C R1 TX D) bU 0 3d 31 Cq i 52 C eg 4X AB $' &) 3 & $ 92 3d 72 3 4F eg T` $' TX D) eg Cp i

    k

    5

    7

    '

    w

    Af eg Af 31 CU TI 72 3 TF eg 02 TF 3H G &) 3H G% uw eg 4F (H 3H Gc 3 9@ TF R1 4X D) 31 02 4F 3H GI $' 2 2 &Y D) bU 0 RH 3H GI $' 0 GF eg &Y D) 72 3

    r (H eg A 2 4X D) G &) 3H G% uw eg 4F (H 3H G 7S DY C 31 4X TX D) 3 GX D b C 3H GX T

    V $g G xU $' &Y DY &) RH 31 C8 58 $' 02 TX 4F 3H G bU 0 3h &) 3H G% uw eg 4F (H 3H G 72 3h (H eg CU T` $g (1 TI 31 CU TX 4F 3 (H 31 &Y 02 DQ (1 Dk 31 T & $ 92 3h 72 3h 4F eg T` $' TX D) eg C

    # 3h bU 02 Dk 72 eg C2 C 3y 5 31 C 2 4F e9 8 3H (1 TX D) eg Cq GX 02 4I i 5@ 2 02 D) GF bU 0 3@ '

    w

    "

    ( )1 03 2 4 56 )7 4

    d

    A B '

    w

    "

    W{ Y X2 ' lk p

    3h TX RH eg 4F E1 Af 3 72 3 &W $a 2 02 D) GF G` $' C (H 3h (1 DY C R1 TX D) bU 0 3d 4F 3H 72 eg C2 C 3h &) 3 AD C1 Af 3d 4F RH GX 02 &Y T` $' TA d

    F E

    )

    G# H

    }

    P I R Q B '

    w

    "

    I

    7S e9 S d

    A B '

    w

    "

    QU T TV UX WY Ta F bA ce d fh g

  • 8/6/2019 Cours Mecanique Du Solide

    29/59

    ) # # $ # 0 )2 13 $ # )2 $

    ) 0 # #

    I( P h r ai e e a Yb a C p hv e e ad " ad W r

    V |l |~ n y s zn o n l m d o o o jl F y o o n n i n ( l j l o y jl

    T

    l m l o y jl

    C

    # "

    % $

    # "

    ' &

    ad " Ul SV uw c` ai eT

    I

    X jl kn |~ n X jX V i A j mo k kn mo n i y n

    V |l |( V m y n i V |l V V Fs n i A

    n

    T

    n (

    j i X

    T

    X 2 F y o o |( l m

    n

    ~ P R ( SV e ad c` S Yb ai eg Ul f rt hv W e " qi fs UX Wb hv uw c` ai e Yb a fs W r Ul f r Yb a

    et c S

    T

    mo k l V i o C

    6

    p {

    p R mo z kn y kn n i V mo 5l n mo z k |( V m

    l m

    T

    n l |~ i jl g l m 7 z j z i zn

    mo z jl p mo o n n i A jl F y o o n n i y V |l |( V m y n i V |l V V Fs n i

    { mo k zn y X m V y

    o n i A n C

    A

    i p

    s z

    n i A jl p mo o n n i A jl mo l y n n i

    V |l V V Fs n i

    n i A jl p mo o n n i A jl |l s o n n i `

    P v hv eg Yb a c b

    Y c SV X r r ad " ad W r Yb a C p hv e e ad " ad W r

    X V y mo C n o i z X k V mo A n jl C o n X |l |~ o k C

    !

    |l X l T

    {

    s z z d zn y n i A jl A p mo o n n i A jl 2 F y o o n n i

    X V y mo

    {

    w P cb hv e e UX W` fs a Yb ai e Ul f rt hv W e " qi fs UX Wb hv uw c` ai e Yb a fs W r Ul f r

    E

    |l l y o V X z C jl mo k zn y jl

    l m

    T

    l jX V X l mo k kn mo n i y n

    C

    # "

    % $

    % $

    7 V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    30/59

    E

    |l l y o V X z C jl mo k zn y jl

    T

    l m

    l jX V X

    jl X z

    T

    # "

    ' &

    ' &

    b y o n kn X j y k g

    T

    ~ V y mo A |l l y o V X z jl zn y X A k z V l y i X jl z i zn C |l l y o V X z jl

    i o n m"

    m o A n i mo

    n

    T

    l C

    T

    w

    % $ ' &

    ad " Ul SV uw c` a

    V l m

    jX V X y z l V i o

    T

    n m V X V y |( V m m V |l |~ m A

    i zn |~ X zn X n b n (

    i zn A n i mo

    T

    n

    o A 7 V l m l X F X mo zn F X

    j 3

    i l y C y mo o i X

    6

    v |( jl A p mo o n n i

    !

    v |( jl 2 F y o o n n i

    !

    ~ P

    X r U rt hv W e UX W` e SV X r r ad " ad W r YR xy cb W e p hv Yb a UX cw r c S YR xy cb W U

    a

    1

    a

    X y jl kn mo X l T o y jl A n T mo V y

    e UX W` e' SV X r r ad " ad W r

    V l o l m j l 5l

    )

    1

    a

    jX V X l mo k kn mo n i y n

    D F

    j l X V y o |l s mo o 7 jl

    b Ul S UX h r a

    X jl X z

    A

    $ 2

    EX k mo n C j n i A zn X kn y i X V |l |l y i X k V o y jl C V |~ i n n |l mo 0 ) zn y l m 7 5l

    )

    l jl l X

    )

    2

    s z

    n i A j X n m y C j o y jl |( V m m V |l |~ m A

    )

    2

    |l mo 0 ) zn y l m

    )

    ` j n i jl o l o y mo z 5 o kn m y n l mo V |l |l y i X k V o y jl v z g |l m y y

    mo z j X n m y

    w |( g Fi V y k n!

    V l mo i X y mo z jl C z i zn A n i mo C z n l zn b n 7 5l C jl mo V y w

    7 6 V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    31/59

    # # # # $ # 13 0 ) # # $ #

    0 )2 13 $ #

    X V y o " n i mo jl n 6 5 o y jl

    C n

    T

    C j o

    b Ul S UX h r a

    w z T j mo g V X p mo o n n i ` |l l y o V X z jl

    zn y X k z V l y i X jl z i zn A jl

    l m

    T

    n jl

    T

    l m

    i l y

    A

    !

    w

    % $ ' &

    r # "

    % $ ' &

    % $ ' &

    s zr l |~ i jl C z i zn n i mo

    n

    T

    ~ mo z C 5l n mo z k |( V m

    l m

    T

    ~ n i A n jl mo z g

    I( P R hv UX hv e W C p hv e et hv i SV a c b S hv et " U rt hv uw c` a

    E

    o n l l l s n n i R |~ o l y jl

    T

    |( V m m V |l |~ m

    l l s n n i jl m V X V y mo zn F X C |( V m V y n y l

    5l

    )

    p hv q

    ! # "

    % $ ' &

    )

    $ 2 $

    % $ ' &

    E

    V y o " F y o y n mo C |( V m 7 V o C

    $ 2

    l y n

    A

    ! # "

    % $

    )

    $ 2

    ! "

    !$ # %

    & ') (

    ~ P R hv UX hv e W SV X rt cb v a c e ` qi S hv uw c` a

    E

    o n l l s n n i |~ o l y T jl

    T

    |( V mg m V |l |~ m

    l l s n n i jl A mo V y V l o l m j l T |~ i

    p hv q

    # "

    % $ ' &

    x T kn V i y z n i mo z g l jl

    n

    T

    E

    V y o mo l y |( V m 7 V o C l j 3

    A

    r # "

    % $ ' &

    % $ ' &

    0

    13 2

    15 4

    68 7@ 93 AC BE DF 9H G

    P R hv UX hv e W h X rg c SV X r Yb a

    E

    o n l l l s n n i R |~ o l y jl

    T

    |( V m m V |l |~ m

    l " l s n n i g jl mo V y & V l o l m j l & 5l

    )

    p hv q

    ! # "

    % $ ' &

    $

    % $ ' &

    I

    $ 2

    E

    & V y o G mo o 7 jl |( V m 7 V o "

    % $ 2 5 P

    6

    z " i l

    jl l X

    A

    Q

    RT S

    U

    V

    R@ W

    X Y a$ bd c) ef ah g

    7 V WY X) Va `c be dg f hp i

  • 8/6/2019 Cours Mecanique Du Solide

    32/59

    C " !# !#

    E $& %' %( $0 )2 13 %5 4 67 )2 89 $0 4 $0 @" A( % BC 6D %( %F EH G2 13 $& %5 I2 $Q P

    T

    BS R# T' TU R# B2 BC 67 TF AW V

    P %( 67 @" AX )2 @ 4 67 )2 89 $0 4 $0 @" AY I2 $` AF TU R# @ %F 1a R# AF E3 67 @b T( $& c0 AF EH 1H E

    F

    @ $d %F )2 Te )2 @

    R

    5

    $

    )

    f

    Vg P $0 Ah )2 @i 4 67 )2 89 $0 4 $0 @" Ap I2 $p T( 67 AU R# AF E3 67 @q R# )2 A( 67 )2 T

    I2 $r c& $0 Ad R

    5

    $D s 45 t 6

    3q u

    v

    w x# "

    % $ ' &

    y

    )

    v

    w$

    2 $&

    v

    w

    % $ ' &

    y

    v

    w$

    2

    R5 1H Ea R# E3 %( 67 @ 89 $0 TF T( 67 )i $& %F AY BS R# T R# EH A( $ %F E

    u

    v

    w

    v

    w$ 2

    y

    $& v

    w

    v

    w$ 2

    y

    $r " )2 E I2 67 @2 @ $

    u

    y

    7

    D

    j2 km lW nS oH kW

    D e z| {Y }7 ~

  • 8/6/2019 Cours Mecanique Du Solide

    33/59

    # ! "$ # % & "$ #' ( ) 0 % #' 2 1( 3 4 &6 5

    7 ") 4 9 8A @B ") & CD 1( "E 7 ! F #'

    GI H

    " !Q P" R P9 6 SU T2 Vb m X W` Y3 a Pc b d W !# e W

    P9 S !7 R f" !#

    g @ ci h 1H EH @ I T( $ I2 $Y 4W R7 %( %( $q ps r9 I2 $Y TU Rt h9 67 @ rD A( 67 )2 TF @S R# @" Au r Vh 1 t EH @ %w v

    AU R# @" A EH @2 EH AF Ea R# 1x r" V 1a Rd 8 EH A( $& %( %( $| R# @ yD )2 1a R# EH T( $Y BC 6D %F EH AF EH 89 $ | R# )2 A( 67 )2 Te I2 $

    %( 67 @ R 2 $c rS $& %F A BC 6D % p %F )2 T )2 @ $p c& 67 TF @2 E 0 T( $D s @ %F )2 B2 BC 6D %( $ " ) $ 13 $

    ci h 1H EH @ I T( $` T( $& %F A( $ $0 @W BC $0 TF 4W R# @ $0 @ c& $ $0 @b c& 67 @" AU R7 c0 AY R& 89 $& c 13 $& %e B2 1a R# @ %

    67 TF E 67 @" AU R# 1 x e $0 AX 89 $0 TF AF E3 c R# 1 x e I2 $ 1a R c& 67 TF @2 E 0 T( $h $0 AX 67 @

    R# B2 BC $0 1H 13 $( j 13 $5 c& 6 $l kW c0 E3 $0 @" Ar I2 $2 yD 1H E3 %( %( $0 4 $0 @" A $0 @" AF T( $ 13 $ ci h 1H EH @ I T( $

    $0 AY 13 $& %Y B2 1a R# @ % I2 $h 1a R' c& 67 TF @2 E 0 T( $D s

    m

    n

    o

    S D

    67 @" AF T( $0 T " ) t R# ) I 0 G2 )2 A` EH 1D h R( yD 1H E3 %( %( $0 4 $0 @" A I ) ci h 1H EH @ I T( $ %F )2 TY 13 $& %Y B2 1a R# @ %2 x | $0 A! x s

    z {

    0 A |0 TF 4' EH @ |0 Te 1 |t } 4 6 I ~2 1 |t }e I |t } c& 67 4' BC 6c }U R# @" A |t }e AU R# @ y |0 @" AF E |0 1H 1 |t }` |0 A @ 67 TF 4W R# 1 |t } I |t } T R7 c0 AF E3 67 @ }e T |t }F Bz |& c0 AF EH 8 |t }e I ~' B2 1a R# @ x

    |0 A2 x } ~2 TY 1 | ci h 1H EH @ I T |7 |0 @g 67 @ c0 AF E3 67 @ I |2 j r p |0 Aq s

    D D

    @i R# B2 B H E3 ~S R# @" AI |h A & 67 T 0 4 |p I ~ 4 67 4 |0 @" Ad c0 EH @ 0 AF E3 ~ |7 |0 @ r2 I 0 A |0 TF 4' EH @ |0 TI a R! 3 67 E 67 TU R# EH T |

    s

    RQ 3 ci ~ |0 T t EH @ }F AU R# @" A

    r RQ ~ ~ |i | ci h H EH @ I T |7 } t EH 4' 4 67 G2 E H E } |D s I ~ |7 } |h BS R } } |h Aw v E d |0 @ } ~2 EH A |d

    z D

    AU R# G H EH T ~2 @Q G2 E a R# @ 0 @ |0 T y 0 AF E3 ~ |2 |0 @" AF T | t EH @ }F AU R# @" A EH @2 EH AF Ea RQ d |0 Aq t EH @ }F AU R# @" A

    7 s

    | 6 |0 @" Ad I t EH @ |0 TF AF E | I t ~2 @ ci h H EH @ I T |r BS R# T` TU R# B2 BC 67 TF Ad V( }( 67 @ R |7 |t }F A

    y

    p s

    GI H

    P R P T 6

    s

    W Y

    d

    d Pc bd W R

    gI }( ~ |

    y i |c r |7 t |i |( r | t h

    Q r |

    v

    |i D |i |

    y

    p

    Q I

    }

    |c r

    ~ |

    |i i |i ~ |i |i |i yc } } |E } ~ ~ 4 } ~

    i h 3 ~ |

    | t |i |$ |i | t h 4 | Q } | i |i |i

    |i |t } | R 2 } ~

    } y Q t |i l r

    ~ |i E |t } Q Q }

    ~

    Q B |i u Q x I B |

    i |6 | }( ~ |

    Q x Q yc |

    '

    x d t 2 2 |i

    t } yc |

    Q j |

    |l k i |i |

    |i |i | yc } } |i |i |i | | }( ~ | |i d }

    7 } ~

    u

    I } |

    } |0 | i |i |i ( c Q |i ~ 2 ~ i 3 ~ | |

    x Q yc |0 |0 t

    |i |i

    rd |0 }( ~ | i Q ( c r } Q }

    |t } } |! Q | D ~

    7 |i 2

    } |

    r

    ~

    |i |

    s

    D

    ~ ( |t }! & ~ Q

    }( ~ v

    i 3 ~ |t }l l

    {

    t |t }2

    p

    y

    }i j

    '

    S D

    |i u r ~ Q ~

    Q |7 }( ~ |

    ~ |7 } Q }q yc } } |i } ~ }

    } ~

    u

    z D

    |i ~ | |7 }( ~ | t |t } } | |

    ~ |i I } Q }q yc } } |i I t c Q |r ~ |i I }

    } ~

    u

    {

    i |i |i x & ~ Q

    ~ |

    i |i 7 c Q |i ~ q |

    r |

    7 x } Q

    | }( ~ |

    |i t | 7 yc } } |i u Q }

    |i |i 7 i |i |i c Q |i ~ i Q |! | r u Q i ~ |i } ( c Q |i ~ I ~ i 3 ~ |c {

    i |i |i |2 i |7 c Q |i ~

    D e z| {Y }7 ~

  • 8/6/2019 Cours Mecanique Du Solide

    34/59

    ~ i 3 ~ |2 |

    |

    t |i q } Q u

    D D

    } ~ |c r | }( ~ |

    ~ |7 |i yc } } Q I } ~ q |7 i h |

    D S z {

    i |i |i I x & ~ Q

    D i |i |i |2 ~

    ~ |i |i |i

    D z

    ~ t }

    ~ | t |i | & ~ Q

    D i |i |i |c r

    } |

    I ~ |i | |t } x & ~ Q

    D i |i |i | i t |

    Q

    i

    |i ~ |( } }

    ~

    |t } |!

    |

    !

    # "% $ & ') (

    "1 0 (3 2 5 4

    r |i

    |l

    |i |t }

    |l k i |i } r6 z r6 $ |i 0 |i

    i

    |t }

    t |t }I ~

    8 7

    i |c r Q } ~ |

    |i 9

    D D

    |i 2 i |i |l vx w v

    x Q yc |

    ~ |& ~ |i | }( ~ |( t

    |d I ~ |i | |t } 7 } c Q |i ~ ~ i 3 ~ | R |

    } |t } } t h |i I |

    ~ |i I ! c Q |i ~ i Q |2 |

    u l

    A @ e z| {Y }7 ~

  • 8/6/2019 Cours Mecanique Du Solide

    35/59

    A 1( " F "$ & e F #' % & # 1 ) &

    S

    gI } h } i |I Q i |i |t }

    } ~ D ~ t |i t |u Q ~

    x 2

    y i |e |) } } |) ps r7 |) t h

    Q r7 |$ t |i |

    rd | |i D |i |

    p

    Q !

    ~

    Q i |c r2 } ~ s | ~ |i } |

    t |$ } Q }

    |i |i ~

    Q |u Q ~ } } 7

    |s ~

    Q i |i | i |

    } } | ps

    | } h } i | Q i |i

    |i ~

    ~ |i Q ~

    ~ 6 ~

    Q i | |i u Q

    !

    |e x 2 " ~ 2 |t } | | Q } |

    i |i |i D y Q t |i $ # x ( & % ( '` 0 ) l r yc t |7 ! |t } Q }

    }

    Q

    Q |t } |i |i |i | x 2 |i |7

    Q | t D 0 c

    I } }

    i | Q ~0 t |i t |u Q ~ |

    i |i |i 1 # x ( d x |

    i Q

    |i

    |i i ~ Q | Q ~

    Q 0 ~ t |i t |u Q ~ I

    } |

    2

    3 %

    x D l

    4" 57 6

    8

    9

    @

    A

    B

    C

    D

    E

    F

    G

    H IQ P

    R

    G

    H IT S

    d

    }

    |U 4 Q }q |

    Q ~ t |i t |u Q ~ r |t } i |i t |

    Q

    2

    W VY X

    l

    I t } yc |i

    Q

    Va `

    x t t i i Q

    |

    |t } Q |i ~ u

    S

    S S

    |i |t } } |2 | Q }! #a Q } b ~ |7 |t } } |7 D |i d c |i |i 2 |

    Q

    e #

    t i

    t |t } |l

    |t } }

    } Q }q 7

    } |

    W Vg f

    Vg h

    Va `

    l t ~ | |

    |i i i i ~ |2 |p 4 |i Q }a # c

    S z T q

    Q i ~ |i I |

    |i i i i ~ |7 | x 2 |i Q }r #

    S D z

    t ~ |7 |

    |i i i i ~ |

    su t

    | |i Q }a # c r Q }q 7

    } |

    W VY f

    Vg h

    W Vg `

    l

    z Q v

    i ~ |i q |

    i |7 ~

    |i I i i i ~ |2 l t ~ |U ~ | !

    } Q |7 |

    su t

    } ~ q x |7 } |

    } |i | t i | ~ |

    |i i |7 |i Q

    |i |7 |t } } |i ~ |t }

    Q Q i |t }

    |i 2

    2

    x w& y

    w&

    l

    D D

    |i 3 ~ | x

    |i ~ 8 7

    |i |t i |i |i ~ |2 Q ~ |2 ~ Q

    ~

    ~ |i |i |i

    i ~ Q |

    i |

    |7 t } ~ Q |( i i i ~ |!

    Q i ~ | a Q }! # {

    |i x |l

    |t } }

    |2 t |i |2 |i Q

    Q Q r r

    |i I |t }

    i t |t }

    Q

    I Q ~ |i

    }I |

    |i 2

    S T qQ i ~ |i I x i |i yc |2 i i i ~ |U r q ~ } h } i | Q }a # c

    z q

    Q i ~ |i x i |i yc |

    |i |i | |

    |t } Q |i ~ Y 7 ~ } h } i |2 Q } # 2

    |i x

    yc | |t }` i |i yc |t }

    |i |i |t }I |i

    '

    l

    D~ } |i x |l } |i t | D ~ |0 i yc Q |

    |i i | |0 x i |i yc | |i t ~ | ~ |0 |i Q

    Q Q rd r

    |i ( |t }

    i t |t }

    Q

    I Q ~ |i

    }I |

    |i 2

    |t }I ~ Q

    }8 7

    |i ~ |t }I |i

    z

    r

    D

    |i

    D

    }

    w v |i |t }

    |i Q |t } ~ } |i I

    |

    } |c

    zI } ~

    } |I Q |i Q u r |i

    ~

    ~ | 2 } ~ | ~

    8 7

    i |c r ~ ~

    |i ~ u r

    |i | x 2 |i |7

    Q t

    } |7 Q ~ t |i t |u Q ~ x 2 ` ~ |

    Q

    Q ~

    ~ I |

    !( |t } } | ~

    |

    Va `

    z S {

    i |i |i |2

    ~

    |

    Vg `

    q |l |i t

    Q I |7

    |i ~ D |i d c |i |i 2 } ~ ( x 2 x Q |! ~

    i

    |

    Q |i Q | ( h Q i ~ |c

    e z| {Y }7 ~

  • 8/6/2019 Cours Mecanique Du Solide

    36/59

    z z z

    |i ! ~ | x

    |i

    ~ |7 x |l

    |t } }

    |

    |i

    i ~ Q I |

    i |2 | x i |i yc |2 i i i ~ |c

    D q

    Q i ~ |i ( u i

    #B | x 2 } ~ 2 ! Q } 7

    } |

    Vg f

    Vg X

    W V

    l I ~ | |i ~ |l vx w v

    S z {

    i |i |i I |t }

    }

    }I D ~

    7 | |i Q

    |p

    Q q

    x 2 l

    z

    ~ |i 7 } 7

    |I t |t }

    }

    } D ~

    7 |c

    {

    i |i |i

    i

    | |t }

    |i }

    ~ |i |i }I Q ~

    ~ |

    } |t }

    }

    }I D ~

    7 |7 Q } | u }

    e z| {Y }7 ~

  • 8/6/2019 Cours Mecanique Du Solide

    37/59

    " 1! 1( "$ & e F #' % & # 1 ) &

    S

    S S

    I

    V

    (3 2 5 4

    VY h

    " & ') (

    Va `

    2

    Va `

    Vg X

    2

    & ') (

    VY f

    |

    |i i i i ~ |7 |p 4 |i Q }q 0 |t } 7

    su t

    !

    p p

    Vg X

    p

    "

    p

    !

    Vg f

    2 & ') (

    (3 2 5 4

    VY h

    " 2 & ') (

    Va `# "

    $

    %' &) (

    0

    13 2 5 4

    0

    13 2 5 6

    $

    %7 &9 8

    @

    @

    $

    %7 &B A

    S z

    su t

    x 2

    2

    Va `

    p

    2

    Vg `

    S D

    su t

    su t

    ! "

    su t

    x 2

    p

    C

    VY f

    2

    & ') (

    (3 2 5 4

    VY h

    "E D

    " & ') (

    G F

    2

    W Vg `# H

    z I

    su t

    IQ P

    R

    t

    Q p

    ! "

    R

    tT S

    V U W

    p

    p

    W Va `

    "

    R

    tT S

    V U W

    q ( Q }

    |i | x 2 |i |

    7Q d i Q

    Q

    Q |

    R

    tT S

    V U W

    Y X

    Va `

    '

    D

    I

    su t

    X

    Va `

    IQ P

    ' a `

    su t

    X

    Va `

    & (c b

    C

    " & ') (

    H

    2

    & (c b @

    e d

    D

    p

    p

    "

    #

    "

    "

    p

    t |t

    I

    IQ P

    V # "

    g f

    V

    Vg X

    t |t

    f2

    V `!

    VY X

    " 2

    V `!

    2

    V `!

    Vg Xh "

    & ') (

    f2

    VY f

    2 & ') (

    Vg h

    iQ p qs ru t' qw v x y G

  • 8/6/2019 Cours Mecanique Du Solide

    38/59

    3

    2

    V `!

    V

    c 2

    (3 2 5 4

    Vg f

    D

    p g f

    W V

    Vg X

    & ') (

    f2

    Vg f

    2

    & ') (

    Vg h

    " Q p 2

    (3 2 5 4

    Vg f

    p

    "

    #

    D Q ~ |

    Q u r 4 } |

    u Q } Q }

    |i |i } ~ | t |i t |u Q ~ r Q

    }7

    #

    X

    V

    D

    |t i

    ~

    i |2 | ( t } ~ Q |2 i i i ~ |7 |p } ~

    V

    | D

    g f

    " 2

    & ') (

    (3 2 5 4

    " & ') (

    2 '

    @

    S

    r

    p

    "

    9 2

    p

    D

    " 2

    C

    & ') (

    "

    H

    F

    z

    p (3 2 5 4

    D

    d ( Q }

    |i |0 x 2 |i q |7

    Q d i Q

    Q

    Q |7 |i x 7

    } |i t |7 |

    |i |i |i | 4 |i ! x 2 `

    i ~ |i !

    " !$ #

    '

    b %3 W

    #

    #

    '

    D

    ' &

    r "

    & b @

    i

    D6

    "

    2

    C

    & ') (

    "

    H

    F" (3 2 5 4

    9

    & b

    ) (

    @

    @

    |t } |i Q

    }! Y d l rd |i 2 @

    }

    I

    |i Q |t }u 1 0 | D |i 2

    I

    IQ P

    a `

    f2

    C

    & ') (

    "

    H

    2

    & ') (

    (3 2 5 4

    ! '

    @

    |i 7

    I

    3 2

    IQ P

    a `

    f

    "

    2 f

    2

    C

    & ') (

    "

    H

    2

    & ') (

    (3 2 5 4

    "

    & ') (2 '

    @

    x vl 4 7

    2

    | ( |i Q

    l

    z

    z S

    I

    su t

    IQ P

    p p

    "

    Va `

    "

    R

    S

    V U W

    s t1 `

    IQ P

    7

    s t1 `

    C

    " & ') (

    H

    2

    b

    2

    & b

    a `

    f2

    '

    Q p

    2 & ') (

    (3 2 5 4

    i6 5 qs ru t' qw v x y G

  • 8/6/2019 Cours Mecanique Du Solide

    39/59

    z z

    I

    r

    IQ P

    R p

    ! "

    X

    2

    7

    r

    p

    D

    " 2

    C

    & ') (

    "

    H

    Fb

    2

    & b

    a `

    f2

    e

    D

    p

    g f

    2

    & ') (

    (3 2 5 4

    "s & ') (

    2

    D

    t }! l r

    g f

    " & ') (

    2

    2

    & ') (

    (3 2 5 4

    I |i

    ~ |2

    Q p

    2

    & ') (

    (3 2 5 4

    D

    p

    p

    "e #

    p

    "

    "

    p

    p

    " #

    D

    #

    Q p

    2

    (3 2 5 4

    VY f

    "

    p

    p 2

    & ') (

    " p (3 2 5 4

    VY X

    " p g f

    " 2

    & ') (

    (3 2 5 4

    " & ') (

    V

    D

    t }!

    g f

    " 2

    & ') (

    (3 2 5 4

    " & ') (

    2 '

    I |i

    ~ |2

    U ~ |

    #

    V

    &

    2 b

    2 e b

    (

    2 4

    (

    (

    3 '

    bc b4

    b4

    b x 2 br

    S

    }

    } D ~

    7 | |i Q

    |U

    Q

    x 2 `

    i ~ |

    V

    b

    g f

    V

    Vg X

    a `

    f

    ! '

    D

    r D

    t }!

    & ') (

    " (3 2 5 4

    '

    |t }

    }

    } D ~

    7 |7 |i Q

    |t }

    |i

    !

    b (3 2 5 4

    # "

    % $

    a `

    $

    z

    ~ i ~ |i ! }

    7 | t |t }

    }

    }q D ~

    7 |c r

    } |i

    2 '

    "' & |i

    ~ } |i 2 x ~ Q

    I

    g f

    " & ') (

    (3 2 5 4

    " & ') (

    2 '

    (

    ' 0 )

    f

    &

    "

    "

    &'

    q

    |i |

    }

    D ~

    7 |2 |t }

    }

    7|c

    (

    '

    )

    f

    & "

    "

    &'

    q|i |

    }

    D ~

    7 |2 |t }

    }

    7|7 }

    1

    |i I |i |7 |t } } 7

    |7 }

    1

    $

    (

    '

    # "

    |i ~ | (3 2 5 4

    # "

    1 2 4 3

    $

    |i

    $

    1

    f

    & " & ') (

    # "

    &'

    i 5 qs ru t' qw v x y G

  • 8/6/2019 Cours Mecanique Du Solide

    40/59

    q

    |i |

    }

    D ~

    7 |2 |t }

    7 }

    7|c

    z

    1

    r

    }

    D ~

    7 |7 }

    7|7

    |t }

    )

    r D

    f

    &"

    "

    &

    '

    d

    i

    | |t }

    1

    @ qs ru t' qw v x y G

  • 8/6/2019 Cours Mecanique Du Solide

    41/59

    A 1( " F % "$ &4 F #' % & # 1 ) & 2 & 1 & # ) #

    #

    #

    I } |

    } |0 D i ~ |i u ~ |i i ~ |t }2

    ~ |i |i } D ~ t |i t |u Q ~ | } } | p |i ( | t h

    #

    q

    |t }!

    ~ |i |i }

    Q ~

    |i ~ Q } |

    Q |i u Q ` |2

    y D ~

    Q

    Q } Q x Q yc | $$ t |t ! x

    Q |c 1 |!

    i 7 |i

    ~

    Q i |t } } ~

    } q

    ~

    ~ } u Q } |i ` |t } u Q i i }

    Q ` ~ 0

    |l k i |i q |

    |i |i | yc } } |i |i

    R |i |

    }

    |i

    } Q l l z I

    } |i

    Vg f

    !

    "

    {

    Q }q

    ~ |

    8 7

    i |

    Q }

    |2 Q }q |

    i |i |i b #$ #d I

    | x

    VY f

    Vg h

    Vg `

    | |

    i | 2 u #$ # } ~

    }

    y Q t |i I t } yc |i

    Q 2

    W VY f

    | |t i |i ~ |t } } | |2 r

    Va `

    | |t i |i ~ |t } } | |

    Q

    ~ t |i t |u Q ~ r

    Vg f

    | |t i |i ~ |t } } | | yc } } |i |i ~ t |i t |u Q ~

    Q q

    Q ~

    Q i c r

    %

    Vg f

    "' &

    VY h

    ! u i

    ~

    Q i 2 } ~ q | t |i t |u Q ~ r

    p$ # |

    |i I D |i |7 ~ t |i t |u Q ~

    Q q

    I 2 x |2

    Va `

    ) ( x } Q

    yc | R 1 0

    l r2 } |

    ~ | |i

    |i q |t }

    }I Q |t }

    } t |t }I Q ~ t |i t |u Q ~ }

    r #

    $

    $

    3 5 4 6 4

    R T

    p

    8 7 c

    y c

    }i t t i i Q

    |

    |t } Q |i ~ l j

    '

    }i #

    @ 9

    }i |i (3 2 5 4 $

    '

    & ') ( $

    |i dR

    s

    ~ q |t }I

    u Q

    ~ i i ~ |t }l

    S B AC 4

    5 D Q

    S S T q

    Q i ~ |i I ( |t } } | | yc } } |i |i

    ( ~ } Q

    P

    S z

    0

    |i I x i |i yc |2 i i i ~ |U F E! ~ t |i t |u Q ~ ! ~ } Q r ~ |i

    ~ |7 |i

    i

    | ps r

    |i a # I

    S D H G

    t | Q ~0

    i | ~ t |i | | } } | |i q ~0

    i | ~

    |i i i i ~ | |i } Q } h

    t } |

    Q i ~ v

    i |7 } ~ q |t }q

    ~ |i |i } ~ t |i t |u Q ~ r

    ~ |i I

    }q |i Q

    }I } u Q Q |t } Q

    wP I

    w&

    |i r #

    w

    2

    w&

    #

    I

    S

    i | |

    i | | x i |i yc | i i i ~ |c rQ |i ( t ~ | ~ |` |i Q

    y i |q ~ |

    ~ } } Q t | Q

    |i #

    I

    S z

    ~ Q

    8 7

    |i ~ |! Q ~

    S

    |t } w v |i |

    |i Q |! | t |i |t }8 7

    |i ~ |t } Q ~

    S D

    S D T q

    Q i ~ |i } Q ! ~ |! @ 9R Q

    X

    "

    y

    @d

    qs ru t' qw v x y G

  • 8/6/2019 Cours Mecanique Du Solide

    42/59

  • 8/6/2019 Cours Mecanique Du Solide

    43/59

    " 1! 1

    % "$ &4 F #' & # 1 ) & 2 & 1% & # ) #

    #

    #

    S S

    " #

    S z

    F E

    p

    " #

    S D

    |

    i |2 | ! t } ~ Q |2 i i i ~ |7 Q } r

    |

    p

    p (3 2 5 4 $ "

    @

    p

    &

    p & ') ( $ @

    5

    |

    i |7 ~

    |i i i i ~ |7 |i r

    |

    p$ #

    @ 5

    S

    p

    " #

    p

    (3 2 5 4 $ "

    p

    (3 2 5 4 $ " p$ #

    I

    " #

    (3 2 5 4 $ " #

    @

    e d

    S z

    r

    ~ }( ~ | ! |i Q

    E @

    } | t ~ |t }q |i Q

    }! Y d |i 2 i

    l

    S D

    #

    #

    #

    p

    2

    X

    (

    z

    z S

    " #

    X

    (

    ~ }( ~

    P

    '

    r

    Vg f

    V f

    R }i |i

    X

    (i

    '

    r |

    ~ |i |i I ~ i |i ~ I ~ t |i t |u Q ~ |t } ~

    ~ |i |i

    W P W

    D 2 |

    ~ |i |i D

    P

    u u s

    i Q I

    u Q |2 |i

    } 7

    X

    (i

    $

    r Q

    }u r D

    t } (

    ~

    |i |i |

    j &

    j p & ') ( $

    z z z {

    t }I t |U ~

    t t t |

    P

    #

    #

    j

    P

    & ') ( $ b

    " #

    j & ') ( $ "E

    P

    T

    X

    (

    z D

    ' a `

    P

    #

    #

    j

    P

    & ') ( $ b

    " #

    j & ') (6 $ "E

    P

    zI

    I

    IQ P

    P

    a `

    P

    P

    z z T

    P

    ( #

    8 7

    X

    (

    8 7

    X

    (

    b

    j p & ') ( $

    " !$ #

    @ i qs ru t' qw v x y G

  • 8/6/2019 Cours Mecanique Du Solide

    44/59

    D

    D S v

    c Q x } Q

    P

    r | t |i t |u Q ~ |t } t |i

    |i |I |i ` |t } } | |I }

    t |i | D |i | }u Q ~ |

    ~

    P

    P

    t |t 7 ~ | |t } } | | yc } } |i |i

    @ 7

    X

    (i

    r

    c r

    Q I |

    P

    P

    r |7 t |i t |u Q ~ |i

    |7

    |i |! t |t

    yc } } |i |i u

    D z

    I

    8 7

    X

    (

    $

    a `

    j &

    j p & ') ( $

    |i

    ~ }( ~ |( |t } |i Q

    }2 i 7

    |t }7 Q }

    Q |

    S

    }

    7

    ~

    ~ } c Q 7

    |t }7 } Q } |t } i

    ~

    ~ |i |i ! ~

    t |i t |u Q ~ r Q

    }I D

    t }

    z

    P

    #

    #

    j

    P

    & ') ( $ b

    " #

    j & ') ( $ "E

    P

    D D

    ' a `

    P

    " #

    j & ') ( $ "E

    #

    #

    j

    P

    & ') ( $ b

    P

    z

    I

    I

    IQ P

    P

    a `

    P

    P

    z z T

    P

    8 7

    ( #

    X

    (

    X

    (

    Q

    S

    (

    P

    P

    r

    '

    b

    X

    (

    D r

    Q I |

    P

    P

    r |7 t |i t |u Q ~ |i |7

    |i |7 } Q }q yc } } |i |i u

    z

    I

    " #

    ' a `

    #

    |i |i ~ } Q |t } |i Q

    }! Y d l r |i ! i

    i 7

    |t }I Q }

    Q |S

    r

    | ~ |

    "

    (3 2 5 4 $

    P

    (

    # b

    p (3 2 5 4 $

    D

    d (

    } i |

    } | } | |i |7

    }( ~ |

    "

    (3 2 5 4 $

    P

    ( ' a `

    P

    (

    (3 2 5 4 $

    |i

    #

    ('

    (

    P

    (

    (3 2 5 4 $

    2

    "

    P

    (

    "

    z

    Q

    #

    P

    (

    ( b

    ('

    Q

    z

    v

    ~ |i | i

    i |

    } |c r |7 t |i t |u Q ~ c ( |t } t |i |2 |i ~ Q } Q }q yc } } |i |i u

    D

    D S

    F E

    F E

    P

    P

    F E

    P

    '

    p

    " #

    p

    " #

    9

    " !

    Q

    @ @ qs ru t' qw v x y G

  • 8/6/2019 Cours Mecanique Du Solide

    45/59

    !

    "

    "

    #% $

    &

    '

    (0 )2 14 36 5 78 5@ 9B AD CE ) FH G IP 3R Q )% 5@ SE SE AB 9U TW VY X ) F` F4 VE 3` AU )2 Q )a 3R Q ) 5@ Vb )a cW 14 3R )2 df eh gi )a 1p df eq ds r2 ) F4 1u t

    v e wy xW r R U p

    P

    d

    e wy xW r R U p wy xj a k l q m4 n o ds rH q n l xH a k Y

    d

    r

    r

    `

    z W {6 |8 } ~

    y

    e n d l eq d n d l eh g

    e w n

    r

    o

    r

    f

    r

    w n

    r

    r

    o

    r r

    r

    e w n

    r

    r

    o

    r r

    r

    g {6 i ~

    (0 )2 14 36 5 78 5@ 9B AD CE ) FH G IP 3R Q )% 5@ SE SE AB 9U TW VY X ) F` F4 VE 3` AU )2 Q )a 3R Q ) 5@ Vb )a cW 14 3R )2 d eh gi )a 1p d eq d ) F4 1u t

    v e wy x n l & r R U p B

    B

    P

    d

    e wy x n l & r R U p

    g {6 i ~

    W f H p P

  • 8/6/2019 Cours Mecanique Du Solide

    46/59

  • 8/6/2019 Cours Mecanique Du Solide

    47/59

    x

    u Q

    ~ i i ~ |

    ~

    p |i

    )

    z D

    0 } ~

    } Q

    } ~ k } Q |i

    Q 7

    |

    ~ r ~ | x

    ~ } } |2 } } |i (3 2 5 4

    r u Q i ~ |i I

    i

    |

    7 |t }

    |i |t }

    } i Q

    }I ~ } h } i |c

    Q | x

    u Q

    ~ i i ~ |

    ~

    ps r

    8 7

    '

    Q

    |i

    }i

    z

    D T q

    Q i ~ |i I x i |i yc |2 i i i ~ |7 ~ } h } i |

    "

    z S D q

    Q i ~ |i x i |i yc |

    |i |i | |

    |t } Q |i ~ Y 7 ~ } h } i |2 I

    |i 7 x

    yc | |t } i |i yc |t }

    |i v

    |i |t } |i

    '

    l

    z S S g

    ~ } |i ~ h

    } |i c Q

    $ | x i |i yc | t u Q i ~ | ~$ } h } i | ( |i |i $ t ~ | ~ | i yc Q |

    |i i |7 ~

    ~ |i |i u

    z S

    d y

    ~ i | I |t } }

    ~ } ~

    ~

    |!

    |i ~ 7

    } Q 7

    |2

    |i

    Q

    7 x | |t }

    Va `

    $

    l

    D i | |

    i |7 ~

    |i i i i ~ |7 | ! y

    ~ i |0 |i

    ~

    ~ }7 Q } x h

    t } |( ~

    ~ |i |i 2 } Q } yc } } |i |i | I } ~ l rz i

    7 x ~ Q

    s D i |i |i |

    ~ } |t

    |2 ( ~ |i |7 } Q }

    Q

    P

    0 t ~ | ~ | |2 t |i |2 D |i |( 4 |

    } } t | ~ |

    }

    D ~

    7 |

    r } i |7 ~ | i y Q

    t i } |i u

    W q|i |

    }

    s D ~

    7 | |t } w vx w v |i | }

    7|d

    ~ x rT ~ |i | |t }

    i

    | |t }

    } i Q

    }2 Q ~

    ~ ! | t |i |

    }

    D ~

    7 |d

    @ p qs ru t' qw v x y G

  • 8/6/2019 Cours Mecanique Du Solide

    48/59

    " 1! 1

    2

    "$ # & # 6

    # 1 ) # & # ) "$ &U 7

    1

    S

    7

    7

    x 2 "

    x 2

    &

    t

    "E

    &" !

    W V

    {

    t

    "E

    &

    @

    e d d

    z

    z S

    2

    q

    i ~ t |2

    p

    #

    V

    &

    Vg X

    " p

    W VY f

    p

    t f

    V

    W VY X

    !

    V

    &

    Vg X

    " p

    W VY f

    {

    p

    t Q f

    " p (3 2 5 4

    @

    e d

    &

    p

    t

    " p & ') (

    @

    e di

    z z

    q

    i

    ~ 2 |i U Q } |

    i |i |iD

    b P

    u

    R W

    p

    @ e d @

    z D

    q

    i ~ 2 |i

    6 &

    @

    e d

    z

    0 i c Q (

    l r |i I |i ~ } Q ( 3 2 l rd

    Q

    ~ }2 l r

    | ~ |

    7

    " p i

    t Q f

    " " p x (3 2 5 4

    2 '

    @

    e d

    z z

    I 0 2 ~

    | x ~ Q

    i v |t } } ~ }

    Q

    |i

    0 i yc |I | dt |i |i | |i |1

    ! '

    |i

    |i | i | |i | |i |

    |i

    7

    " p i

    t

    " p x z & ') (

    & ') (

    u @

    e dp

    q

    |

    t

    % $

    0 a `

    & ') (

    $

    & ') (

    |i

    0 )

    )

    c

    z D

    l rd i

    l rd

    |i 2 p

    |i !

    7

    " p

    p (3 2 5 4

    &

    p

    7

    " p

    9

    "

    7

    p & ') (

    " p & ') (

    !

    z

    T q

    |

    0 )

    )

    r

    |t } q

    ~

    ! e

    &

    f

    7 " p

    p (3 2 5 4

    @ 5 qs ru t' qw v x y G

  • 8/6/2019 Cours Mecanique Du Solide

    49/59

    {

    | i | & |t } q

    ~

    2 '

    (

    & & %3 W

    p & ') (

    I Q ~ (

    ~

    ~ }

    ~ |i |i } Q }q yc } } |i |i }

    j

    $

    &

    f

    & & %3 W

    7

    " p

    b 4

    T

    j

    $

    Q

    z D

    ~ Q

    D i |i |i |2 i t |

    Q

    |i |i u r Q } t | u }2

    f

    "

    2 '

    t |t

    " p x

    7 " p i

    t

    {

    i

    | D

    } i Q

    |t } 7

    7

    " p i

    t

    " p x

    T

    7

    z

    D

    i |i yc |2 i i i ~ |2 |

    r

    r u " r u

    &

    "

    p

    #

    "

    z

    6 &

    "

    p

    t

    "

    2

    p

    z S D

    i |i yc |

    |i |i |2 |

    |t }