2011-2012 Bulletin – PDF - SEAS Bulletin - Columbia University

ENME E4363y Multiscale computational
science and engineering
3 pts. Lect: 3. Professor Fish.
Prerequisites: ENME E4332, elementary
computer programming, linear algebra.
Introduction to multiscale analysis. Informationpassing
bridging techniques: among them,
generalized mathematical homogenization
theory, the heterogeneous multiscale method,
variational multiscale method, the discontinuous
Galerkin method and the kinetic Monte
Carlo–based methods. Concurrent multiscale
techniques: domain bridging, local enrichment,
and multigrid-based concurrent multiscale
methods. Analysis of multiscale systems.
ENME E6220x Random processes in
mechanics
3 pts. Lect: 3. Professor Deodatis.
Prerequisites: CIEN E4111 and ENME E4215
(or equivalent). Review of random variables.
Random process theory: stationary and ergodic
processes, correlation functions, power spectra.
Nonstationary and non-Gaussian processes.
Linear random vibration theory. Crossing rates,
peak distributions, and response analysis of
nonlinear structures to random loading. Major
emphasis on simulation of various types of
random processes. Monte Carlo simulation.
ENME E6315x Theory of elasticity
3 pts. Lect: 2.5. Professor Dasgupta.
Foundations of continuum mechanics. General
theorems of elasticity. Application to stress
analysis and wave propagation.
ENME E6333y Finite element analysis, II
3 pts. Lect: 3. Professor Waisman.
Prerequisite: ENME E4332. FE formulation
for beams and plates. Generalized eigenvalue
problems (vibrations and buckling). FE
formulation for time-dependent parabolic and
hyperbolic problems. Nonlinear problems,
linearization, and solution algorithms. Geometric
and material nonlinearities. Introduction to
continuum mechanics. Total and updated
Lagrangian formulations. Hyperelasticity and
plasticity. Special topics: fracture and damage
mechanics, extended finite element method.
EMME E6364x Nonlinear computational
mechanics
3 pts. Lect: 3. Professor Fish.
Prerequisites: ENME 4332 or equivalent,
elementary computer programming, linear
algebra. The formulations and solution strategies
for finite element analysis of nonlinear problems
are developed. Topics include the sources of
nonlinear behavior (geometric, constitutive,
boundary condition), derivation of the governing
discrete equations for nonlinear systems such
as large displacement, nonlinear elasticity, rate
independent and dependent plasticity and other
nonlinear constitutive laws, solution strategies
for nonlinear problems (e.g., incrementation,
iteration), and computational procedures for large
systems of nonlinear algebraic equations.
ENME E8320y Viscoelasticity and plasticity
4 pts. Lect: 3. Professor Dasgupta.
Prerequisite: ENME E6315 or equivalent, or
instructor’s permission. Constitutive equations
of viscoelastic and plastic bodies. Formulation
and methods of solution of the boundary value,
problems of viscoelasticity and plasticity.
ENME E8323y Nonlinear vibrations
3 pts. Lect: 2.5. Not offered in 2011–2012.
Prerequisite: ENME E4215 or 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.
Courses in Graphics
GRAP E1115x and y Engineering graphics
3 pts. Lect: 1. Lab: 3. Professor Sánchez.
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: $300. 1220 S. W. Mudd
Building.
GRAP E2005y Computer-aided engineering
graphics
3 pts. Lect: 1.5. Lab: 2.5. Professor Dasgupta.
Prerequisite: MATH V1105. 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, handson
computer-aided graphics laboratory work.
Term project.
GRAP E3115y Advanced computer modeling
and animation
3 pts. Lect: 1. Lab: 3. Professor Sánchez.
Prerequisite: GRAP E1115 or instructor’s
permission. Explores applications of 3D
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: $300.
GRAP E4005y Computer graphics in
engineering
3 pts. Lect: 3. 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 twoand
three-dimensional curve and surface objects
in C++ and Mathematica; special projects of
interest to electrical and computer science.
101
engineering 2011–2012