continuum_mechanics : slope and deflection method now returns complete answer

[jashan498]

Brief description of what is fixed or changed

>>> L = symbols('L', positive=True)
>>> b = Beam(L, E, I)
>>> b.apply_load(R2, L, -1)
>>> b.apply_load(R1, 0, -1)
>>> P=symbols('P')
>>> b.apply_load(-P, L/2, -1)

Now for the above beam this integrates the bending_moment twice ignoring that for every integral a constant has to be added (which is solved with help of boundary conditions provided). 0n current master:

>>> b.slope()
(-P*SingularityFunction(x, L/2, 2)/2 + R1*SingularityFunction(x, 0, 2)/2 + R2*SingularityFunction(x, L, 2)/2)/(E*I)
>>> b.deflection()
(-P*SingularityFunction(x, L/2, 3)/6 + R1*SingularityFunction(x, 0, 3)/6 + R2*SingularityFunction(x, L, 3)/6)/(E*I)

In case of deflection coefficient of x vanishes due to this.

This sometimes is misleading, hence constants are required to mark the incomplete solution.

>>> b.slope()
C3 + (-P*SingularityFunction(x, L/2, 2)/2 + R1*SingularityFunction(x, 0, 2)/2 + R2*SingularityFunction(x, L, 2)/2)/(E*I)
>>> b.deflection()
C3*x + C4 + (-P*SingularityFunction(x, L/2, 3)/6 + R1*SingularityFunction(x, 0, 3)/6 + R2*SingularityFunction(x, L, 3)/6)/(E*I)

Release Notes

• physics.continuum_mechanics
  • slope and deflection methods now return integral constants along with expression if insufficient boundary conditions to solve those constants are passed.

[jashan498]

@moorepants please review

[Abdullahjavednesar]

@moorepants can you please have a look, thanks!

[moorepants]

@jashan498 Please update wrt to master and add a release note.

[moorepants]

@jashan498 Can you explain why this doesn't affect all beams (the ones that already work)?

[sympy-bot]

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#### Brief description of what is fixed or changed
```
>>> L = symbols('L', positive=True)
>>> b = Beam(L, E, I)
>>> b.apply_load(R2, L, -1)
>>> b.apply_load(R1, 0, -1)
>>> P=symbols('P')
>>> b.apply_load(-P, L/2, -1)
```
Now for the above beam [this](https://github.com/sympy/sympy/blob/3a5515d19bfd48ed680da2c4a23289f2500065b3/sympy/physics/continuum_mechanics/beam.py#L494) integrates the bending_moment twice ignoring that for every integral a constant has to be added (which is solved with help of boundary conditions provided). 0n current master:
```
>>> b.slope()
(-P*SingularityFunction(x, L/2, 2)/2 + R1*SingularityFunction(x, 0, 2)/2 + R2*SingularityFunction(x, L, 2)/2)/(E*I)
>>> b.deflection()
(-P*SingularityFunction(x, L/2, 3)/6 + R1*SingularityFunction(x, 0, 3)/6 + R2*SingularityFunction(x, L, 3)/6)/(E*I)
```
In case of `deflection` coefficient of `x` vanishes due to this.

This sometimes is misleading, hence constants are required to mark the incomplete solution. 
```
>>> b.slope()
C3 + (-P*SingularityFunction(x, L/2, 2)/2 + R1*SingularityFunction(x, 0, 2)/2 + R2*SingularityFunction(x, L, 2)/2)/(E*I)
>>> b.deflection()
C3*x + C4 + (-P*SingularityFunction(x, L/2, 3)/6 + R1*SingularityFunction(x, 0, 3)/6 + R2*SingularityFunction(x, L, 3)/6)/(E*I)

```

#### Release Notes

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* physics.continuum_mechanics
  * slope and deflection methods now return integral constants along with expression if insufficient boundary conditions to solve those constants are passed.
<!-- END RELEASE NOTES -->

Your release notes are in good order.

Here is what the release notes will look like:

• physics.continuum_mechanics
  • slope and deflection methods now return integral constants along with expression if insufficient boundary conditions to solve those constants are passed. (#14446 by @jashan498)

This will be added to https://github.com/sympy/sympy/wiki/Release-Notes-for-1.2.1.

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Update

The release notes on the wiki have been updated.

[jashan498]

@moorepants actually it's due to the reason in most of our test cases we have provided all boundary_conditions applied on our Beam, so most of the time constants originated were solved.

[moorepants]

We need a way for the user to set this symbol or access it. So either an optional argurment or an attribute, or both. They should be able to set the base character(s) or symbol or pass in a generator. SymPy has a generator for creating sequential symbols. cse uses it.

[jashan498]

@moorepants I missed b.bc_deflection in this example of .rst file (due to which it was returning constants in this PR). I corrected that example.

[jashan498]

This job failed due to some CondaHTTPError.

[jksuom]

Restarted.

[jashan498]

Thanks @jksuom !