IV. Nature of Finite Element Solutions

•FE Model – A mathematical model of the real structure, based on many approximations.

•Real Structure -- Infinite number of nodes (physical points or particles), thus infinite number of DOF’s.

•FE Model – finite number of nodes, thus finite number of DOF’s.

ÖDisplacement field is controlled (or constrained) by the values at a limited number of nodes.

Recall that on an element :

4

u= ∑Nαuα

α=1

Stiffening Effect:

•FE Model is stiffer than the real structure.

•In general, displacement results are smaller in magnitudes than the exact values.

Hence, FEM solution of displacement provides a lower bound of the exact solution.

∆ (Displacement)

Exact Solution

FEM Solutions

No. of DOF’s

The FEM solution approaches the exact solution from below.

This is true for displacement based FEA!