Elastic/Plastic Behavior of Infinitely Long Cylinders Subject to

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Elastic/
Plastic

Behavior of Infinitely Long
Cylinder
s 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 w
ill examine th
e elastic
-
plastic behavior of both thin
-
walled and thick
-
walled

infinitely long cylinder
s

with plan
e
-
s
tress

and plane
-
strain

conditions at the end
s

subject to axisymmetric
mechanical

(pressure) and thermal

loading.



APPROACH/METHODOLOGY

Init
ially, 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 pressu
re 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 b
aselines 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 Ma
ple 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 Mathem
atical 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 is
otropic 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 duri
ng 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

457
-
461.


[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, “Thermoelastopla
stic 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., Basavara
ju, 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



E
lastic
-
plastic FEA analysis

o

Pressure loading with thermal effects, thin/thick
-
shells



11/18



Final draft
(Deliverable)


11/25



Final report

(Deliverable)



12/9