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
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 equatio
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
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 ,
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 questi
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 t
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 Lo
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
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
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
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 i
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 merel
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
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
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 var
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
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
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 ch
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, equiv
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. Wh
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 o
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
be
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?
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 com
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 problem
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-Mec