E173 Applied
Elasticity
Harvey Mudd College
Fall 2005
(Last edited at 9:00 AM on 1 December 2005.)
Particulars:
Lectures:
Tuesday, Thursday 9:35–10:50 in TG 208
Instructor: Prof.
Clive Dym, clive_dym@hmc.edu,
Parsons 2373B; 621–8853
Office
Hours: Monday,
Wednesday 9:00–11:00 or drop by
Grader:
Prof. Clive Dym
Textbook: R.
D. Cook and W. C. Young, Advanced Mechanics of Materials,
2nd Edition; at Huntley Bookstore
My goals for this course are that you
will:
· develop
an understanding of how the theory of elasticity can be applied to model some
mechanical and structural behaviors;
· learn
the principles that underlie the energy-based modeling of engineering solids
and structures;
· obtain
exact and approximate solutions for a variety of problems in solid mechanics;
and
· experience
some sense of how engineers think about problems in solid mechanics.
Course emphases:
The theory of
elasticity is concerned with modeling the deformations of and stresses in
continuous media characterized by linear relationships between stress and
strain. Applied elasticity is about developing and applying geometry-based
idealizations of real physical situations and structures. This introduction to
applied elasticity will focus on:
· introducing
the three-dimensional theory of elasticity;
· introducing
minimum energy principles to derive mathematical models of the behaviors of
elastic solids;
· using
kinematic assumptions and minimum energy principles to derive idealized models
of elastic behavior in one- and two-dimensional solids;
· solving
a variety of solid mechanics problems exactly and approximately; and
· developing
physical intuition about mechanical behavior and its role in analyzing and designing
solid bodies.
Course topics:
1 The
linear theory of elasticity: Strain, stress, constitutive laws,
equilibrium and compatibility for three-dimensional solids.
2 Energy
methods: The calculus of variations; the Principle of Minimum
Potential Energy; the Principle of Minimum Complementary Energy; the (two)
Castigliano Theorems.
3 Failure
criteria: Criteria for different material behaviors; cracks;
fatigue.
4 Two-dimensional
formulations and problems: Plane stress; plane strain; beams as plane
stress problems; thick-walled cylindrical and spherical pressure vessels;
rotating disks.
5 Torsion:
St. Venant theory; membrane analogy; torsion with warping of thin-walled beams
and tubes; torsional failure.
6 Energy
methods for beams: Deriving classical beam theory; comparison
with elasticity theory solution; Timoshenko beam theory; energy-based
approximate solutions for beams.
7 Column
buckling: Stability; bifurcation and limit points; nonlinear and linearized
models of column behavior; the elastica; Koiter’s postbuckling theory;
beam-columns; energy-based approximate solutions to buckling eigenvalue
problems.
8 Beams
on elastic foundations (if time permits): Motivation; derivation of equations; limits and special
cases; analogy with axisymmetric deformation of circular cylindrical shells.
Course activities:
This particular
introduction to applied elasticity will involve your:
· active
participation in course discussions of the concepts and their application; and
· mastering
the skills to solve solid mechanics problems in homework and exams.
Materials posted online (I): Syllabus
and miscellaneous readings
Materials posted online (II): Homework
assignments
Grading:
There will be two
75-minute exams. Dates for the two exams — one around half-way, the other
at the end — will be decided as the course unfolds. These exams are
likely to be closed book and notes. The components of your final course grade
are weighted as follows: 30% for the homework and 35% for each exam.
Additional references (generally available
at Sprague Library):
W. B. Bickford, Advanced Mechanics of
Materials, Addison Wesley, 1998.
A. P. Boresi and P. P. Lynn, Elasticity in
Engineering Mechanics, Prentice Hall, 1974.
A. P. Boresi, R. J. Schmidt and O. M. Sidebottom, Advanced Mechanics
of Materials, John Wiley, 1993.
R. G. Budynas, Advanced Strength and Applied Stress
Analysis, McGraw-Hill, 1977.
C. L. Dym, Stability Theory and Its Applications to
Structural Mechanics, Noordhoff, 1974 and Dover Publications,
2002.
C. L. Dym and I. H. Shames, Solid Mechanics:
A Variational Approach, McGraw-Hill, 1973.
J. M. Gere and S. P. Timoshenko, Mechanics of
Materials, PWS Publishing, 1997.
H. W. Haslach, Jr., and R. W. Armstrong, Deformable Bodies
and Their Material Behavior, John Wiley, 2004.
H. L. Langhaar, Energy Methods in Applied Mechanics,
Krieger, 1989.
E. P. Popov, Engineering Mechanics of Solids,
Prentice Hall, 1990.
H. Reisman and P. S. Pawlik, Elasticity:
Theory and Applications, John Wiley, 1980.
I. H. Shames and C. L. Dym, Energy and Finite
Element Methods in Structural Mechanics, Taylor and Francis,
1985.
S. P. Timoshenko, History of Strength of Materials,
Dover Publications, 1983.
S. P. Timoshenko and J. N. Goodier, Theory of
Elasticity, McGraw-Hill, 1970.
A. C. Ugural and S. K. Fenster, Advanced Strength
and Applied Elasticity, Prentice Hall, 1995.