A thinwalled, filamentwound pressure vessel is pressurized such that at a point in the wall is in the figure below. ?=[ ????????0 (c)the magnitude of the normal stress acting on the filaments, and (d)the magnitude of the shear stress (b)the magnitude of the traction vector acting alongthe direction of the filament winding. −????????0 Determine:
A thinwalled, filamentwound pressure vessel is pressurized such that at a point in the wall is
in the figure below.
?=[
????????0
(c)the magnitude of the normal stress acting on the filaments, and
(d)the magnitude of the shear stress
(b)the magnitude of the traction
−????????0
Determine:
]
suitable stress tensor ?′for a rotated coordinate axis. (You can use Matlab or a calculator to
The filament winding angle is ?=53.13°from the longitudinal axis ofthe pressure vesseas shown
Noting that the transformation matrix to rotate the x-y coordinate system anticlockwise by ?is:
(e)find the magnitude of the normal stress and shear stress acting on the filaments by finding a
(a)Write down the stress tensor in the xyzcoordinate system.
under a plane-stress state with ???=10.946MPa, ???=21.892MPaand ???=0MPa.
001
perform the tensor multiplications)
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