Hello MathCAD People,
I am working on a shaft redesign project, and I start out with trying to plot the deflection of a more simplified model. I write the momentum function in Macaulay’s method and think plotting a deflection curve using odesolve should be a fast way to figure out where the max deflection happens by solving the differential equation and the boundary conditions. However, the plot just ended up with part of the deflection curve and say the ode function has limited range. Can you guys help resolve the error and get Mathcad plot the full cure?
I really appreciate if you can guide me through this problem, as I really need a math model to validate my simulation results.
Thank you in advance.
ACCEPTED SOLUTION
Accepted Solutions
OdeSolve will always use the lowest value in the initial conditions as its starting value and in case of your solve block this is "a".
To get what you are looking for in one go you would have to provide the value for delta.x(0) as initial condition.
You may look up the functions "bvalfit" and especially "sbval" in the help to see if the can be of any help to determine that IC - I lack the experience here as I never have used these functions so far.
https://support.ptc.com/help/mathcad/r6.0/en/index.html#page/PTC_Mathcad_Help%2Fderiving_initial_conditions_for_an_ode.html%23
But Prime allows us to solve from its starting value upwards or downwards. So we can create two separate solve blocks and combine the two functions found.
Prime 6 worksheet attached
In your call of the odesolve() function, you have Delta and its parameter x labelled as 'units'. I guess they should be 'variables'.
Other than that, some of your variables are labelled 'automatic', some are labelled 'variable'.
I've set all variables to 'variable' but that didn't remove the error message.
Since it's a Prime 6 file, I hope someone smarter than me, can find what (else) is wrong.
Since your differential equation is relatively simple (a second derivative of a function Delta equals a known expression), here's what I did:
(Note that some of the expressions continue past the line ).
The maximum deflection is 0.033 mm, the minimum is -0.188 mm.
Success!
Luc
The function Φ(x) is the Heaviside step function. It is defined as:
Φ(x) = 0 for x<0
Φ(x) = 1 for x>0
For x=0 the function usually delivers 1, but it may be 1 or 1/2, depending on preference. This may cause problems in some cases.
Mathcad is pretty strict:
it leaves the numerical answer for Φ(0) symbolically.
Prime (4) gives:
I don't know what it delivers symbolically.
But in fact you can do a mathematically sound IF function with Φ.
Knowing/using the fact that 1 means true and 0 means false you'll have
Φ(x-a) means ' x > a ', since if x > a, then x-a is positive, and Φ will return 1 (true)
Φ(a-x) means ' x < a ', the opposite.
The symbolic functions in Mathcad don't accept if statements, so if you need the IF construct in symbolics, you can/have to use the function Φ.
Success!
Luc
OdeSolve will always use the lowest value in the initial conditions as its starting value and in case of your solve block this is "a".
To get what you are looking for in one go you would have to provide the value for delta.x(0) as initial condition.
You may look up the functions "bvalfit" and especially "sbval" in the help to see if the can be of any help to determine that IC - I lack the experience here as I never have used these functions so far.
https://support.ptc.com/help/mathcad/r6.0/en/index.html#page/PTC_Mathcad_Help%2Fderiving_initial_conditions_for_an_ode.html%23
But Prime allows us to solve from its starting value upwards or downwards. So we can create two separate solve blocks and combine the two functions found.
Prime 6 worksheet attached
Werner - Do you know any reason why your worksheet is good with Prime 6, but the odesolve() fail with Prime 7 and Prime 8?
