Nonlinear Finite Element Analysis of Concrete Structures

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K^IO 10 -!) cos 2 a
is added to element K 2i-l,2i-l
K-, (10 -1) cosasin: is added to element K 2i-lf 2i
10 2
1^(10 -1) sin a is added to element K 2i,2i
where
2 2
K. = K-. , ^. , cos a + 2K_. ., _. cosasina + K_. .. sin a
1 2X-1,2J-1 2i-l,2i 2i,2i
(B-l)
The modified stiffness matrix continues to be symmetric. Correspondingly,
the following contributions should be added to elements
in the vector F in eq. (4.6-1)
P, cosa is added to element F_._,
P, sina is added to element F 2i
where
,10
P, = K 1 10 Y - * F 2i-l cosa + F ?i sinot )
and K. is given by eq.*(1).
Similarly, if the displacement in Z*-direction at nodal point i
is prescribed to be Y then the following modifications of
matrix K and vector F in eq. (4.6-1) are carried out
K 2 (10 10 -1) sin 2 a
is added to element K 2i-l,2i-l
- K 2 (10 -1) sinacosa is added to element K 2i , _.
K 2 (10 10 -1) cos 2 a
is added to element K 2i,2i