2008-2009 Bulletin – PDF - SEAS Bulletin - Columbia University

102
ential equations. Fluid statics. Fundamental principles
and concepts of flow analysis. Differential
and finite control volume approach to flow analysis.
Dimensional analysis. Application of flow
analysis: flow in pipes, external flow, flow in open
channels.
ENME E4113x Advanced mechanics of solids
Lect: 3. 3 pts. Professor Chen.
Stress and deformation formulation in two- and
three-dimensional solids; viscoelastic and plastic
material in one and two dimensions.
ENME E4114y Mechanics of fracture and
fatigue
Lect: 3. 3 pts. Professor Testa.
Prerequisite: Undergraduate mechanics of solids
course. Elastic stresses at a crack; energy and
stress intensity criteria for crack growth; effect of
plastic zone at the crack; fracture testing applications.
Fatigue characterization by stress-life and
strain-life; damage index; crack propagation; fail
safe and safe life analysis.
ENME E4202y Advanced mechanics
Lect: 3. 3 pts. Professor Smyth.
Prerequisite: ENME E3105 or the equivalent.
Differentiation of vector functions. Review of kinematics.
Generalized coordinates and constraint
equations. Generalized forces. Lagrange’s equations.
Impulsive forces. Collisions. Hamiltonian.
Hamilton’s principle.
ENME E4215x Theory of vibrations
Lect: 3. 3 pts. Professor Betti.
Frequencies and modes of discrete and continuous
elastic systems. Forced vibrations–steadystate
and transient motion. Effect of damping.
Exact and approximate methods. Applications.
ENME E6220x Random processes in mechanics
Lect: 2.5. 3 pts. Professor Deodatis.
Prerequisite: ENME E4215 or the equivalent.
Random variables, stationary and ergodic random
processes, correlation functions, and power
spectra. Input-output relations of linear systems:
analysis of response of discrete and continuous
structures to random loadings. Crossing rates,
peak distributions, and response analysis of
nonlinear structures to random loading.
Simulation of stationary random processes.
ENME E6315x Theory of elasticity
Lect: 2.5. 3 pts. Instructor to be announced.
Foundations of continuum mechanics. General
theorems of elasticity. Application to stress analysis
and wave propagation.
ENME E8320y Viscoelasticity and plasticity
Lect: 3. 4 pts. Not given in 2008–2009.
Prerequisite: ENME E6315 or the equivalent, or
the instructor’s permission. Constitutive equations
of viscoelastic and plastic bodies. Formulation
and methods of solution of the boundary value,
problems of viscoelasticity and plasticity.
COURSES IN GRAPHICS
GRAP E1115x or y Engineering graphics
Lect: 1. Lab: 3. 3 pts. Mr. Sanchez.
Open to all students. Visualization and simulation
in virtual environments; computer graphics methods
for presentation of data. 3-D modeling; animation;
rendering; image editing; technical drawing. Lab
fee: $200.
GRAP E2005y Computer-aided engineering
graphics
Lect: 1.5. Lab: 2.5. 3 pts. Not given in
2008–2009.
Prerequisite: CALC Is. Basic concepts needed to
prepare and understand engineering drawings
and computer-aided representations: preparation
of sketches and drawings, preparation and
transmission of graphic information. Lectures
and demonstrations, hands-on computer-aided
graphics laboratory work. Term project.
GRAP E3115x or y Advanced computer modeling
and animation
Lect: 1. Lab: 3. 3 pts. Mr. Sanchez.
Prerequisite: GRAP E1115 or the instructor’s permission.
Explores applications of 3-D modeling,
animation, and rendering techniques in the arts,
architecture, engineering, entertainment, and science.
Visualization through conceptual modeling
and animation techniques for product design and
realistic presentations. Lab fee: $200.
ENME E4214y Theory of plates and shells
Lect: 3. 3 pts. Professor Dasgupta.
Prerequisite: ENME 3113. Static flexural response
of thin, elastic, rectangular, and circular plates.
Exact (series) and approximate (Ritz) solutions.
Circular cylindrical shells. Axisymmetric and
non-axisymmetric membrane theory. Shells of
arbitrary shape.
ENME E8323y Nonlinear vibrations
Lect: 2.5. 3 pts. Not given in 2008–2009.
Prerequisite: ENME E4215 or the equivalent.
Free and forced motion of simple oscillators with
nonlinear damping and stiffness. Exact, perturbation,
iteration, and graphical methods of solution.
Stability of motion. Chaotic vibrations.
GRAP E4005y Computer graphics in engineering
Lect: 3. 3 pts. Professor Dasgupta.
Prerequisites: Any programming language and
linear algebra. Numerical and symbolic (algebraic)
problem solving with Mathematica. Formulation
for graphics application in civil, mechanical, and
bioengineering. Example of two- and three-dimensional
curve and surface objects in C++ and
Mathematica; special projects of interest to electrical
and computer science.
SEAS 2008–2009