User:Eml4500.f08.ateam.shah/Week 6

Continuation from the Lecture: Friday 7, Nov 2008



Stiffness Terms:





Assume displacement u(x) for xi <= x <= xi+1
 * (i.e. x belongs to [xi, xi+1])

Motivation for linear interpolation of u(x): 2 Bar Truss



Deformed shape is a straight line, i.e. there was an implicit assumption of linear interpolation of displacement between 2 nodes.

Consider the case where there are only axial displacements (i.e. 0 translational displacement).

Question: Express u(x) in terms of di=u(xi) and di+1=u(xi+1) as a linear function in x (i.e. linear interpolation)

u(x) = Ni(x)di + Ni+1(x)di+1

where Ni(x) and Ni+1(x) are linear function of x.

N i+1 (x)= (x - xi) * (xi+1 - xi)-1