Rasmus ÿstergaard forside 100%.indd - Solid Mechanics

454 R. C. ØSTERGAARD ET AL.
(a)
(b)
P
∼H/4
Figure 4. Loading and mesh used for extracting the mode mixity.
In all cases the relative deviation between numerical and analytical values
was less than 0.005. Furthermore, by comparing the results with results
found with meshes having significantly more elements and G calculated
by (10) and (11), respectively, were shown to be mesh-independent. Figure 4
shows a typical mesh used for the calculation. In order to resolve the stress
and displacement field at the crack tip, the mesh was refined near the crack
tip [8,11].
Extracting the Load-independent Phase Angle x from a Load Case
As described in the section ‘Mode mixity’, the load-independent phase
angle ! should be determined for a single load case for each sandwich
structure. Using Equation (10), the mode mixity can be extracted from a
finite element solution of the sandwich loaded with any combination of the
loads Mn, Pn, n ¼ 1 ...3. A convenient choice is to take P 6¼ 0 and M ¼ 0
(Figure 4). Then according (9) to ! ¼ .
The following results are found from the finite element calculations with
l ¼ h ¼ 40.0 mm.
Configuration x
GFRP/H80 60.2
GFRP/H130 66.0
Λ