1 Introduction
2 Analytical Formulae and Optimization
2.1 Theoretical Formulation
2.2 Facesheet Wrinkling
2.3 Bending
2.4 Torsion
2.5 Shear
2.6 Buckling Interaction
2.7 Dimensioning Procedure of Sandwich Composites
3 FEM Analysis
3.1 FEM Approach for Linear Buckling
3.2 Material Failure Criteria Applied in the Nastran
4 Verification of FEM Model
4.1 Comparison of Buckling Loads
Bending(Nm) | Shear(N) | Torsion(Nm) | |
---|---|---|---|
analytical | 2.6E7 | 1.9E6 | 6.3E6 |
FEM | 2.2E7 | 1.4E6 | 6.1E6 |
Deviation | 16% | 26% | 3.2% |
4.2 Comparison of Sizing Results for the Sandwich Cylinder
4.3 Parametric Optimization of Sandwich Cylinder
4.3.1 Step 1: Determine the Minimum Layers Number
4.3.2 Step 2: Determination of the Optimum Fiber Orientation
4.4 Optimization for Sandwich Composites Cylinder with C Frame
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Frame height H and width W <20 mm, 100 mm>
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Frame thickness t and t 1 <0.5 mm, 10 mm>
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Fiber orientation < −90, 90>
4.5 The Core Materials
Core Materials | Weight(Kg) | Max_ constraint | [0/30/45/60/90]s
| W/H/t/t1(mm) | |
---|---|---|---|---|---|
Hexcel® | Al 1/4-ACG-.003 | 1876 | 0.006 | [9/1/1/1/3]s | 17/65/0.7/2 |
Aramid HRH-10-1/8 | 1988 | 0.006 | [8/1/1/1/3]s | 41/81/0.9/2 | |
Honeycomb | Glassfiber HRP-3/16 | 2093 | 0.01 | [9/1/1/1/2]s | 31/72/0.6/2 |
Al 5/32-5052-0.002 | 1827 | 0.003 | [7/1/1/1/3]s | 100/100/0.5/0.9 | |
Rohacell ® Foam | 200 WF | 1450 | 0.02 | [1/1/1/1/2]s | 100/100/0.5/4.8 |
110 WF | 1833 | 0.02 | [8/1/1/1/3]s | 61/100/0.5/1.2 |
4.6 ANOVA Optimization Design Towards Frame Pitch and Core
Core thickness(mm) | Frame space(m) | Weight(Kg) | Max_constraint | [0/30/45/60/90]s | W/H/t/t1(mm) |
---|---|---|---|---|---|
5 | 2 | 1419 | 0.07 | [4/1/1/1/2]s | 100/100/1.9/4.9 |
1 | 1130 | 0.003 | [1/1/1/1/2]s | 100/100/0.5/3.5 | |
0.5 | 1129 | 0.002 | [1/1/1/1/2]s | 87/100/0.5/2.1 | |
10 | 2 | 1310 | 0.04 | [1/1/1/1/3]s | 100/100/1.5/4.9 |
1 | 1249 | 0.003 | [1/1/1/1/2]s | 63/100/0.6/5.6 | |
0.5 | 1245 | 0.003 | [1/1/1/1/2]s | 70/100/0.5/2.4 | |
20 | 2 | 1450 | 0.02 | [1/1/1/1/2]s | 100/100/0.5/4.8 |
1 | 1454 | 0.0008 | [1/1/1/1/2]s | 100/100/1.7/2.4 | |
0.5 | 1461 | 0.003 | [1/1/1/1/2]s | 44/100/0.5/1.4 |
Core thickness | Frame pitch | Result | |
---|---|---|---|
Experiment 1 | 1 | 1 | 1129 |
Experiment 2 | 1 | 2 | 1130 |
Experiment 3 | 1 | 3 | 1419 |
Experiment 4 | 2 | 1 | 1245 |
Experiment 5 | 2 | 2 | 1249 |
Experiment 6 | 2 | 3 | 1310 |
Experiment 7 | 3 | 1 | 1461 |
Experiment 8 | 3 | 2 | 1454 |
Experiment 9 | 3 | 3 | 1450 |
Average of level 1 | 1226.0 | 1278.3 | |
Average of level 1 | 1267.7 | 1277.3 | |
Average of level 1 | 1455.0 | 1393.0 | |
Extreme Level difference | 229.0 | 115.7 |
5 Conclusion
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For sandwich cylinder without any stiffeners, the buckling constraint is critical. The addition of frames can efficiently improve the structural stability.
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The 200FW foam is more efficient than honeycomb materials for the fuselage. In addition, the normal stress in the radial direction is different between the two kinds of core materials.
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For the frame stiffened sandwich cylinder, the core thickness has a larger influence on the final weight than the frame spacing.
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Increase of the fiber orientation in the axial direction is the most effective to increase the buckling load when the bending moment is dominant.
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It is not much precise to set the layer number and orientation at the same time for the optimization using the classical algorithm. The two-step optimization is a good choice to determine the thickness and the fiber orientation.
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The sandwich cylinder with core thickness of 5 mm and frame space of 0.5 m exhibit the minimum weight.
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Finally, one should note that the interface between the skin and the core is not modeled in this paper. If debonding between skins and the core is one of main issues of failure modes, a bonding layer should be added into the model.