Page 111 - Process Modelling and Simulation With Finite Element Methods
P. 111
98 Process Modelling and Simulation with Finite Element Methods
XI d d d
Ik(T)= /[iN,T,['N,q +-N,T, +-N,T, +-N,T, 11 dx+
dx dx dx dx
4
d d d
N2T2 + - N3T3 t - N4T4
dx dx (2.74)
I1
d N2T2 + - N3T3 i- - N4T4 dw +
d
d
dx dx
XI d d d
j[; N4T4 [$ N,T, + N2T2 + - N3T3 + - N4T4
dx dx
x,
In the minimization process we differentiate Ik(T ) w.r.t. each Ti and set each
derivative to zero. This procedure generates a number of equations equal to
number of nodes. For instance the differentiation of (2.74) gives
Likewise, there will be three more equations. In matrix form it gives the stiffness
matrix.
K=
(2.75)
