オリジナル
sympyで不静定はりを解く
https://qiita.com/tehen_/items/78de14be5de482d84a26
参考資料
Statically indeterminate beams＜
WolframAlpha
勉強中
単純梁（中心荷重）
単純梁（等分布荷重）
自乗の表示が間違っています。sympy
単純梁（中心荷重）
PartialScript.py
def _main():
from sympy.core import symbols
from sympy.plotting import plot
l = symbols('l', positive=True, real=True)
RA, RB = symbols('R_A, R_B')
P = symbols('P')
E, I = symbols('E, I')
x = symbols('x')
loads = [
(-RA, 0, -1),
(-RB, l, -1),
(P, 0.5*l, -1),
(0, 0, -2),
(0, l, -2)
]
b = Beam(l, E, I)
for load in loads:
b.apply_load(*load)
b.bc_deflection = [
(0, 0),
(l, 0)
]
b.solve_for_reaction_loads(RA, RB )
print(b.reaction_loads)
print("v(x)=",b.deflection())
print("v(l/2)=",b.deflection().subs({x: 0.5*l}))
print(" 1/48=",1/48)
# こことんでもなく雑な数字
constants = {l: 1, P: 1, E: 1, I: 1}
plot(
# b.shear_force().subs(constants),
b.bending_moment().subs(constants),
# b.slope().subs(constants),
# b.deflection().subs(constants),
(b.variable, 0, b.length.subs(constants))
)
if __name__ == '__main__':
_main()
# {R_A: 0.5*P, R_B: 0.5*P}
# v(x)= (0.0625*P*l**2*x - 0.0833333333333333*P*SingularityFunction(x, 0, 3) + P*SingularityFunction(x, 0.5*l, 3)/6 - 0.0833333333333333*P*SingularityFunction(x, l, 3))/(E*I)
# v(l/2)= 0.0208333333333333*P*l**3/(E*I)
# 1/48= 0.020833333333333332
単純梁（等分布荷重）
PartialScript.py
def _main():
from sympy.core import symbols
from sympy.plotting import plot
l = symbols('l', positive=True, real=True)
RA, RB = symbols('R_A, R_B')
E, I = symbols('E, I')
x = symbols('x')
w = symbols('w')
loads = [
(-RA, 0, -1),
(-w, 0, 0, l),
(-RB, l, -1),
(0, 0, -2),
(0, l, -2)
]
b = Beam(l, E, I)
for load in loads:
b.apply_load(*load)
b.bc_deflection = [
(0, 0),
(l, 0)
]
b.solve_for_reaction_loads(RA, RB )
print(b.reaction_loads)
print("v(x)=",b.deflection())
print("v(l/2)=",b.deflection().subs({x: 0.5*l}))
print("-5/384=",-5/384)
# こことんでもなく雑な数字
constants = {l: 1, w: 1, E: 1, I: 1}
plot(
# b.shear_force().subs(constants),
b.bending_moment().subs(constants),
# b.slope().subs(constants),
# b.deflection().subs(constants),
(b.variable, 0, b.length.subs(constants))
)
if __name__ == '__main__':
_main()
# {R_A: -l*w/2, R_B: -l*w/2}
# v(x)= (-l**3*w*x/24 + l*w*SingularityFunction(x, 0, 3)/12 + l*w*SingularityFunction(x, l, 3)/12 - w*SingularityFunction(x, 0, 4)/24 + w*SingularityFunction(x, l, 4)/24)/(E*I)
# v(l/2)= -0.0130208333333333*l**4*w/(E*I)
# -5/384= -0.013020833333333334