[GSoC] physics/continuum_mechanics: solve Method along with documentation and tests added for the Truss class

[AdvaitPote]

References to other Issues or PRs

Brief description of what is fixed or changed

After the implementation of the truss class with the initialising methods like add_node and add_method along with many others, the main solving method responsible for solving a given Truss added. After calling the solve method for a given truss, the reaction_loads and internal_forces are updated with the calculated values.

Other comments

Release Notes

• physics.continuum_mechanics
  • Added the solve method for solving a given truss for its reaction loads and internal forces.

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• physics.continuum_mechanics
  • Added the solve method for solving a given truss for its reaction loads and internal forces. (#23755 by @AdvaitPote)

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#### Brief description of what is fixed or changed
After the implementation of the `truss` class with the initialising methods like `add_node` and `add_method` along with many others, the main solving method responsible for solving a given Truss added. After calling the `solve` method for a given truss, the `reaction_loads` and `internal_forces` are updated with the calculated values. 

#### Other comments


#### Release Notes

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* physics.continuum_mechanics
  * Added the `solve` method for solving a given `truss` for its reaction loads and internal forces. 
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Update

The release notes on the wiki have been updated.

[github-actions]

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[AdvaitPote]

@Psycho-Pirate

[Psycho-Pirate]

Please mention what signs the compressive and tensile forces are using.

[Psycho-Pirate]

I tried solving the following problem

Here is the code:

from sympy.physics.continuum_mechanics.truss import Truss
import math
t = Truss()

>>> t.add_node("A", -4, 0)
>>> t.add_node("B", 0, 0)
>>> t.add_node("C", 4, 0)
>>> t.add_node("D", 8, 0)
>>> t.add_node("E", 6, 2/math.sqrt(3))
>>> t.add_node("F", 2, 2*math.sqrt(3))
>>> t.add_node("G", -2, 2/math.sqrt(3))

>>> t.add_member("AB","A","B")
>>> t.add_member("BC","B","C")
>>> t.add_member("CD","C","D")
>>> t.add_member("AG","A","G")
>>> t.add_member("GB","G","B")
>>> t.add_member("GF","G","F")
>>> t.add_member("BF","B","F")
>>> t.add_member("FC","F","C")
>>> t.add_member("CE","C","E")
>>> t.add_member("FE","F","E")
>>> t.add_member("DE","D","E")

>>> t.apply_support("A","pinned")
>>> t.apply_support("D","roller")
>>> t.apply_load("G", 3, 90)
>>> t.apply_load("E", 3, 90)
>>> t.apply_load("F", 2, 90)
>>> t.solve()
>>> t.reaction_loads
{'R_A_x': 3.98027755288532e-16, 'R_A_y': -4.00000000000000, 'R_D_y': -4.00000000000000}

It solves the internal forces correctly but for reaction forces, R_A_x should equal to zero.

[AdvaitPote]

@Psycho-Pirate I have made the required changes. For the second issue, there wasn't any major flaw with how equations were solved but just that when dealing with floats, it just returned a term tending to an infinitesimal term. To get around this, I just found out the minimum load applied and then iterated through the forces_matrix and if there happened to be a force which is smaller than min_load by a certain degree, 1E-10 in this case, then that force would just be reduced to zero.

[AdvaitPote]

@Psycho-Pirate

[Psycho-Pirate]

Looks good to me! Merging!