Buckling analysis of ElipticalTube2





Author: H. Wieman


Company: LBNL


Date: 14-Jan-05



  1. Introduction
  2. Description
  3. File Information
  4. Materials
  5. Load & Restraint Information
  6. Study Property
  7. Displacement Results
  8. Deformation Results
  9. Design Scenario Results
  10. Mode List
  11. Conclusion
  12. Appendix



1. Introduction



A new small radius thin walled beam pipe is needed
for the HFT inner vertex detector at STAR. This is
a study of the buckling with a pipe that varies from
elliptical to round



2. Description



The elliptical pipe has a major axis of 29 mm and
the minor axis is varied from round to 40% of the
major to find the effect on the first 3 buckling modes

The pipe is made of beryllium with a 0.5 mm wall.
There are two 4 mm by 4 mm rings at either end.
There is no tension support.

The study is carried out with a normal 1 atm
vacuum load. The load factors stated here are
just number of atm.



3. File Information



Model name: ElipticalTube2
Model location: C:\Documents and Settings\Howard Wieman\My Documents\aps project\mechanical\beam pipe\Beryllium Eliptical Stress Study\ElipticalTube2.SLDPRT
Results location: C:\temp
Study name: elipse buckle




4. Materials



No. Shell Name Material Thickness
1 Shell-1 beryilliumCosmosChPois 4 mm
2 Shell-2 beryilliumCosmosChPois 0.5 mm



5. Load & Restraint Information



Restraint
Restraint-1 <> on 1 Edge(s) fixed.
Description:


Load
Pressure-1 <> on 3 Face(s) with Pressure 15 psi along direction normal to selected face
Description:




6. Study Property



Mesh Information
Mesh Type: Shell mesh using surfaces
Mesher Used: Standard
Automatic Transition: Off
Smooth Surface: On
Jacobian Check: 4 Points
Element Size: 4.9028 mm
Tolerance: 0.24514 mm
Quality: High
Number of elements: 2304
Number of nodes: 4636



Solver Information
Quality: High
Solver Type: Direct sparse solver
Number of Buckling Modes: 3








7. Displacement Results



Name Type Min Location Max Location
Plot1 URES: Resultant displacement
0 mm
Node: 43
(14.4978 mm,
-0.25306 mm,
0 mm)
4.46197 mm
Node: 4080
(14.4978 mm,
-0.25306 mm,
388.65 mm)
Plot2 URES: Resultant displacement
0 mm
Node: 43
(14.4978 mm,
-0.25306 mm,
0 mm)
5.67091 mm
Node: 3731
(0.101231 mm,
5.79912 mm,
50.55 mm)
Plot3 URES: Resultant displacement
0 mm
Node: 43
(14.4978 mm,
-0.25306 mm,
0 mm)
3.5997 mm
Node: 288
(3.9622 mm,
-5.63801 mm,
57.9 mm)



ElipticalTube2-elipse buckle-Displacement-Plot1
JPEG
VIEW



ElipticalTube2-elipse buckle-Displacement-Plot2
JPEG
VIEW



ElipticalTube2-elipse buckle-Displacement-Plot3
JPEG
VIEW



8. Deformation Results



Plot No. Mode Shape Load Factor Scale Factor
1 1 71.499 3
2 2 159.37 3
3 3 160.83 1



ElipticalTube2-elipse buckle-Deformation-Plot1
JPEG
VIEW



ElipticalTube2-elipse buckle-Deformation-Plot2
JPEG
VIEW



ElipticalTube2-elipse buckle-Deformation-Plot3
JPEG
VIEW



9. Design Scenario Results



Input Parameters Units Set1 Set2 Set3 Set4
AspectRatio mm 29 23.2 17.4 11.6




Buckling Load Factor Units Set1 Set2 Set3 Set4
Result Status Summary Summary Summary Detailed
1 48.635 67.294 96.549 71.499
2 48.923 67.89 99.412 159.37
3 61.295 76.772 103.1 160.83





ElipticalTube2-elipse buckle-Design Scenario Results-Graph1
JPEG
VIEW






10. Mode List



Mode List
Mode Number Load Factor
1 71.499
2 159.37
3 160.83






11. Conclusion



Surprisingly the load factor increases with a more
elliptical shape



12. Appendix



Material name: beryilliumCosmosChPois
Description:
Material Source: Library files
Material Library Name: hwmaterials
Material Model Type: Linear Elastic Isotropic
Unit system: English (IPS)

Property Name Value
Elastic modulus 4.3954e+007 psi
Poisson's ratio 0.27
Shear modulus 1.9583e+007 psi
Mass density 0.066836 lb/in^3
Tensile strength 53673 psi
Yield strength 34815 psi
Thermal expansion coefficient 6.1111e-006 /Fahrenheit
Thermal conductivity 0.0026758 BTU/(in.s.F)
Specific heat 0.43598 Btu/(lb.F)