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engineering – 1D Wave Equation: Vertical Rod and Displacement vs. Textbook Solution

I am trying to setup Mathematica to analyze a vertical round rod under its own weight, fixed on one end free on the other. I have the 1D wave equation and a distributed load to represent the self weight of the round rod.

Vertical Rod Layout

The problem is when I compare the Mathematica solution to the textbook solution the two do not agree.

Sample problem is given below.

Y = 199*^9; (*Young's modulus in Pa *)
(Rho) = 7860; (* Steel density in kg/m^3*)
dia = 1/39.37; (* 1" dia converted to meters*)
c = Sqrt(Y/(Rho));
len = 1000; (*length in meters*)
tmax = 5; (* Max time for analysis*)
area = (Pi)*dia^2/4; (*Round rod cross sectional area*)
wtfactor = (Rho)*9.81*area/len;

frwt(x_) := (Rho)*
   area*9.81*(1 - 
     x/len); (*Rod Self weight imposed as a distributed load*)
nsol6 = NDSolve({!(
*SubscriptBox(((PartialD)), ({t, 2}))(z(x, t))) == c^2*!(
*SubscriptBox(((PartialD)), ({x, 2}))(z(x, t))) + frwt(x) + 
     NeumannValue(0, x == len),
   z(0, t) == 0}, z(x, t), {x, 0, len}, {t, 0, tmax},
  Method -> {"FiniteElement", 
    "MeshOptions" -> {"MaxCellMeasure" -> 10}}
  )
fnnsol6(x_, t_) = nsol6((1, 1, 2))
Plot3D(fnnsol6(x, t), {x, 0, len}, {t, 0, tmax}, 
 PlotLabels -> Automatic, AxesLabel -> Automatic)

deltaL = (((Rho)*9.81*len^2)/(
 Y*2)) (*Textbook elongation for a vertical rod under self weight*)
calcdeltaL = 
 fnnsol6(len, 
  5) (*Calculated delta Length from PDE solution.  Should match 
textbook*)

deltaLfunc(x_, l_) := (Rho)*9.81*
  x*(2*len - x)/(2*Y) (*Verified Correct*)
xydata = Thread({Range(0, 1000, 100), 
    deltaLfunc(x, 1) /. {x -> Range(0, 1000, 100)}});
xydata2 = 
 Thread({Range(0, 1000, 100), 
   Reverse(a)}); (*Same answer different calc format for debugging*)
Show(Plot(fnnsol6(x, 0), {x, 0, len}, PlotLabels -> {"PDE Val"}, 
  PlotRange -> All
  ),
 ListLinePlot(xydata2, PlotStyle -> Green, PlotLabels -> {"Correct"}))

If you’ve read this far, thank you.

In summary my question is: Is this a Mathematica issue or a PDE setup problem? The PDE is right out of a textbook so I don’t think that’s the problem but Mathematica gives no errors and I am out of troubleshooting ideas so looking for some help.

Thank You

Developer Documentation Builder – Software Engineering Stack Exchange

I am trying to build a developer documentation for my web app in the style of this: https://firebase.google.com/docs/firestore/query-data/get-data

The features I am looking for is that it has a left vertical navigation bar, and the documentation text is on the right, along with code sections. Instead of me creating everything from HTML/CSS from scratch, I am wondering if there is a website builder that I can use to drag and drop the features I want such as the vertical navigation bar, and code blocks, etc, or any other methods to create such documentation?

usability engineering – A / B testing: is this how you calculate the average number of "Clicks to content" for participants?

I am currently calculating using Excel some collected quantitative data that I have from the participants. So far I have reached this score%:

enter the image description here

Note: I know the metrics for Task completion time it is calculated as follows:

(max_score - participant_score)/(max_score - minimum_score)

My main question:
Is there a similar equation / formula for "number of participant clicks" on a specific page?

Usability Engineering – A / B Testing: Completion of Tasks% Score

I am currently calculating using Excel some collected quantitative data that I have from the participants. So far I have reached this score%:

enter the image description here

Now I'm kind of stuck. Since I'm not sure, I will take the next step and average everything, especially since I can't find any details in the books related to "doing UX studies", therefore I am curious if anyone knows what it is like this done correctly

enter the image description here

Task completion rate percentage but based on the number of mouse clicks, then should you basically calculate the average?

Social engineering: Is it a good idea to use a non-ASCII name in the United States?

There are even Chinese in the United States. They name their children 李某. Would that be a problem? No. Some systems support these names, some use versions converted to ASCII through romanization. The only non-ascii character in X Æ A-12, Æ, p is used. in Danish names like Ægidius, converted to ascii Aegidius.

A good example of such a conversion is machine-readable passports: the last two lines of each passport contain only the characters A – Z, 0–9 and the padding character <. For passports, all the names in the world are converted to ascii.

Sometimes using simple ascii can be more problematic than non-ascii characters that are easily encoded in UTF-8: Coffee tables Bobby It has a name as unique as the little baby musk. This Robert does not have a social security number since he is a fictional character, but for real people the name is not an obstacle.

Exploits of a mom

Social engineering: Is it a good idea to use non-ascii names in the United States?

Grimes and Elon Musk called their baby: X Æ A-12. How bad a idea is to use non-ascii names? For example, would the COBOL unemployment platform support your name? Would it be possible to get a social security number for the baby?

I think it exposes your baby to being an easier target to pose as unicode hacking attacks

usability engineering: UX A / B Testing, Click% Score to achieve your goal

I am currently calculating using Excel some collected quantitative data that I have from the participants. So far I have reached this score%:

enter the image description here

Now I'm kind of stuck. Since I'm not sure, I will take the next step and average everything, especially since I can't find any details in the books related to "doing UX studies", therefore I am curious if anyone knows what it is like this done correctly

usability engineering – UX Click% Score to achieve your goal

I am currently calculating using Excel some collected quantitative data that I have from the participants. So far I have reached this score%:

enter the image description here

Now I'm kind of stuck. Since I'm not sure, I will take the next step and average everything, especially since I can't find any details in the books related to "doing UX studies", therefore I am curious if anyone knows what it is like this done correctly

Self Improvement – Online Course for Backend Engineering with Java / Kotlin Knowledge

I'm not sure if that question belongs to this community, but I couldn't find anything better.

I have been developing Android apps professionally with Java / Kotlin for several years and now I would like to start learning modern backend development in JVM.

I asked and heard good feedback about Udacity's Java Backend Developer course: https://www.udacity.com/course/java-developer-nanodegree–nd035. Unfortunately, it is under reconstruction at the moment and I cannot start.

Can you recommend any other similar online courses?