Elastic/Plastic Behavior of Infinitely Long Cylinders Subject to
Mechanical and Thermal Loads
by
Peter P. Poworoznek
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF MECHANICAL ENGINEERING
Approved:
_________________________________________
Professor Ernesto Gutierrez-Miravete, Project Advisor
Rensselaer Polytechnic Institute
Hartford, CT
December, 2008
PROPOSAL
This project will examine the elastic-plastic behavior of both thin-walled and thickwalled infinitely long cylinders with plane-stress and plane-strain conditions at the ends
subject to axisymmetric mechanical (pressure) and thermal loading.
APPROACH/METHODOLOGY
Initially, the elastic solution to an infinitely long cylinder subject to an internal pressure
will be derived analytically using classical shell theory. Then the effects of adding a
thermal load on top of an existing pressure will be examined. Next the pressure loads
will be increased to induce plasticity in the cylinder for a strain-hardening material.
Finally thermal effects will be added to complete the elastic-plastic analysis.
Once the analytical solution is complete, the exact solutions will be used as baselines to
validate the finite-element analyses. Using both shell and solid finite elements, solution
convergence (vs. mesh size) and solution methods will be examined to determine the
best approach.
TOOLS
For the theoretical part of the project, both Maple and MathCad will be used. For the
finite-element portion, the ABAQUS non-linear finite-element code will be employed.
REFERENCES
[1] Young, W.C., 1989, Roark’s Formulas for Stress & Strain, McGraw-Hill, New
York, NY.
[2] Hill, R., 1950, The Mathematical Theory of Plasticity, Oxford University Press,
London, UK.
[3] Ugural, A.C, 1999, Stresses in Plates and Shells¸ McGraw-Hill, Boston, MA.
[4] Batra, R.C., Iaccarino, G.L., 2008, “Exact solutions for radial deformation of a
functionally graded isotropic and incompressible second-order elastic cylinder,”
International Journal of Non-Linear Mechanics 43 383-398.
[5] Bhattacharyya, A., Appiah, E.J., 2000, “On the exact solution of elastoplastic
response of an infinitely long composite cylinder during cyclic radial loading,” Journal
of the Mechanics and Physics of Solids 48 1065-1092.
[6] Desikan, V., Sethuraman, R., 2000, “Analysis of material nonlinear problems using
pseudo-elastic finite element method,” Journal of Pressure Vessel Technology 122 457461.
[7] Gao, X.L., 2003, “Elasto-plastic analysis of an internally pressurized thick-walled
cylinder using a strain gradient plasticity theory,” International Journal of Solids and
Structures 40 6445-6455.
[8] Jahanian, S., 1996, “Thermoelastoplastic stress analysis of a thick-walled tube of
nonlinear strain hardening,” Transactions of the ASME 118 340-346.
[9] Loghman, A., Wahab, M.A., “Loading and unloading of thick-walled cylindrical
pressure vessels of strain-hardening material,” Journal of Pressure Vessel Technology
116 105-109.
[10] Tarn, J.Q., 2001, “Exact solutions for functionally graded anisotropic cylinders
subjected to thermal and mechanical loads,” International Journal of Solids and
Structures 38 8189-8206.
[11] Yi, W., Basavaraju, C., 1996, “Cylindrical shells under partially distributed radial
loading,” Transactions of the ASME 118 104-108.
[12] Zhao, W., Seshadri, R., Dubey, R.N., 2003, “On thick-walled cylinder under
internal pressure,” Journal of Pressure Vessel Technology 125 267-273.
SCHEDULE

Proposal draft (Deliverable) – 9/23

Linear elastic stresses and strains (analytical)
o Pressure loading, thin/thick-shells – 10/7
o Pressure loading with thermal effects, thin/thick shells– 10/14

First progress report (Deliverable) – 10/14

Elastic-plastic stresses and strains (analytical)
o Pressure loading with thermal effects, thin/thick shells – 10/28

Linear elastic FEA analysis
o Pressure loading with thermal effects, thin/thick-shells – 11/4

Second progress report (Deliverable) – 11/4

Elastic-plastic FEA analysis
o Pressure loading with thermal effects, thin/thick-shells – 11/18

Final draft (Deliverable)– 11/25

Final report (Deliverable) – 12/9