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## Problem with Differential equation of the elastic curve (solve block)

For solving this simple differential equation I used ODE solve block , but when it comes to define the solution parameters , I face problem making MATHCAD understand them !!!

I wrote the solution in the attached file and it can be easily solved by hand , but I wonder how MATHCAD does it !

Can someone please check this and solve this simple differential equation for finding the deflection of a beam ?

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1 ACCEPTED SOLUTION

Accepted Solutions

## Re: Problem with Differential equation of the elastic curve (solve block)

Here is an even simpler solution. Also I included a way to do it manually, but let Mathcad do the work. Unfortunately Mathcad does not offer modules to solve ODEs symbolically (other than using laplace) but in this two times integral do the work and so its easy to let Mathcad do it.

• a typo, I guess. You demanded the impossible - the second derivative of omega to be 0 at L. You meant omega itself should be zero. Erase the two prime symbols and go.
• you demanded to calculate the output from L to L. The initial value is determined by the initial conditions and is L in your case, the terminal point is the second parameter and this was L again in your sheet. As you are interested in the interval 0..L you can set this terminal point to 0 as it is allowed to be smaller than the initial value.
11 REPLIES 11

See attached.

Alan

## Re: Problem with Differential equation of the elastic curve (solve block)

Here is an even simpler solution. Also I included a way to do it manually, but let Mathcad do the work. Unfortunately Mathcad does not offer modules to solve ODEs symbolically (other than using laplace) but in this two times integral do the work and so its easy to let Mathcad do it.

• a typo, I guess. You demanded the impossible - the second derivative of omega to be 0 at L. You meant omega itself should be zero. Erase the two prime symbols and go.
• you demanded to calculate the output from L to L. The initial value is determined by the initial conditions and is L in your case, the terminal point is the second parameter and this was L again in your sheet. As you are interested in the interval 0..L you can set this terminal point to 0 as it is allowed to be smaller than the initial value.

## Re: Problem with Differential equation of the elastic curve (solve block)

I see !

I'd seen some tutorial in net about finding the deflection . People were using difficult ways by manualy entering the deflection's quation to find and plot it !
Since I was already familiar with differential equation of elastic curves , decided to solve it the easier way !
thanks to you , it works !

By the way ! I like your way too, as it can express the solving process and gives simplified equations after integrating , they may become handy !

Thanks Cheers !

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## Re: Problem with Differential equation of the elastic curve (solve block)

You're right about the sign , I mistyped it !

Your solution is also correct and I appreciate it but it's easier to go from the open side of the beam to the end support and while it can be solved the easier way , why should make it harder then ?!

Best regards

## Re: Problem with Differential equation of the elastic curve (solve block)

 Ahmad Jamialahmadi wrote:Since I was already familiar with differential equation of elastic curves , decided to solve it the easier way !Thanks Cheers !

1. You can use units by solving ODE in Mathcad Prime.

2. Welcome to tht Group - http://communities.ptc.com/groups/dynamic-models-in-mathcad

## Re: Problem with Differential equation of the elastic curve (solve block)

May be it is my error or?

## Re: Problem with Differential equation of the elastic curve (solve block)

Looks like an empty sheet, but if I dig into the file using an editor I see ther is content. Seems to be corrupted but no error message.

## Re: Problem with Differential equation of the elastic curve (solve block)

 Werner Exinger wrote:Looks like an empty sheet, but if I dig into the file using an editor I see ther is content. Seems to be corrupted but no error message.

Prime 3 without save as Prime 2 or 1

## Re: Problem with Differential equation of the elastic curve (solve block)

And what's wrong with the units in your opinion?