Deformation of Pressure Vessels with Varying Elastic Modulii
by
Matthew Nealon
A Thesis Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved:
_________________________________________
Professor Ernesto Gutierrez-Miravete, Thesis Adviser
Rensselaer Polytechnic Institute
Troy, New York
May, 2009
(For Graduation August, 2009)
1. Proposal
Pressure vessels can be found in many different shapes and sizes. Most of your basic
engineering classes dealing with pressure vessels will only discuss a thin-walled vessel
with homogeneous material properties. Similar to what was done my Tutunca and
Ozturk, I want to look at cylindrical graded pressure vessel and see how varying the
material properties (Elastic Modulus) will affect the deformation when a consistent
internal pressure is applied.
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2. Methodology
I will use a cylindrically shaped pressure vessel with clamped ends (to hold the length
constant), a constant wall-thickness, and a constant pressure. Similar to Nelson, I will
solve the exact formula for a pressure vessel with homogeneous material properties.
Using COMSOL, I will set up the same situation as my exact solution so that I know that
my model is correct. Once the baseline is established, I will vary the Elastic modulus to
see how it affects the deflection of the pressure vessel.
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3. Status
So far, I have solved the exact formula for the homogeneous in Maple and
compared it to my COMPSOL simulation. Based on my parameters, I found that Maple
gave me a displacement of 1.8142e-4 in and a stress of 4.5556e7 Pa and that COMPSOL
gave me a displacement of 1.814e-4 in and a stress of 4.573e7 Pa. This means that the
stress is only off by .383% and the displacement is off by a measly 0.011%.
With this level of accuracy, I felt confident moving on to the non-homogeneous
situations. Using COMPSOL, I was able to examine the non-homogeneous situations.
All that remains is to complete the final report.
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4. Timeline
The timeline for the project, including milestone and deadlines is shown below.
Proposed
Completed
Description
January 28
Yes
Proposal Due
February 7
Yes
Exact Homogeneous Solution Completed
February 14
Yes
Homogeneous Model Established
February 18
Yes
First Progress Report Due
March 7
Yes
Non-Homogeneous Situations Examined
March 11
Dropped
Second Progress Report Due
April 1
Final Draft Due
April 15
Final Report Due
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5. References
Nelson, Byron A., “Stress Analysis of a Functionally Graded Hollow Cylinder subject to
Axisymmetric Steady-State Loads”, Link to Portfolio, May 2008
Shao, Z.S., “Mechanical and thermal stresses of a functionally graded circular hollow
cylinder with finite length”, International Journal of Pressure Vessels and Piping
82 (2005) 155–163, March 31 2004
Tutuncu, Naki and Ozturk, Murat, "Exact solutions for stresses in functionally graded
pressure vessels”, Composites: Part B 32 (2001) 683-686, December 19 2000
You, L.H., Zhang, J.J., and You, X.Y., “Elastic analysis of internally pressurized thickwalled spherical pressure vessels of functionally graded materials”, International
Journal of Pressure Vessels and Piping 82 (2005) 347–354, March 24 2004
Chen, Y.Z. and Lin, X.Y., “Elastic analysis for thick cylinders and spherical pressure
vessels made of functionally graded materials”, Computational Materials Science
44 (2008) 581–587, April 8 2007
Simplified Methods in Pressure Vessel Analysis, New York : American Society of
Mechanical Engineers, 1978
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