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1.1 INTRODUCTION

In this report we explore different available design solutions to limit the strain below the yield stress and com-pare them based on their respective stress and volume.

Pressure vessel with a uniform wall thickness which meets the stress criteria is chosen as baseline for the study. It is compared with a pressure vessel with non-uniform wall thickness and non-uniform wall thickness with ribs on outer surface.

Material used for all the parts is: Inconel 718. The material properties are tabulated below

ELEMENT PRO CASE STUDY: PRESSURE VESSEL RIBS

Material Inconel 718

Elasticity Modulus (MPa) 2.10e+5

Poisson’s Ratio 0.294

Density (kg/m^3) 8.19e+3

Yield Stress (MPa) 723.95

Ultimate Tensile Stress (MPa) 1034.21

Figure 1: Table with material properties of Inconel 718

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1.2 PRESSURE VESSEL WITH UNIFORM WALL THICKNESS

It was found that for the part to be below the yield stress, the wall thickness should be more than 5.50 mm. The results for uniform wall thickness ranging from 5.50 mm and 6.00 mm are provided below:

Figure 2: X-Z and Y-Z planes section view for uniform wall thickness

Figure 4: Volume, Weight and Stress information for uniform wall thickness (5.65 mm)

Figure 3: Volume, Weight and Stress information for uniform wall thickness (5.50 mm)

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Figure 5: Volume, Weight and Stress information for uniform wall thickness (5.75 mm)

Figure 6: A comparison between different parts with uniform wall thickness

Uniform Wall Thickness(mm)

Volume (mm^3)

Mass (Kg) Maximum Von Mises Stress(MPa)

5.50 629785 5.16 781.35

5.65 648269 5.31 699.10

5.75 660534 5.41 662.34

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1.3 PRESSURE VESSEL WITH NON UNIFORM WALL THICKNESS

It was found from the analysis shown above that the stress values are significant only in the elliptical region of the pressure vessel. These stress values were used as modifiers to drive the non uniform thickening of wall. Maximum Stress values were calculated for a set of different minimum and maximum shell thickness values. The results obtained are compiled below.

Figure 7: X-Z and Y-Z planes section view for non uniform wall thickness

Figure 8: Volume, Weight and Stress information for non uniform wall thickness varying between 0.50 to 8.00 mm

Figure 9: Volume, Weight and Stress information for non uniform wall thickness varying between 0.7 to 8.2 mm

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Non Uniform Wall ThicknessMinimum (mm)

Non Uniform Wall Thickness Maximum (mm)

Volume(mm^3)

Mass(Kg)

Maximum Von Mises Stress(MPa)

0.50 8.00 266367 2.18 792.23

0.70 8.20 289104 2.37 715.43

0.70 8.70 304357 2.49 664.08

Figure 11: A comparison between different parts with non uniform wall thickness

Figure 10: Volume, Weight and Stress information for non uniform wall thickness varying between 0.7 to 8.7 mm

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1.4 PRESSURE VESSEL WITH NON UNIFORM WALL THICKNESS AND NON UNIFORM RIBS STRUCTURE ON OUTER SURFACE

To optimize for the weight we created diagrid rib structures with variable height and width on the outer wall (variably thickened) based on the stress value modifiers. The results obtained are presented below.

Figure 12 : X-Z and Y-Z planes section view for non uniform ribs structure on outer wall

with non uniform thickness

Figure 13: Non uniform wall thickness with 0.55 to 3.00 mm and non uniform ribs height and width varying from 0 to 12 mm and

0 to 1.9 mm respectively

Figure 14: Non uniform wall thickness with 0.55 to 3.00 mm and non uniform ribs height and width varying from 0 to 12.50 mm

and 0 to 2.00 mm respectively

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Non Uniform Wall Thickness Minimum (mm)

Non Uniform Wall Thickness Maximum (mm)

Non Uniform Ribs Height Maximum (mm)

Non Uniform Ribs Width Maximum (mm)

Volume (mm^3)

Mass (Kg) Maximum Von Mises Stress (MPa)

0.55 3.00 12.00 1.90 246976 2.02 734.70

0.55 3.00 12.50 2 248833 2.04 664.63

0.55 3.5 11.00 2.50 296527 2.43 600.63

Figure 16: A comparison between different parts with non uniform wall thickness with non uniform ribs structure

Figure 15: Non uniform wall thickness with 0.55 to 3.50 mm and non uniform ribs height and width varying from 0 to 11 mm and 0 to 2.5 mm respectively

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1.5 COMPARATIVE STUDY/RESULTS

Based on the Maximum Von Mises Stress of ~ 664.00 MPa (Safety Factor = 1.1) the three different designs for each cases are compared below. The part with uniform wall thickness is taken as the baseline for this study.

Uniform Wall Thickness Non Uniform wallthickness

Non Uniform wallthickness with Non Uniform ribs structure

Maximum Von Mises Stress (MPa)

662.34 664.08 664.63

Volume (mm^3) 648269 304357 248833

Mass (Kg) 5.31 2.49 2.04

Percentage Volume reduction (baseline: Uniform Wall Thickness)

- 53.05 61.62

Percentage Volume reduction (baseline: Non Uniform Wall Thick-ness)

-53.05 - 18.24

There has been a significant volume/weight reduction (61.62 %) for the part with variable wall thickness with variable ribs structure. The stress data from the FEA analysis was used as a modifier to drive the variability both of wall thickness and ribs structure’s parameter mainly height and width.

Figure 17: Comparison between different designs with Maximum Von Mises Stress (of around 664 MPa)