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AhmadJami1-Visitor
1-Visitor
March 17, 2013
Solved

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

  • March 17, 2013
  • 11 replies
  • 5948 views

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 ?

Thanks in advance....

Best answer by Werner_E

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.

In your sheet you made two errors:

  • 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

AlanStevens19-Tanzanite
19-Tanzanite
March 17, 2013

See attached.

Alan

    AhmadJami1-VisitorAuthor
    1-Visitor
    March 17, 2013

    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

    Werner_E
    Werner_E25-Diamond IAnswer
    25-Diamond I
    March 17, 2013

    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.

    In your sheet you made two errors:

    • 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.
      AhmadJami1-VisitorAuthor
      1-Visitor
      March 17, 2013

      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 !

      ValeryOchkov24-Ruby IV
      24-Ruby IV
      March 18, 2013

      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

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