AM 601 - (3) (Y)
Advanced Mechanics of Materials
Prerequisites: Undergraduate mechanics and mathematics
Review of basic stress-strain concepts; constitutive relations.
Study of unsymmetrical bending, shear center, and shear flow.
Analysis of curved flexural members, torsion, bending, and twisting
of thin walled sections. Theories of failure, other selected topics.
(Cross-listed as CE 601)
AM 602 - (3) (Y)
Continuum Mechanics With Applications
Introduction to continuum mechanics and mechanics of deformable
solids. Vectors and cartesian tensors, stress, strain, deformation,
equations of motion, constitutive laws, introduction to elasticity,
thermal elasticity, viscoelasticity, plasticity, and fluids. Cross-listed
as APMA 602, CE 602, MAE 602.
AM 603 - (3) (Y)
Computational Solid Mechanics
Variational and computational mechanics of solids, potential
energy, complementary energy, virtual work, Reissner's principle,
Ritz and Galerkin methods. Displacement, force and mixed methods
of analysis. Finite element analysis, including shape functions,
convergence and integration. Applications in solid mechanics.
Cross-listed as CE 603 and MAE 603.
AM 604 - (3) (E)
Plates and Shells
Prerequisites: APMA 541, AM 601 or 602
Classical analysis of plates and shells. Plates of various shapes
(rectangular, circular, skew) and shells of various shape (cylindrical,
conical, spherical, hyperbolic, paraboloid). Closed-form numerical
and approximate methods of solution governing partial differential
equations. Advanced topics (large deflection theory, thermal stresses,
orthotropic plates). Cross-listed as CE 604 and MAE 604.
AM 606 - (3) (Y)
Applied Boundary Element Analysis
Prerequisites: AM 671 or AM 603
Fundamental concepts of Green's functions, integral equations,
and potential problems. Weighted residual techniques and boundary
element methods. Poisson type problems, including cross-sectional
analysis of beams and flow analyses. Elastostatics. Other applications.
AM 612 - (3) (SI)
Theory of Elasticity
Prerequisite: AM 602 or permission of instructor
Review of the concepts of stress, strain, equilibrium, compatibility.
Hooke's law (isotropic materials). Displacement and stress formulations
of elasticity problems. Plane stress and strain problems in rectangular
coordinates (Airy's stress function approach). Plane stress and
strain problems in polar coordinates, axisymmetric problems. Torsion
of prismatic bars (semi-inverse method using real function approach).
Thermal stress. Energy methods.
AM 613 - (3) (Y)
Mathematical Foundations of Continuum Mechanics
Prerequisites: Linear Algebra, Vector Calculus, Elementary
PDE (or concurrently)
This course describes the mathematical foundations of continuum
mechanics from a unified viewpoint. The relevant concepts from
linear algebra, vector calculus and Cartesian tensors; the kinematics
of finite deformations and motions leading to the definition of
finite strain measures; the process of linearization; and the
concept of stress. Conservation laws of mechanics yield the equations
of motion and equilibrium and description of constitutive theory
leading to the constitute laws for nonlinear elasticity, from
which the more familiar generalized Hooke's law for linearly elastic
solid is derived. Constitutive laws for a Newtonian and non-Newtonian
fluid are also discussed. The basic problems of continuum mechanics
are formulated as boundary value problems for partial differential
equations. Cross-listed as APMA 613.
AM 620 - (3) (Y)
Energy Principles in Mechanics
Prerequisite: Permission of instructor
Derivation, interpretation, and application to engineering problems
of the principles of virtual work and complementary virtual work.
Related theorems such as the principles of the stationary value
of the total potential and complementary energy, Castigliano's
Theorems, theorem of least work, and unit force and displacement
theorems. Introduction to generalized, extended, mixed, and hybrid
principles. Variational methods of approximation, Hamilton's principle,
and Lagrange's equations of motion. Approximate solutions to problems
in structural mechanics by use of variational theorems. Cross-listed
as CE 620 and MAE 620.
AM 621 - (3) (Y)
Analytical Dynamics I
Prerequisites: Differential equations, undergraduate dynamics
course
Kinematics of rigid body motion, Eulerian angles, Lagrangian equations
of motion, inertia tensor, momental ellipsoid. Rigid body equations
of motion, Euler's equation, force-free motion, polhode and herpolhode,
theory of tops and gyroscopes, variational principles. Hamiltonian
equations of motion, Poinsote representation. Cross-listed as
MAE 621.
AM 623 - (3) (SI)
Vibrations
Prerequisite: Permission of instructor
Free and forced vibrations of undamped and damped single-degree-of-freedom
systems and undamped multi-degree-of-freedom systems. Use of Lagrange's
equations. Laplace transform, matrix formulation, and other solution
methods. Normal mode theory. Introduction to vibration of continuous
systems. Cross-listed as CE 623 and MAE 623.
AM 629, 630 - (3) (IR)
Special Problems in Applied Mechanics
Detailed study of special topics in mechanics.
AM 631 - (3) (Y)
Fluid Mechanics I
Prerequisite: Permission of instructor
Hydrostatics, including surface tension. Kinematics. Non-inertial
reference frames. Rigorous formulation of conservation equations
for mass, momentum, and energy. Euler and Bernoulli equations.
Vorticity dynamics. Two-dimensional potential flow theory, complex
potentials; applications to airfoils. The Navier-Stokes equations:
selected exact and approximate solutions. Cross-listed as MAE
631.
AM 632 - (3) (Y)
Fluid Mechanics II
Prerequisite: AM 631
The laminar boundary layer equations, differential and integral.
Elementary similar and integral solutions. Introduction to and
modeling of turbulent flows. Surface waves. Quasi-one-dimensional
compressible, perfect gas dynamic analysis. Practical applications.
Cross- listed as MAE 632.
AM 644 - (3) (SI)
Theoretical Acoustics
Prerequisite: APMA 341
Theoretical description of sound-transmission processes. Derivation
of basic gas dynamic equations, behavior of plane waves. The basic
processes of transmission, reflection, and absorption. Transmission
in non-uniform, shearing atmospheres. Sound waves in two and three
dimensions; line sources, monopoles, dipoles, quadrupoles. The
Heimholtz integral equation. Sound transmission in ducts and resonators.
Cross-listed as MAE 644.
AM 665 - (3) (Y)
Mechanics of Composite Materials
Prerequisites: ENGR 306, APMA 206
Properties and mechanics of fibrous, laminated composites, 2D
and 3D anisotropic constitutive equations, classical lamination
theory, thermal stresses, material response and test methods,
edge effects, design considerations, computerized implementation.
Cross-listed as CE 665.
AM 666 - (3) (Y)
Stress Analysis of Composites
Prerequisite: AM 565
3-D anisotropic constitutive theory, interlaminar stresses, failure
criteria, micromechanics, cylindrical bending, laminated tubes,
laminated plates, damage mechanics, and hygro-thermal effects.
Cross-listed as CE 666.
AM 671 - (3) (Y)
Applied Finite-Element Analysis
Prerequisite: Permission of instructor
Introduction to finite element methods for solving problems in
heat transfer, fluid mechanics, solid mechanics, and electrical
fields. Basics of one, two, and three-dimensional elements. Applications
to bars, electrical networks, trusses, conduction and convection
heat transfer, ideal and viscous flow, electrical current flow,
plane stress, plane strain, and elasticity. Development of computer
codes to implement finite element techniques. Cross-listed as
MAE 671.
AM 675 - (3) (SI)
Theory of Structural Stability
Prerequisite: Permission of instructor
Introduction to the elastic stability of structural and mechanical
systems. Classical stability theory and buckling of beams, trusses,
frames, arches, rings and thin plates and shells. Derivation of
design formulas. Computational formulation and implementation.
Cross-listed as CE 675.
AM 693 - (Credit as arranged) (Y)
Independent Study
Detailed study of graduate course material on an independent
basis under the guidance of a faculty member.
AM 695 - (Credit as arranged) (Y)
Supervised Project Research
Formal record of student commitment to project research
under guidance of a faculty advisor. Registration may be repeated
if necessary.
AM 703 - (3) (Y)
Thermal Structures
Prerequisite: AM 602 or permission of instructor, corequisite:
AM 612
Fundamentals of thermal structural analysis. Mechanical and thermodynamic
foundations. Formulation of heat transfer and thermal-structural
problems. Heat transfer in structures. Thermal stresses in rods,
beams, and plates. Thermally induced vibrations. Thermoelastic
stability. Computational methods.
AM 704 - (3) (SI)
Theory of Shells
Prerequisites: AM 602, AM 604
Introduction to the nonlinear, thermoelastic theory of shells.
Governing equations are derived by a mixed approach in which those
equations of three-dimensional continuum mechanics that are independent
of material properties are used to derive the corresponding shell
equations, whereas the constitutive equations of shell theory
which, unavoidably, depend on experiments, are postulated. Emphasizes
efficient, alternative formulations of initial/boundary value
problems, suitable for asymptotic or numerical solution, and discusses
variational principles. Some comparisons made with exact, three-dimensional
solutions.
AM 708 - (3) (SI)
Inelastic Solid Mechanics
Prerequisite: AM 602
Emphasizes the formulation of a variety of nonlinear models. Specific
topics include nonlinear elasticity, creep, visco-elasticity,
and elasto-plasticity. Solutions to boundary value problems of
practical interest are presented in the context of these various
theories in order to illustrate the differences in stress distributions
caused by different types of material nonlinearities. Cross-listed
as APMA 708.
AM 712 - (3) (SI)
Advanced Theory of Elasticity
Prerequisites: AM 602 or permission of instructor, AM
612
Generalized Hooke's law, strain-energy density, uniqueness. Classes
of boundary value problems (Navier's and Beltrami-Mitchell equations).
Torsion (Dirlichlet and Neumann problems). Flexure. Complex variable
formulation of torsional (Dirlichlet and Neumann problems) and
two-dimensional problems. General solution methodologies based
on complex variable techniques and elements of potential theory
for torsional and two-dimensional problems. Three-dimensional
problems. Wave propagation. Energy methods.
AM 714 - (3) (SI)
Nonlinear Elasticity Theory
Prerequisite: AM 602
Describes the theory of finite (nonlinear) elasticity governing
large deformations of highly deformable elastic solids. New features
not present in the linear theory are emphasized. These include
instabilities (both material and geometric), normal stress effects,
non-uniqueness, bifurcations and stress singularities. A variety
of illustrative boundary value problems will be discussed which
exhibit some of the foregoing features. Both physical and mathematical
implications considered. The results are applicable to rubber-like
and biological materials and the theory serves as a prototype
for more elaborate nonlinear theories of mechanics of continuous
media. Cross-listed as APMA 714.
AM 722 - (3) (O)
Analytical Dynamics II
Prerequisites: Differential equations, AM 621 or
permission of instructor
Formulation and application of the generalized principles of classical
particle and continuum mechanics. Lagrangian mechanics; Hamiltonian
mechanics. Cannonical transformation theory. Dynamics of variable-mass
systems. Dynamics of connected, rigid-body systems. Stability
analysis of dynamical systems. Analysis of nonlinear systems by
perturbation methods. Applications to space and machine dynamics.
Cross-listed as MAE 722.
AM 724 - (3) (Y)
Advanced Vibrations
Prerequisite: AM 623
Study of the motion of large scale systems including model testing
and reanalysis theory. Shock and wave analysis. Shock and vibration
isolation. Integration of linear and nonlinear governing equations.
Use of general purpose analysis systems. Cross-listed as MAE 724.
AM 725 - (3) (SI)
Random Vibrations
Prerequisites: Background in probability theory and vibration
analysis
Review of probability theory. Stochastic processes, with an emphasis
on continuous, continuously parametered processes. Mean square
calculus, Markov processes, diffusion equations, Gaussian processes,
and Poisson processes. Response of SDOF, MDOF, and continuous
linear and nonlinear models to random excitation. Upcrossings,
first passage problems, fatigue and stability the considerations.
Monte Carlo simulation, analysis of digital time series data,
and filtered excitation models. Cross-listed as CE 725.
AM 728 - (3) (SI)
Skeletal Biomechanics
Prerequisite: BIOM 603 or permission of instructor
The focus of this course is the study of forces (and their effects)
which act on the musculoskeletal structures of the human body.
Based on the foundations of functional anatomy and engineering
mechanics (rigid body and deformable approaches), students are
exposed to clinical problems in orthopaedics and rehabilitation.
Cross-listed as BIOM 728.
AM 729 - (3) (IR)
Selected Topics in Applied Mechanics
Prerequisite: Permission of instructor
Subject matter varies from year to year depending on interest
and needs of our students. Typical topics may include geophysics,
astrodynamics, waterwaves, or nonlinear methods.
AM 732 - (3) (Y)
Fracture Mechanics of Engineering Materials
Prerequisite: MS 731 or permission of instructor
Development of the methods for fracture control through defect
tolerant life prediction, materials characterization, mechanistic
behavior modeling and metallurgical alloy development. Discussion
of the continuum and microscopic mechanics of material fracture
modes. Cross-listed as MS 732.
AM 767 - (3) (SI)
Micromechanics of Heterogeneous Media
Prerequisite: AM 602
Averaging principles, equivalent homegencity, effective moduli,
bounding principles, self-consistent schemes, composite spheres,
concentric cylinders, three phase model, repeating cell models,
inelastic and nonlinear effects, thermal effects, isotropic and
anistropic media, strength and fracture. Cross-listed as APMA
767 and CE767.
AM 793 - (Credit as arranged) (Y)
Independent Study
Detailed study of graduate course material on an independent
basis under the guidance of a faculty member.
AM 822 - (3) (SI)
Biomechanics
Prerequisite: Permission of instructor
Rheological properties of biological tissues and fluids, with
emphasis on methods of measurement and data organization. Basic
principles of continuum mechanics and their application to mechanical
problems of the heart, lung, and peripheral circulation. Criteria
for selecting either lumped or continuous models to simulate mechanical
interaction of biological systems (and mechanical prostheses)
and application of such models under static and dynamic loading
conditions.
AM 895 - (Credit as arranged) (Y)
Supervised Project Research
Formal record of student commitment to project research
for Master of Engineering degree under the guidance of a faculty
advisor. Registration may be repeated as necessary.
AM 897 - (Credit as arranged) (S)
Graduate Teaching Instruction
For Master's students.
AM 997 - (Credit as arranged) (S)
Graduate Teaching Instruction
For Doctoral students.