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## Area and centroid position

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 while others don't

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

Suggestions?

Kind regards, D.

11 REPLIES 11

## Re: Area and centroid position

 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=02. I need to calculate the corresponding area3. 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.

Mike

## Re: Area and centroid position

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.

## Re: Area and centroid position

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.

## Re: Area and centroid position

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.)

## Re: Area and centroid position

Thanks for the tip!

Kind regards, D.

## Re: Area and centroid position

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)

## Re: Area and centroid position

 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.

## Re: Area and centroid position

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.

## Re: Area and centroid position

Take your straight line points and look for "line", "slope", and intercept". You can do a least squares fit to more than two points to get the equation for the line.

## Re: Area and centroid position

Thanks for the idea.

I'll be looking into it!

Kind regards, D.

## Re: Area and centroid position

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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