Quiz 2
For Froblems 1w6, circle the correct answer. No work is requires! and no partial credit is possible. Each question is
MATH 1071
worth 1 point.
1) What is the deny the function f(x) : «ix + 3?
m) If.
C) [3/ 0°) (3! m)
2) Findf(1)for f(x)=
Notes
MATH 1071
Applications of Linear Programming
(Section 7.3)
November 7, 2012
Section 7.1 :
Homework #10 (Due 11/12): Section 7.2 :
Section 7.3 :
# 56
#8
# 8, 16, 20
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Patrick Newberry
Applications of
20
CHAPTER 1 Solving Equations and Inequalities
SECTION 4 Solving Linear and Absolute Value Inequalities
Solving Linear Inequalities
Now that we have studied equations, and specifically linear equations, we are going to change
our focus to inequalities. I
Homework 9:
(Due on 11/17/06)
1. Consider the trianular element in Figure 1. The nodal coordinates are: node 1,
(0,0); node 2: (3,3); and node 3: (-1,3). The top edge of this element is subjected
to a distributed load, which is a function of local coordin
Homework 8:
(Due on 11/08/06, Wednesday)
We formulated the element stiffness matrix in the class. Please answer the following
questions:
1. Problem 6.3.
2. Problem 6.7. (You only need to determine x , y , and xy for (a) and (d) ).
Homework 5:
(Due on 10/04/2005)
Beam elements are one of the most complicated elements because they have a rotation
degree of freedom. Read section 4.1-4.3 in Chapter 4 and answer the following questions:
1. Problem 4.3
2. Problem 4.7 (Please obtain the g
Homework 3:
(Due on 09/20/2006)
Truss elements behave like spring elements. By visiting truss elements, we introduced
many important concepts in FEA. Read section 3.1 and 3.2 in Chapter 3 and answer the
following questions:
1. Problem 3.14
2. Problem 3.8
Homework 1:
(Due on 09/06/2006)
1. Matrix Algebra is the most commonly used math in FEA. Please read Appendix 1
Matrix Algebra of Logans book, and finish the following problems:
1.1) Problem A.7 in Logans book.
1.2) Problem A.8.
1.3) Problem A.9.
2. For a
Finite Element Analysis MCEN 4173/5173 / Fall 2006
LABORATORY 1 2D TRUSS
The tutorials used in the reference book are based on an older version of ANSYS.
We will be using a more recent version but the basic behavior is the same. The step
numbers listed be
Homework 2:
(Due on 09/13/2006)
The spring element is one of the simplest elements in FEA, but it offers a picture of how
matrixes are used in FEA. Please answer the following question:
1. Problem 2.1
2. Construct the global stiffness matrix for the syste
Homework 7:
(Due on 10/27/06)
Please prove that the shape functions for plane linear triangular element have the
following properties:
1 at
0 at
1. N i =
( x, y ) = ( x i , y i )
(x, y ) = (x j , y j ) or (x m , y m )
2. N i + N j + N k = 1 (please do no
Finite Element Analysis MCEN 4173/5173
Fall 2006
Homework #1 (Due: Beginning of laboratory on 09/08/06)
Problem 1-2 in the Problems section of the reference book
HINTS:
The procedure to be followed is similar to that described in the exercise. There are
The following is a set of 20 multiple-choice problems covering material from the course this semester.
This is NOT meant to be a practice exam nor an exhaustive list of questions to study. It is merely a set of multiple-choice
questions to help prepare yo
30
CHAPTER 2 Systems of Equations and Inequalities
SECTION 1 Solving Systems of Linear Equations in Two Variables
The Solution of a System of Equations
A system of linear equations is simply a set of two or more linear equations that may have two or
more
1
CHAPTER 1 Solving Equations and Inequalities
SECTION 1 Solving Linear, Power, and Quadratic Equations in One Variable
First of all, when we solve an equation in a single variable that means we will find the precise
value (or values) of the indicated var
10
CHAPTER 1 Solving Equations and Inequalities
SECTION 2 Radical, Rational, and Absolute Value Equations
RADICAL EQUATIONS
Definition: Radical equation
A radical equation is an equation where the variable in the equation occurs in a square
root, cube roo
71
CHAPTER 3 - Matrices
SECTION 1 Matrix Operations
Recall the definition of a matrix.
Definition: Matrix
A matrix is a rectangular array of numbers.
We say that a matrix with m rows and n columns has size m n .
Matrices of certain sizes are of particular
88
CHAPTER 3 Matrices
SECTION 5 Input-Output Analysis
In 1973, Wassily Leontief was awarded the Nobel Prize in economics because of the
impact that his work, applying matrices and their inverses, had on economic planning for
industrialized nations. In pa
78
CHAPTER 3 Matrices
SECTION 3 Matrix Inverse
The number 1 in the real numbers has a powerful multiplicative property. Namely, for any real
number a, a 1 = a = 1 a . So, multiplication by 1 doesnt change the value of the number a.
Now that we know how to
123
CHAPTER 4 Probability
SECTION 5 Principles of Counting
The key to solving many problems in mathematics and specifically probability lies in
counting the number of ways an event can occur or, equivalently, counting the number of
possible ways there are
110
CHAPTER 4 Probability
SECTION 3 Independent Events
A friend asks you whether or not you are going to buy that new cell phone that all the cool kids
have these days, and you say that it depends. What does it depend on? Well, it may depend on
whether yo
98
CHAPTER 4 Probability
SECTION 1 Classical and Empirical Probability
Experiments, Sample Space, and Events
The goal of probability is to determine the likelihood that a particular event will occur or has
occurred, and to then quantify that likelihood in
Homework 4:
(Due on 09/27/2006)
1. Consider the 2D truss structure as shown in Figure 1. The angle between two trusses
is shown in Figure 1. Assume all the truss have the same E and A. The distance
between node 1 and node 5 is L. The global nodal displace
MCEN 4173/5173
Chapter 12
FEA: Miscellaneous
Fall, 2006
1
Modeling procedure
Step 1: Understanding the physics of problem
What is the problem about?
Static? Dynamic? Transient?
Stress? Displacement?
Crack initiation? Crack propagation? Plastic?
Interfaci
MCEN 4173/5173
Chapter 9
Isoparametric Formula
Fall, 2006
Chapter 10 in textbook
1
Isoparametric Formula
In reality, triangular elements and rectangular elements can not meet our
needs in modeling complicated geometry. Isoparametric elements are
therefore
Summary of the Class After Exam 1
Linear Elasticity and Variational Method
Principle of virtual displacements and principle of minimum potential
energy
Finite Element for 2D Problem
2D plane problems
2D linear triangular elements
Isoparametric Formula
MCEN 4173/5173
Chapter 7
Linear Elasticity and Energy Method
Fall, 2006
1
Linear Elasticity
Linear elasticity is the most common problem in a variety of
engineering applications
Machine Design
Bio-Mechanics
2
Linear Elasticity
Linear Elasticity
What is li
MCEN 4173/5173
Chapter 8
Finite Elements for 2D Plane Problem
Fall, 2006
Chapter 6 and Chapter 8 in textbook
1
2D Plane Problem
2D plane problem is a simplification of a 3D problem. It is
widely used due to its efficiency.
Aragonite Mineral
5m
Organic Mat