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7th Report - Ardalan Amiri - 840734 OPTIMUM DESIGN OF COMPOSITE GAS VESSEL
In order to investigate the correlation between reinforced fiber polymer plane strengths and their designing parameters in a given loading condition, the following problem was defined and solved by Matlab and Abaqus. With Matlab coding a semi-automatic optimizer was scripted to find the lightest and cheapest solution manipulating number and orientation of laminae, composite stacking sequence and material type with respect to the given design restrictions. Finally, by means of Abaqus, the obtained optimized configuration was assessed in terms of structural integrity using Tsai-Hill criterion imbedded in FEA.
Problem
A 1.83-m-long cylindrical pressure vessel with an inner diameter of 0.889 m is subjected to an internal gauge pressure of 1 MPa. The vessel operates at room temperature. The cost of a graphite/epoxy lamina is 550 units/kg and the cost of a glass/epoxy lamina is 250 units/kg. Only 0°, +45°, –45°, +60°, –60°, and 90° plies can be used with symmetric laminate configuration can be used. Only graphite/epoxy and glass/epoxy laminae, as given in the following tables, were available, but hybrid laminates made of these two laminae were allowed. The thickness of each lamina is 0.127 mm. The mass and cost of the pressure vessel end caps was neglected. And finally, safety factor was set to minimum of 2.
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As can be seen the critical load is aligned in hoop direction. Therefore, we need to exploit the laminate mostly in that direction by having the strong fibers in hoop direction. Yet due to Poisson's effect leaving axial direction without perfectly aligned fibers will result in either a heavy vessel or a hazardous one. Accordingly, the only efficient configuration would be a laminate comprising of 0 and 90 degree plies and acting purposefully in hoop and axial directions of the cylinder. Moreover, since the solution is instructed to be symmetric in layup sequence then we are not concern about the coupling effect as the B matrix is inherently diffused.
There is also no exerted unit moment upon the composite so the D matrix also loses its role in the final solution. Finally, the only stiffness matrix that matters in the current study is the one of extensional, i.e. A. Regarding the fact that our failure phenomenological approach here is focused on the failure of each individual ply, the stacking sequence, apart from its imposed symmetry, does not influence the overall strength of the laminate and can be set arbitrarily.
The following is the result of the written Matlab optimizing code. The script can be found in appendix.
n0 =
12
n90 =
8
TH0 =
0.7156
TH90 =
0.9417
mass =
32.7703 kg
cost =
1.8024e+04 units
Yet with removing one ply from axial fiber aligned laminae and violating the safety factor for very little amount we can reduce the mass for almost 1.5 kg and subside the cost for almost 1000 units.
n0 =
12
n90 =
7
TH0 =
0.8333
TH90 =
1.0029
mass =
31.1296
cost =
1.7121e+04
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Where n0 is number of plies in hoop direction.
n90 is number of plies in axial direction
TH0 is Tsai-Hill number for zero plies
TH90 is the same for 90 degree plies
And the material is Graphite epoxy.
This solution found to be both lightest and cheapest one bearing the given loading condition.
Abaqus FEM assessment
In Abaqus the second solution with 19 plies was modeled and the following is the process and result of its FEA.
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End of 7 th report Ardalan Amiri Politecnico di Milano December 16 th 2016
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