Two dimensions
=
xx
yy =
xx + yy
2
xx + yy
2
+
xx yy
2
xx yy
2
cos 2 + xy sin 2 = xx cos 2 + yy sin 2 + 2 xy sin cos ,
cos 2 xy sin 2 = xx sin 2 + yy cos 2 2 xy sin cos ,
xx yy
=
sin 2 + xy cos 2 =
xy
( xx yy ) sin cos + xy ( cos 2 sin 2 ) .
2
Change of length of a bar
Consider a bar AB and let x A and x B be the position vectors of its end points. Vector AB can be written in the form
AB = x B x A = n ,
xB x A
where=
the unit vector in the direction from A to B .
x B x A is the length of the b
The strain deviator
Let the strain matrix be
11 12 13
[ ] = 12 22 23 .
13 23 33
The volumetric strain v is defined as
v tr [ ] = 11 + 22 + 33 .
The strain deviator [ e] is defined as
[ e ] [ ]
where [ I ] is the 3 3 identity matrix, i.e.,
e11
[e]= e1
Cooling a Fluid Flowing in a Pipe Using
a Thin Circular Fin
Portonovo S. Ayyaswamy and Michael A. Carchidi
February 9, 2010
1. The Statement Of The Problem
A circular fin of inner radius ro , outer radius ro , and thickness is attached to
a cylindrical pi
PROBLEM 2.50
KNOWN: An electric cable with an insulating sleeve experiences convection with adjoining air and
radiation exchange with large surroundings.
FIND: (a) Verify that prescribed temperature distributions for the cable and insulating sleeve satisf
PROBLEM 1.84
KNOWN: Long bus bar of rectangular cross-section and ambient air and surroundings temperatures.
Relation for the electrical resistivity as a function of temperature.
FIND: (a) Temperature of the bar with a current of 60,000 A, and (b) Compute
PROBLEM 3.127
KNOWN: Dimensions of disc/shaft assembly. Applied angular velocity, force, and torque. Thermal
conductivity and inner temperature of disc.
FIND: (a) Expression for the friction coefficient , (b) Radial temperature distribution in disc, (c) V
PROBLEM 3.96
KNOWN: Cylindrical shell with uniform volumetric generation is insulated at inner surface
and exposed to convection on the outer surface.
h, T and k, (b)
FIND: (a) Temperature distribution in the shell in terms of ri , ro , q,
Expression for
PROBLEM 12.84
KNOWN: Diffuse, gray opaque disk (1) coaxial with a ring-shaped disk (2), both with prescribed
temperatures and emissivities. Cooled detector disk (3), also coaxially positioned at a prescribed
location.
FIND: Rate at which radiation is inci
PROBLEM 6.14
KNOWN: Radial distribution of local convection coefficient for flow normal to a circular
disk.
FIND: Expression for average Nusselt number.
SCHEMATIC:
ASSUMPTIONS: Constant properties.
ANALYSIS: The average convection coefficient is
1
hdAs
A
PROBLEM 8.14
KNOWN: Geometry and coolant flow conditions associated with a nuclear fuel rod. Axial
variation of heat generation within the rod.
FIND: (a) Axial variation of local heat flux and total heat transfer rate, (b) Axial variation of
mean coolant
PROBLEM 5.52
KNOWN: Thickness, initial temperature and properties of steel plate. Convection conditions at both
surfaces.
FIND: Time required to achieve a minimum temperature.
SCHEMATIC:
=7800 kg/m3
cp = 500 J/kg-K
k = 45 W/m-K
Steel plate:
Ti = 300oC
T(0
MEAM 520
Rotational Parameterizations
Katherine J. Kuchenbecker, Ph.D.
Mechanical Engineering and Applied Mechanics Department
University of Pennsylvania
Lecture 4: September 8, 2016
1
Put on Your Name Tag
Flo
2
Review from last class: Interpretations o
MEAM 520
Introduction to Robotics
Katherine J. Kuchenbecker, Ph.D.
Mechanical Engineering and Applied Mechanics Department
University of Pennsylvania
Lecture 1: August 30, 2016
1
Who?
What?
How?
Why?
2
Who am I?
Katherine J. Kuchenbecker, Ph.D.
Asso
MEAM 520
Homogeneous Transformations
Where is
Katherine J. Kuchenbecker, Ph.D.
my hand in
Mechanical Engineering and Applied Mechanics Department
space?
University of Pennsylvania
Lecture 5: September 30, 2016
1
Put on Your Name Tag
Baxter
2
Review from
MEAM 520
Rotation Matrices
Katherine J. Kuchenbecker, Ph.D.
Mechanical Engineering and Applied Mechanics Department
University of Pennsylvania
Lecture 3: September 6, 2016
1
Graspy
Put on Your Name Tag!
I already know some of you, but I may
have forgott
By
Lei Qian
Yulun Tong
Xiang Zhang
Ruichao Zou
PROCESSES IN THE GLASS INDUSTRY
MIXING
1. Raw materials sand, lime, soda ash and
feldspar
2. Batch processing system or batch house
TRIBOLOGICAL COMPONENT
Conveying belt:
1.Consist of two of more pulleys and
A STUDY OF TRIBOLOGICAL SYSTEMS IN THE
STEEL AND ROLLING MILL INDUSTRY
Xu Gu
Priyanka Shirsat
Shashank Acharya
A Report prepared in partial fulfillment of the course on
Tribology (MEAM 504)
November 2013
INTRODUCTION
Steel i
A STUDY OF TRIBOLOGICAL SYSTEMS IN THE GLASS
MANUFACTURING INDUSTRY
Lei Qian
Yulun Tong
Xiang Zhang
Ruichao Zou
A Report prepared in partial fulfillment of the course on
Tribology (MEAM 504)
December 2015
INTRODUCTION
Glass is a non-crystalline solid that
A STUDY OF TRIBOLOGICAL SYSTEMS IN
THE STEEL AND ROLLING MILL INDUSTRY
By
Xu Gu
Priyanka Shirsat
Shashank Acharya
PROCESSES IN THE STEEL INDUSTRY
CHALLENGES IN THE STEEL INDUSTRY
1. High temperatures
2. High impact loads
3. Fire resistant
Tieqi Heavy Indu
MEAM 520
Background
Katherine J. Kuchenbecker, Ph.D.
Mechanical Engineering and Applied Mechanics Department
University of Pennsylvania
Lecture 2: September 1, 2016
1
Put on Your Name Tag!
I already know some of you, but I may
have forgotten your name.
MEAM 520
Forward Kinematics
Katherine J. Kuchenbecker, Ph.D.
Mechanical Engineering and Applied Mechanics Department
University of Pennsylvania
Lecture 6: September 15, 2016
1
Put on Your Name Tag
Obama
2
Review from last class: Rigid Motions and Homoge
Spring, 2014
CIT 590
Programming Languages and Techniques
Midterm
Please write your name (your official name please) and email in the space provided below.
Do not turn over the page until we say so.
Remember to answer in the space provided. And please rem
Spring, 2016
CIT 590
Programming Languages and Techniques
Homework 2
All HW deadlines as per canvas
This homework deals with the following topics
* writing functions
* more practice with loops
General Idea
Hammurabi is a very old computer game, in which y
MEAM 527
Finite Element Method and its Applications
Spring 2016
Instructor
Professor Nick Aravas, LRSM 322 (3231 Walnut St.)
e-mail: aravas@seas.upenn.edu
Phone: 215-573 4397
Office Hours: Mondays and Wednesdays 10:30-12:00 am, 322 LRSM
Lectures
Mondays a
MEAM 527
Fall 2016
Instructor: N. Aravas
Assignment 5 Due Monday 04/04/2016 9:00 am
Problem 1
Consider the one-dimensional boundary value problem (BVP)
d 2u ( x )
dx 2
0,
+6x =
u ( 0) = 1 ,
0 < x < 1,
u (1) = 4 .
i) Solve that problem with COMSOL using 10
MEAM 527
Spring 2016
Instructor: N. Aravas
Assignment 6 Due Tuesday 04/25/2016 9:00 am
Problem 1
We use the three-node triangular element shown below for the solution of the classical two-dimensional
linear heat conduction problem in a homogeneous, isotro
Conducting Finite Element Convergence Studies using
COMSOL 4.0
David W. Trott and Matthias K. Gobbert
Department of Mathematics and Statistics, University of Maryland, Baltimore County,
1000 Hilltop Circle, Baltimore, MD 21250, cfw_dtrott1, gobbert@umbc.e
Name
Midterm Exam
MEAM 520, Introduction to Robotics
University of Pennsylvania
Katherine J. Kuchenbecker, Ph.D.
November 8, 2012
You must take this exam independently, without assistance from anyone else. You may bring
in a calculator and two 8.511 sheet
Name
Midterm Exam
MEAM 520, Introduction to Robotics
University of Pennsylvania
Katherine J. Kuchenbecker, Ph.D.
October 30, 2014
You must take this exam independently, without assistance from anyone else. You may bring
in a calculator and two one-sided 8