# Presentation: 072722

- V.Demitchev, A.Timofeev
- (*RDP Corp. KOMPOZIT, Korolev*)

- Buckling analysis of the Vacuum Subsystem elements(KOPIO experiment)

## General remarks about analysis

- This work concerns the numerical simulation of the structural behavior of the KOPIO Vacuum Subsystem under external pressure. An ANSYSTM Program is used for the analyses.
- The work has carried out at IHEP (Protvino) in close contact with specialists from the KOMPOZIT Corp. (*Korolev*).
-  Two types of the analysis have been performed:
_***Nonlinear Buckling analysis***_  allows us to determine *critical pressure** *at which geometrical instability of a structure begins to develop. From this analysis a *stability safety factor* of the structure can be calculated. It is defined as a ratio of the critical pressure to the nominal one (1 atm).
_***Static Structural analysis***_ of the vacuum subsystem under the nominal external pressure of 1 atm. At this stage the *stress safety factors* can be determined. These factors show the reliability of the structure with respect to material failure.

## FE Model: General View

- Vacuum Vessel (Cylinder):
- D=3.2m, L= 4m,
- t=12.7mm (1/2”)

- Reinforcing Ring
- t=19.05mm (3/4”)

- Cover (Dome)
- t=12.7 mm (1/2”)

- Pipe Flange
- t=19.05mm (3/4”)

- Beam Pipe: t=6.35mm(1/4”)

- Ribs: t=9.525mm (3/8”)

## Materials used in the analyses

- Two approximations of the composite materials have been used in the FE analyses. The mechanical properties of these materials were presented by the *KOMPOZIT Corp*.
**Monolayer Composite Material**** ****(MM)** based on carbon fibers with unidirectional monolayer properties. Mechanical properties are:

| Young’s Modulus E, GPa: along the fibers (E1)
	                             across the fibers (E2) | 150
10 |
| --- | --- |
| Shear Modulus G12, GPa  | 6 |
| Major Poisson’s ratio 12 | 0.25 |
| Density , g/cm3 | 1. 5 |

**2.****  ****Isotropic Composite Material (IM)** may be used for simulation of multi-layered composite material with complex layer configurations. Mechanical properties are:
-                  **Young’s modulus** E = 75 GPa,   Poisson’s Ratio 12 = 0.25

## About multi-layered materials

- Multi-layered composite element consists of a few mono-layers. Fibers in each mono-layer are oriented in a direction which is defined by an angle  with respect to X-axis of the Element Coordinate System. So, a Layer Configuration is defined as a sequence of the angles: LC=(1, 2, 3,...). The thickness and  material properties for each layer are also defined.

- The Layer Configuration  shown in the picture is:
- LC=(-30,90,45,35)

## About Layer Configurations

| Number of Layers | Layer Configuration | Maximal Displacement, mm |
| --- | --- | --- |
| 1 | (0) | 15. |
| 1 | (90) | 17. |
| 2 | (0,90) | 7.3 |
| 2 | (35,-55) | 7.7 |
| 2 | (40,-50) | 6.6 |
| 2 | (55,-35) | 6.0 |
| 2 | (45,-45) | 5.6 |
| 2 | (50,-40) | 5.3 |
| 4 | (0,-45,45,90) | 4.8 |
| 8 | (0,-22.5,-45,-67.5,22.5, 45,77.5,90) | 4.7 |

- This table demonstrates an effect of layer configuration of the dome material on the maximal displacements of dome points. Calculations were carried out at nominal boundary and loading conditions. In all tests the total thickness of dome wall was  12 mm, the layers had equal thickness.

## CYL: Buckling Analysis, test_1

_**Result:**_ Critical Pressure is about **0.7 **atm

- Pic. 1: Load-Deflection Curve

- Pic. 2: Radial Displacements at Pcr=0.73atm

_**Conditions:**_ UZ=0 on Rings; Gravity; CPV weight (360kg);
- Two-point Ring’s support; Monolayer Material; Layer Configuration (0,90)

## CYL: Buckling Analysis, test_2

_**Result:**_ Critical Pressure is not less than **2.7 **atm

- Pic. 1: Load-Deflection Curve

- Pic. 2: Radial Displacements at Pcr=2.7 atm

_**Conditions:**_ Fixed Rings; Gravity; CPV weight (360kg);
- Monolayer Material; Layer Configuration (0,90)

## CYL: Displacement Ur  (Static)

- Max U=0.185 mm.  t0=10.8 mm, t90=1.2 mm

_**Conditions:**_
- Fixed Rings;
- P = 1 atm;
- Monolayer Material;
- Gravity;
- Distributed weight of 360kg (CPV).

## CYL: Dependences on t0/ttotal

- t0

- ttotal=1/2”

- Layer configuration of the Cylinder composite material: NL=2, LC=(0,90)

- Layer 0o

- 

- z

- r

- Layer 90o

- L90_top

- L0_bot

- Good work zone

## CYL: Conclusions

-  Stability is the main problem for the Cylinder.
-  Free rotations of the Rings in cross-plane should not be allowed, because the  geometrical instability begins to develop under the pressure less than 1 atm.
-  Fixing of the Rings rigidly to an outer massive frame helps to avoid an instability of the cylinder up to external pressure of 2.7 atm.
-  Stress safety for the cylinder material is not a problem. Safety factor  is very large – of about 20.

## D&BP(MM): Buckling Analysis 1

_**Conditions:**_ Fixed Dome’s edges and pipe flange; Gravity; CPV weight on pipe (90 kg); Monolayer Material; Dome’s Layer Configuration is (0,-45,45,90)

- Pic. 2: USUM Displacements at Pcr=1.3 atm

- Pic. 1: Load-Deflection Curve

_**Result:**_ Critical Pressure is about **1.3 **atm

- Critical Zone

## D&BP(MM): Buckling, _1, Displ.

_**Result:**_ Maximal vertical displacements are reached at the middle parts of the pipe and equal to 4 mm at the Pcr=1.3 atm.

- Result: Maximal axial displacements are reached at the weak place of the Dome. Uz for the pipe is not greater than 1 mm

## D&BP (IM): Buckling Analysis_2

_**Conditions:**_ Fixed Dome’s edges and pipe flange; Gravity; CPV weight on pipe (90 kg); Isotropic Material for Dome, Monolayer Materials for other parts.

- Pic. 1: Load-Deflection Curve

- Pic. 2: USUM Displacements at Pcr=2.4 atm

_**Result:**_ Critical Pressure is not less than **2.4 **atm

- Critical Zone

## D&BP: Conclusions

- The Dome should be fabricated from the multi-layered composite material with isotropic properties. In this case a stability safety factor is at least 2.4.