Update beam.py to allow solving reaction moments #14681

cym1 · 2018-05-01T15:49:12Z

The previous version doesn't allow applying reaction moments.

Example, a beam has length l and fixed supports at both ends. A 1000N load is applied at the center.

E = Symbol('E')
I = Symbol('I')
l = Symbol('l', positive=True)
R1, R2 = symbols('R1, R2')
M1, M2 = symbols('M1, M2')

b = Beam(l, E, I)
b.bc_deflection = [(0, 0),(l, 0)]
b.bc_slope = [(0, 0),(l, 0)]

b.apply_load(R1, 0, -1)
b.apply_load(M1, 0, -2)
b.apply_load(R2, l, -1)
b.apply_load(M2, l, -2)
b.apply_load(-1000, 0.5*l, -1)

Method solve_for_reaction_loads will not solve M1 and M2. A new method solve() is proposed here to find M1, M2.

A new method extrema() also proposed to find the maximum deflection points

References to other Issues or PRs

Brief description of what is fixed or changed

Other comments

The previous version doesn't allow applying reaction moments. Example, a beam has length l and fixed supports at both ends. A 1000N load is applied at the center. E = Symbol('E') I = Symbol('I') l = Symbol('l', positive=True) R1, R2 = symbols('R1, R2') M1, M2 = symbols('M1, M2') b = Beam(l, E, I) b.bc_deflection = [(0, 0),(l, 0)] b.bc_slope = [(0, 0),(l, 0)] b.apply_load(R1, 0, -1) b.apply_load(M1, 0, -2) b.apply_load(R2, l, -1) b.apply_load(M2, l, -2) b.apply_load(-1000, 0.5*l, -1) Method solve_for_reaction_loads will not solve M1 and M2. A new method solve() is proposed here to find M1, M2. A new method extrema() also proposed to find the maximum deflection points

moorepants · 2018-05-01T16:34:31Z

These look like great improvements. It will need some tuning to get merged. First is that you need to follow the deprecation policy for API changes (i.e. removing the method). Secondly, please improve the docstrings for the new methods, ideally with parameters, returns, examples etc.

moorepants · 2018-05-01T16:35:14Z

Meant to link to this: https://github.com/sympy/sympy/wiki/Deprecating-policy

moorepants · 2018-05-01T16:39:26Z

@jashan498 It would be good to have you review this.

jashan498 · 2018-05-01T17:42:43Z

sympy/physics/continuum_mechanics/beam.py

        self._reaction_loads = {}
+        self.C3 = Symbol('C3')
+        self.C4 = Symbol('C4')


is there any particular reason to declare C3 and C4 inside the constructor? I think declaring them inside the function itself should work.

If number of fixed supports >= 2, number of bc_slope applied will be also >=2, when solving C3 in slope(), the system of equations will be in the form of:
[C3, C3 + an expression with symbols R1&M1]

The solution is C3 =0 or an expression of R1&M1, linsolve will return an empty set.

In this case, reactions R1 and M1 must be solved before calling slope(). In the process of solving R1 and M1, C3 and C4 are also solved, so why don't just remember the value of C3 and C4 such that re-calculation is not needed in slope() and deflection()?

Yeah it does make sense, but I think there would be some test failures due to this. Let's see if there are some during travis build up.

jashan498 · 2018-05-01T17:50:02Z

sympy/physics/continuum_mechanics/beam.py

-        -8*SingularityFunction(x, 0, -1) + 6*SingularityFunction(x, 10, -1)
-            + 120*SingularityFunction(x, 30, -2) + 2*SingularityFunction(x, 30, -1)
-        """
+    def solve(self):


I think we can go with the same name. In that way, we don't need to deprecate the API.

jashan498 · 2018-05-01T17:52:34Z

sympy/physics/continuum_mechanics/beam.py

+
+        else:
+            for position, value in self._boundary_conditions['slope']:
+                eqs = sympify(slope_curve.subs(x, position) - value)


Shouldn't there be simplify instead of sympify?

Best to avoid simplify calls in library code, as they can be time consuming. It is better to let the user call simplify if they want to.

jashan498 · 2018-05-01T17:59:36Z

sympy/physics/continuum_mechanics/beam.py

-            bc_eqs.append(eqs)
-
-        constants = list(linsolve(bc_eqs, C4))
-        deflection_curve = deflection_curve.subs({C4: constants[0][0]})


After removing the above the chunk of code, how would we find the values of integration constants(C3 and C4)?

jashan498 · 2018-05-01T18:01:16Z

sympy/physics/continuum_mechanics/beam.py

-        deflection_curve = deflection_curve.subs({C4: constants[0][0]})
+
+        slope_curve = integrate(self.bending_moment(), x) + self.C3
+        deflection_curve = integrate(slope_curve, x) + self.C4


C3 and C4 can be evaluated by using self._boundary_conditions['slope'] and self._boundary_conditions['deflection'] respectively.

jashan498 · 2018-05-01T18:03:16Z

sympy/physics/continuum_mechanics/beam.py

+
+    def extrema(self):
+        """
+        Return a list of extrema in form of tuple of x and deflection


Also, add an example for docstring.

jashan498 · 2018-05-01T18:05:06Z

sympy/physics/continuum_mechanics/beam.py

        return S(1)/(E*I)*deflection_curve
+
+    def extrema(self):


Can we name it something like max_delfection to make it clear whose extrema we are talking about?

jashan498 · 2018-05-01T18:13:40Z

sympy/physics/continuum_mechanics/beam.py

+        else:
+            deflection_curve = integrate(slope_curve, x) + C4
+
+            for position, value in self._boundary_conditions['deflection']:


I think there is no need to keep this loop inside if-else block. If not self._boundary_conditions['deflection'] is true then the loop would never be used.
Same goes for above loop.

jashan498 · 2018-05-01T18:26:08Z

@cym1 this issue is not specific to reaction moments as you mentioned in the description.
As far I know this applies to all the beam systems having more than 2 reaction forces(as the previous code used only 2 equations to solve for reactions). I proposed something similar here and i think this is what your code is doing.

Also you need to add required test cases to show that this PR does its work here in this file.

jashan498 · 2018-05-02T08:05:38Z

sympy/physics/continuum_mechanics/beam.py

@@ -432,27 +462,17 @@ def slope(self):
        >>> b.apply_load(R2, 30, -1)
        >>> b.apply_load(120, 30, -2)
        >>> b.bc_deflection = [(10, 0), (30, 0)]
-        >>> b.solve_for_reaction_loads(R1, R2)
+        >>> b.solve()


Now as we are keeping the same name, you can change it back to solve_for_reaction_loads

Yes, I think we shouldn't change the name.

jashan498 · 2018-05-02T08:18:27Z

sympy/physics/continuum_mechanics/beam.py

+
+    def max_deflection(self):
+        """
+        Return the maximum deflection point in form of tuple of x and deflection


You should also include a working example in the method's docstring(see other methods in the class).

jashan498 · 2018-05-02T08:20:02Z

Also, add few test cases to show that your PR can solve the problem it proposes.

cym1 · 2018-05-02T17:34:46Z

sympy/physics/continuum_mechanics/tests/test_beam.py

+    assert p == q
+
+    p = b5.max_deflection()
+    q = (l/2, -F*l**3/(192*E*I))


The answer can be checked here

Abdullahjavednesar · 2018-05-05T19:06:49Z

Ping @jashan498 @moorepants

jashan498 · 2018-05-05T19:16:31Z

except for the failing test, this PR looks fine to me

Abdullahjavednesar · 2018-05-06T18:46:24Z

test_beam.py seems to fail.

cym1 · 2018-05-08T17:25:28Z

The codes of solvers.py changed in sympy-1.1.2.dev.
It causes error as there are interval solutions (x beyond the boundaries) in solving slope() = 0. My idea may be replacing the value of slope() at x beyond the boundaries to S.NaN right before passing it to solve.

jashan498 · 2018-05-08T18:50:45Z

I think it just meant solution to be coming as Interval instance? Does using solveset instead of solve helps?

jashan498 · 2018-05-08T19:01:07Z

For example

>>> solveset(SingularityFunction(x,2,1).rewrite(Piecewise), x,domain=S.Reals)
Interval(-oo, 2)

but using solve for the same gives NotImplementedError:

>>> solve(SingularityFunction(x,2,1).rewrite(Piecewise), x,domain=S.Reals)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/home/jashan/sympy/sympy/solvers/solvers.py", line 1155, in solve
    solution = _solve(f[0], *symbols, **flags)
  File "/home/jashan/sympy/sympy/solvers/solvers.py", line 1458, in _solve
    'solve cannot represent interval solutions')
NotImplementedError: solve cannot represent interval solutions

cym1 · 2018-05-09T02:05:19Z

solveset doesn't work for multivariate expressions, e.g. SingularityFunction(x,b,1)

It requires a new multivariate as_set() in sympy\logic\boolalg.py

jashan498 · 2018-05-29T18:26:04Z

Sorry for the late response, was busy with exams.
Btw see if this diff is of any help. Worked for me in #14753

+ moment_curve = Piecewise((float("nan"), self.variable<=0),
+                (self.bending_moment(), self.variable<self.length),
+                (float("nan"), True))

- extreme_points = solve(self.slope().rewrite(Piecewise), self.variable, domain=S.Reals)
+ points = solve(moment_curve.rewrite(Piecewise), self.variable, domain=S.Reals)

jashan498 · 2018-05-29T18:30:44Z

sympy/physics/continuum_mechanics/tests/test_beam.py

@@ -171,3 +171,26 @@ def test_Beam():
    raises(ValueError, lambda: b4.apply_load(-3, 0, -1, end=3))
    with raises(TypeError):
        b4.variable = 1
+
+    M1, M2 = symbols('M1, M2')
+    F = Symbol('F')


I think we should create separate test functions for both the methods(something like test_statically_indeterminate() and test_max_deflection()).
All tests inside test_beam function look confusing.

cym1 · 2018-05-29T23:12:36Z

This works when the boundaries/fixtures are applied at x= 0 or x= length.

But someone could apply fixed support at other points, e.g. if someone applies fixed support at x = length/10, then there will still be an interval solution between 0 and length/10.

moorepants added the physics.continuum_mechanics label May 1, 2018

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continuum_mechanics: statically indeterminate beam problem can be solved #14467

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Update beam.py to allow solving reaction moments #14681

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Update beam.py to allow solving reaction moments #14681

Update beam.py to allow solving reaction moments #14681

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cym1 commented May 1, 2018

References to other Issues or PRs

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