project15
$30-100 USD
Πληρώθηκε κατά την παράδοση
Stress strain curves provide important information concerning the
material properties of many different types of materials. Stress
strain curves can be generated when a material is stretched while
recording both the force and the displacement of the material.
This project involves the analysis of an experimentally obtained
data set which includes force and displacement information for a
silicone thin film material.
You will be given a data set of which you will be required to process the raw data and then perform
several different numerical analyses as follows:
1. Signal conditioning of data
2. Curve fitting - Stress Strain Powerfit
3. Integration - Strain energy
4. Finite Differences - rate of change of strain energy
## Deliverables
Stress strain curves provide important information concerning the
material properties of many different types of materials. Stress
strain curves can be generated when a material is stretched while
recording both the force and the displacement of the material.
This project involves the analysis of an experimentally obtained
data set which includes force and displacement information for a
silicone thin film material.
You will be given a data set of which you will be required to process the raw data and then perform
several different numerical analyses as follows:
1. Signal conditioning of data
Import data
The data is stored as ASCII, tab delimited text in the following file: StressStrainSi3.txt.
You will need to read this data into MATLAB. Because this is a large data set, and it includes a
header file, the command dlmread can be used to perform this task. This command uses
the following form (use help for more information)
Result=dlmread('filename','\t', first line of numerical data, first column to import)
This command will return a matrix of all of the data, which will then need to be
separated into separate vectors: Vdisp, and Vforce.
Filter noise
Plot the voltage signal of the force data, and observe the noise in the signal. This 60 Hz noise
must be removed before processing the data. This can be done by applying the 60 Hz notch
filter using the provided file: NotchFilter.m . Compare the filtered data with the raw data
to confirm that the filter has removed the noise without altering the data otherwise.
Convert voltage signals to measurements.
The data provided is the raw voltage measurements from a strain gauge force transducer and an
optical displacement sensor. In order to use the data, you must convert the signals from voltage
into force and displacement.
The conversion for each of the measurement devices are given as follows:
Strain gauge: F=[url removed, login to view] +2.4447 SG
Optical transducer: 0.437 0.1 OT
V x e− =
Thin the data set
Under some situations, it is necessary to reduce the number of data points by thinning the data
set. In this case we will do this to increase the stability of the integration and differentiation.
For the set of data provided, this can be done using the colon operator with an increment of
100. The end result should be a data set with 700, rather than 70,000 data points. (One note of
0.4 0.5 0.6 0.7 0.8 0.9 1
2.6
2.8
3
3.2
3.4
3.6
3.8
x 10
4 Stress Strain Curve
Strain
Stress
Sample
Figure 1: Stress strain curve for
Polymer Material
caution: thinning can damage your data and remove or distort high frequency information in
some situations, so this technique should not be used in all applications.)
Crop data set
Once the data is conditioned, you must decide what data to retain from the test. If you plot
Stress vs. Strain for the entire data set, you will see a jumble of curves, however, when the data
for one stretching motion is separated from the rest of the data, a curve similar to that shown in
this figure is created similar to that shown in figure 1. The choice of data can be found by
plotting the filtered stress data and choosing endpoints starting at the largest peak and ending
at the first minimum after that.
2. Curve fitting - Stress Strain Powerfit
The engineering stress, s , and strain, e , are defined as follows:
F
A
s = ,
L
L
e
D
=
Where F is the force, DL is the change in length, 0 0 0
A = t w is the initial cross-sectional area and 0
L is the
original length of the sample. For the given sample, the original dimensions are:
0.1524 ; 0.1016 ; 0.008 o o o
L = m w = m t = m.
The stress-strain curve in the region beyond yielding is often described by the power model:
b s =ae
Use the data prepared in part 1 to curve fit the data to the power model using the linearization method
developed in class. Compare this with a polynomial model (you decide the appropriate order).
Discuss which method is preferable and why. Make sure to use quantitative values such as the
coefficient of determination (r2) in your assessment as well as qualitative assessments such as
comparing the curve fit with the original data.
Please note that you may use cftool to check your work, however, you must perform these operations
using the codes developed in class.
3. Integration - Strain energy
The strain energy U (strain energy describes the amount of potential energy stored in a spring element
when it is stretched) of a material specimen can be written as:
U = s de
Use numerical integration to calculate the strain energy associated with the material using a first and
second order integration for unevenly spaced data (this will be developed based on the ideas of the
trapezoidal, and Simpson's 1/3 rules).
Compare results with those obtained by directly integrating (by hand) the power fit and polynomial
model and by using the MATLAB built-in function trapz.
4. Finite Differences - rate of change of strain energy
Obtain the relation of the rate of change of the strain energy,
U
e
?
?
, as a function of the strain using
finite difference for unevenly spaced data, based on strain energy data obtained using the two different
orders of integration from part 3.
Compare your results of your different values with the original data, s .
Report Requirements
You may work on your project with your group, however, you must turn in individual reports which are
your own unique work.
The key to this project is ORGANIZATION. Your code should be well organized, and the report also must
be clear and concise. The report will be graded based on the rubric provided to confirm that you have
covered the following areas:
Executive Summary or Abstract: In 1-2 paragraphs, summarize the problem and solution methods as
well as briefly stating results and primary conclusions which can be drawn. Should be written after
rests of report is finished. If someone only read the Abstract, they should understand the purpose
and results of your entire project.
Introduction: The introduction should provide a brief description of the science behind the problem
statement. For this I would recommend that you use a source that is able to be referenced such as
one of the many e-books available through the WSU library system. You must properly reference
all sources used.
Solution Method: This section should describe in detail each of the method that are being used. This is
your opportunity to demonstrate that you understand how curve fitting, numerical integration and
finite difference methods work. You must provide should provide a clear, brief description of each
method, referring to your well documented code (which can be presented either in part or whole
and can be contained in an appendix if necessary).
Results: In a well organized way, clearly and concisely display your data. Based on the results of your
calculations and how you will be referring to them in the discussion session you must determine
the best way to display your results. Please describe the results of each section separately in a
clear and concise way.
Discussion: Your discussion section should use the results presented in the previous section to discuss
the different methods used in the project. Here are some questions to help direct your discussion
session (note, you do not need to answer every single question, this is provided to give you a
starting point for discussion) :
What were some of the issues with the original data set, and how were they overcome?
How does the choice of the function used to fit the data affect the resulting fit?
Is is possible to extrapolated data based on the curve fits used?
How can curve fits be used to estimate other values concerning the given data?
Was integrating the curve fit more effective or numerically integrating the data?
What are the strengths and weaknesses of the different finite difference methods?
Conclusion: Use the conclusion to help the reader understand the value of your results. After briefly
summarizing what you found, describe any conclusions which can be drawn from the report,
and/or any ways in which these results could be helpful for problems solving in the future.
References: You must list all of your references. Make sure to cite references where they are used in
the paper as well. Although there are no points allocated for this section, you will not receive full
credit for the report if it is not included.
Ταυτότητα Εργασίας: #3434421