Attribution

This page is adapted from https://github.com/saiudayagiri/GSoC/blob/main/Test cases using alex algorithm.ipynb

Test problem 4

import micropip
await micropip.install('../../packages/sympy-1.15.0.dev0-py3-none-any.whl')
#takes a while

%pip install git+https://github.com/saiudayagiri/sympy.git@borek-27130

from sympy.physics.continuum_mechanics.structure2d import Structure2d
from sympy import symbols
s = Structure2d()
E, I, A = symbols('E I A')
s.add_member(0, 0, 4, 0, 10**4, 10**4, 10**4)
s.add_member(4, 0, 8, 3, E, I, A)
s.add_member(8, 3, 11, -1, E, I, A)
s.apply_load(4, 0, 15, 0, -1)
s.apply_load(0, 0, 16, 270, -1)
s.apply_support(11,-1,"fixed")

s.draw(show_load_values=True);

s.solve_for_reaction_loads()

{R_v (x=11,y=-1): -16, R_h (x=11,y=-1): -15, T (x=11,y=-1): -161}

s.plot_axial_force();

s.plot_shear_force_on_structure();

s.plot_bending_moment_on_structure();

s.plot_deformation_on_structure();

s.summary();

===================== Structure Summary =====================

Reaction Loads:
R_v   (x=11.00,y=-1.00)  (unwrapped x=14.00)       = R_v (x=11,y=-1)
R_h   (x=11.00,y=-1.00)  (unwrapped x=14.00)       = R_h (x=11,y=-1)
T     (x=11.00,y=-1.00)  (unwrapped x=14.00)       = T (x=11,y=-1)

Points of Interest - Bending Moment:
bending_moment at (x=0.00,y=0.00)  (unwrapped x=0.00) = 0
bending_moment at (x=2.00,y=0.00)  (unwrapped x=2.00) = -32
bending_moment at (x=4.00,y=0.00)  (unwrapped x=4.00) = -64
bending_moment at (x=4.00,y=0.00)  (unwrapped x=4.00) = -64
bending_moment at (x=6.00,y=1.50)  (unwrapped x=6.50) = -237/2
bending_moment at (x=8.00,y=3.00)  (unwrapped x=9.00) = -173
bending_moment at (x=8.00,y=3.00)  (unwrapped x=9.00) = -173
bending_moment at (x=9.50,y=1.00)  (unwrapped x=11.50) = -167
bending_moment at (x=11.00,y=-1.00)  (unwrapped x=14.00-) = -161.000002400000

Points of Interest - Shear Force:
shear_force at (x=0.00,y=0.00)  (unwrapped x=0.00+) = -16
shear_force at (x=4.00,y=0.00)  (unwrapped x=4.00-) = -16
shear_force at (x=4.00,y=0.00)  (unwrapped x=4.00+) = -109/5
shear_force at (x=8.00,y=3.00)  (unwrapped x=9.00-) = -109/5
shear_force at (x=8.00,y=3.00)  (unwrapped x=9.00+) = 12/5
shear_force at (x=11.00,y=-1.00)  (unwrapped x=14.00-) = 12/5

Points of Interest - Axial Force:
axial_force at (x=0.00,y=0.00)  (unwrapped x=0.00+) = 0
axial_force at (x=4.00,y=0.00)  (unwrapped x=4.00-) = 0
axial_force at (x=4.00,y=0.00)  (unwrapped x=4.00+) = -12/5
axial_force at (x=8.00,y=3.00)  (unwrapped x=9.00-) = -12/5
axial_force at (x=8.00,y=3.00)  (unwrapped x=9.00+) = -109/5
axial_force at (x=11.00,y=-1.00)  (unwrapped x=14.00-) = -109/5