Page 461 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

CURVED PIPES CONVEYING FLUID 433

where
I I:

after substituting < = 0 for the jth node and < = <e for the j + 1 node.
From equations (6.76), (6.82) and (6.83), one obtains

Substituting equation (6.85) into (6.78) yields the final form of the element mass, damping
and stiffness matrices:

The coefficients al, bl, a2, b2 are associated with no and its derivative no‘. These are
generally nonlinear functions of <, but within each element they are approximated by the
linear expressions
l7’ = a1 + a2<, l7“ = bl + b2<; (6.87)

hence, a1 = Dolj, a2 = (l7’l,+l - Z7°1;)/<e, and similarly for 61 and b2.