Incorrect Question 8 0 I 1 pts
Which of the following equations describes the reaction of
copper metal with dilute nitric acid?
cum + 4H30+(aq) + 2N03'laq) Cu2+(aq) + 2N02(g)
4Cu(s) + 10H3o+(aq) + 2No3-(aq) 4Cu2+(aq) +
N209) + 15 H200)
Find the exact value of sin(oc- [3) if sin (I = W and sin [3 = E and 0c and [3 are between 0 and m2.
Use the identity for the sine of a difference.
sin (or [3)=sin occos [3-cosocsin [3
To calculate sin or cos [3 - cos 0c sin [3, you need to know the
Finite Elements for 2D Plane Problem
Chapter 6 and Chapter 8 in textbook
2D Plane Problem
2D plane problem is a simplification of a 3D problem. It is
widely used due to its efficiency.
Linear Elasticity and Energy Method
Linear elasticity is the most common problem in a variety of
What is li
Summary of the Class After Exam 1
Linear Elasticity and Variational Method
Principle of virtual displacements and principle of minimum potential
Finite Element for 2D Problem
2D plane problems
2D linear triangular elements
Chapter 10 in textbook
In reality, triangular elements and rectangular elements can not meet our
needs in modeling complicated geometry. Isoparametric elements are
Beam is one of commonly used structural elements. Many engineering
structures can be modeled as beams.
Airplane wing modeled as beam
Mechanics of Beams
Textbook, 10.4 and 10.5
In practice, the element stiffness is calculated numerically.
Numerical Integration Schemes:
2D and 3D Truss Elements
Truss is one of the simplest, yet very commonly used structural elements.
Features of a truss
Forces can only be transmitted along the axial
direction. Or a truss can only be
Summary of the Class before Exam1
Building a FEA Model
Ingredients of a FEA software package
Steps in building a FEA model
1D Spring/Truss Elements
Single 1D spring/truss element
Global stiffness matrix; properties
% Program to work problem 4.3
% FEA HW 5
% Kevin Long, October 4, 2006
% MCEN 4173 FAll 2006, University of Colorado
% Note, the conventions for this code are different
% The image is flipped so that the pin is on the right side
% and the nodes are labele
Heat Transfer and Temperature Field
Textbook, Chapter 13
Understanding heat transfer is the first step to investigate thermomechanical problems
Governing equations for heat
We are studying the energy method, which provides a foundation for developing 2D
plane elements and 3D solid elements. The following questions are designed for you to
get familiar with tools that we will use.
1. At a given materia
SPM and FEA:
Nanometer Scale to Macroscopic Scale
Dr. H.J. Qi
What is an AFM?
Atomic Force Microscope (AFM) or Scanning Probe
Originally Designed for imaging 3D surface profile with
Step 1: Understanding the physics of problem
What is the problem about?
Static? Dynamic? Transient?
Crack initiation? Crack propagation? Plastic?
(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
(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
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