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Dumitru1-Visitor
1-Visitor
July 9, 2011
Question

Area and centroid position

  • July 9, 2011
  • 11 replies
  • 7467 views

Hello there!

I have a no. of curves (x - strain and y - stress, shown in red) that are aproximated by a function of 50 data points (split in two - from zero strain and stress to maximum stress and corresponding strain and from there on to zero stress and maximum strain, shown in blue). Some curves end in zero stress New Picture (1).bmpwhile others don'tNew Picture.bmp

I have the following three problems:

1. I need to "extend" my curves to end on zero stress (those that don't) - knowing the last two data sets by intersecting the coresponding line with axis y=0

2. I need to calculate the corresponding area

3. I need to calculate the corresponding centroid position

I am currently here New Picture (2).bmp

Suggestions?

Kind regards, D.

11 replies

MikeArmstrong1-Visitor
1-Visitor
July 9, 2011
1. I need to "extend" my curves to end on zero stress (those that don't) - knowing the last two data sets by intersecting the coresponding line with axis y=0

2. I need to calculate the corresponding area

3. I need to calculate the corresponding centroid position

Firstly I would suggest breaking your request down into sections. You could have first created a thread to ask help with extrapolation of your data to sort your graphs out. You can use the predict function or one of the Spline functions to achieve this.

Calculating the area and centroid can be done and I have a few examples from older threads.

Another point is the size of your worksheet, downloading a worksheet that size instantly puts me off.

Mike

wayne12-Amethyst
12-Amethyst
July 10, 2011

Dumitru,

Just looked at quickly,

but you are integrating vectors, you need to express a functions.

For example, you could use linterp function or a spline function to get from G(strain), then integrate over the limits. d(strain) in the integral is not a variable itself, you are using discrete values, I have added some suggestions in green.

Dumitru1-VisitorAuthor
1-Visitor
July 10, 2011

Thank you, Wayne! At a first glance your answer is want I needed to achieve. I'm going to look into in in greater details to fully understand what you did.

Thanks again.

Kind regards, D.

Fred_Kohlhepp23-Emerald I
23-Emerald I
July 10, 2011

You can't integrate vectors, I think that's what you're trying to do.

Create functions and enetgrate those. (Look for green highlighted regions in your attached sheet.)

Dumitru1-VisitorAuthor
1-Visitor
July 10, 2011

Thanks for the tip!

Kind regards, D.

Dumitru1-VisitorAuthor
1-Visitor
July 15, 2011

Hello, there!

The attached is the answer to the initial post.

As it shows, the curves I'm working on have two slopes up to the maximum (stress) - one is a preload while the other is the test itself.

1. If I need to eliminate the preload, a function of tangent for consecutive points may show the maximum change (therefore the end of preloading and beginning of the test itself), right? Is there another (better way)?

2. Once I have that point, by using it and the next consecutive one, how can I "extend" the curve down to zero strain (horizontal axis)? Does "linterp" work at the beginning not just at the end ? (thanks again for suggestions, worksheets and time dedicated for solving that)

Fred_Kohlhepp23-Emerald I
23-Emerald I
July 15, 2011

As it shows, the curves I'm working on have two slopes up to the maximum (stress) - one is a preload while the other is the test itself.

1. If I need to eliminate the preload, a function of tangent for consecutive points may show the maximum change (therefore the end of preloading and beginning of the test itself), right? Is there another (better way)?

2. Once I have that point, by using it and the next consecutive one, how can I "extend" the curve down to zero strain (horizontal axis)? Does "linterp" work at the beginning not just at the end ?


1. Can you take the start of the test as "zero" and simply ignore the preload data?

2. "linterp" is a linear interpolation; it will not extrapolate beyond either end point of the vectors that define it.

Dumitru1-VisitorAuthor
1-Visitor
July 15, 2011

Yes I can "take the start of the test as "zero" and simply ignore the preload data" but I need to extrapolate the beginning of the curve from that point down to zero strain (horizontal axis). I could write an equation of a line defined by two points, one of which has zero stress (working on it - I was hoping there is an automated way of doing that similar to linterp; I'll do it "manually").

Thanks for the help!

Kind regards, D.

Tezza20101-Visitor
1-Visitor
December 6, 2011

Dumitru,

File below calculates areas and centroids of area defined points. Points are two vectors of x and y coordinate values.

Clockwise or anticlockwise around shape gets + or - area.

Good luck

Terry

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