System of ordinary differential equation solver

[smilani]

Hi,

how can I solve a system of ordinary differential equation (with relative boundary condition) in mathcad 15?

I must determined an elastic linear equation for a beam fixed to an extremity and with to transverse force applied in different point.

Best regards

[LucMeekes]

I suppose that E and Jx are constants, and you know M(x)...?

Luc

[smilani]

I Luc,

yes are constant. E is young Modulus and Jx is moment of inertia.

Stefano

[ValeryOchkov]

Wolfram|Alpha: Computational Knowledge Engine

[Fred_Kohlhepp · Accepted solution]

A cantilever beam is a simple problem:

[smilani]

Thanks Fred,

and how can I obtain the graph of rotation of sections dy(x)/dx? I try to differentiate the expression but I obtain a wrong distribution

[Fred_Kohlhepp]

Right-click on Odesolve(x,Len), and choose "fixed" instead of "Adams/BDF", then:

Quirks of numeric solvers!

[smilani]

Thanks Fred,

if in general I have a system of (two) differential equation, how can I set the solution in mathcad? for example if I would like to set a congruence beetween a flat end and a shell of a pressure vessel.

Best regards

S

[ValeryOchkov]

It better do in Prime - with units!

[Fred_Kohlhepp]

I don't understand the question.

[smilani]

in this case (cantilever beam) the solution is obtained by solve a single differential equation.

In other cases (for example when I must set a displacement congruence for two different component like flat plate and shell in a pressure vessel) I must solve a system of a differential equation and set as a boundary condition a displacement  and extremity rotation.

In this case how can I set it in mathcad?

Thanks

Regards

S

[Fred_Kohlhepp]

There are many options:

1. You might write one equation that covers the entire problem.  (It's legal to write E and Jx as functions of x.)  You still need two "initial" conditions.
2. You may solve systems of equations.  Here (assuming two equations) you would need four additional constraints, two of which should be setting deflections and slopes equal at the intersection.

[smilani]

For my problems I prefer the second option.

If possible, can you send me a mathcad file for this example with two elastic line equation (1 for each domain).

Thanks again for your explanation.

Best regards

S

[Fred_Kohlhepp]

Take your best shot; post what you have.  Gives us all a better place to start than a blank page.

[smilani]

Ok I'm trying and I send in a next post the results

Best regards

S