> with(linalg):
Warning, the protected names norm and trace have been redefined and
unprotected

> L[1]:=xi -> xi;

                           L[1] := xi -> xi

> L[2]:=xi -> 1-xi;

                         L[2] := xi -> 1 - xi

> N[1]:=xi ->
> (1/2)*(L[1](xi)-2*L[2](xi))*(2*L[1](xi)-L[2](xi))*L[2](xi);

  N[1] := xi ->

        1/2 (L[1](xi) - 2 L[2](xi)) (2 L[1](xi) - L[2](xi)) L[2](xi)

> N[2]:=xi -> -(9/2)*L[1](xi)*L[2](xi)*(L[1](xi)-2*L[2](xi));

     N[2] := xi -> -9/2 L[1](xi) L[2](xi) (L[1](xi) - 2 L[2](xi))

> N[3]:=xi -> (9/2)*L[1](xi)*L[2](xi)*(2*L[1](xi)-L[2](xi));

     N[3] := xi -> 9/2 L[1](xi) L[2](xi) (2 L[1](xi) - L[2](xi))

> N[4]:=xi ->
> (1/2)*(L[1](xi)-2*L[2](xi))*(2*L[1](xi)-L[2](xi))*L[1](xi);

  N[4] := xi ->

        1/2 (L[1](xi) - 2 L[2](xi)) (2 L[1](xi) - L[2](xi)) L[1](xi)

> Formfunktionen:=matrix(1,4,[N[1],N[2],N[3],N[4]]);

           Formfunktionen := [N[1]    N[2]    N[3]    N[4]]

> Nd:=map(collect,map(diff,Formfunktionen(xi),xi),xi);

  Nd :=

        [                2                      2
        [- 11/2 - 27/2 xi  + 18 xi , 9 + 81/2 xi  - 45 xi ,

                       2                      2       ]
        - 9/2 - 81/2 xi  + 36 xi , 1 + 27/2 xi  - 9 xi]

> J:=multiply(transpose(Nd),Nd):
> p:=map(int,J,xi=0..1);

                      [ 37     -189     27     -13 ]
                      [ --     ----     --     --- ]
                      [ 10      40      20     40  ]
                      [                            ]
                      [-189            -297     27 ]
                      [----    54/5    ----     -- ]
                      [ 40              40      20 ]
                 p := [                            ]
                      [ 27     -297            -189]
                      [ --     ----    54/5    ----]
                      [ 20      40              40 ]
                      [                            ]
                      [-13      27     -189     37 ]
                      [---      --     ----     -- ]
                      [40       20      40      10 ]

> K:=(E*A/(l*40))*evalm(40*p);

                           [ 148    -189      54     -13]
                           [                            ]
                           [-189     432    -297      54]
                       E A [                            ]
                           [  54    -297     432    -189]
                           [                            ]
                           [ -13      54    -189     148]
             K := 1/40 ----------------------------------
                                       l

