本文整理汇总了Python中sympy.physics.continuum_mechanics.beam.Beam类的典型用法代码示例。如果您正苦于以下问题：Python Beam类的具体用法？Python Beam怎么用？Python Beam使用的例子？那么恭喜您, 这里精选的类代码示例或许可以为您提供帮助。
在下文中一共展示了Beam类的15个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于系统推荐出更棒的Python代码示例。
示例1: test_composite_beam
def test_composite_beam():
E = Symbol('E')
I = Symbol('I')
b1 = Beam(2, E, 1.5*I)
b2 = Beam(2, E, I)
b = b1.join(b2, "fixed")
b.apply_load(-20, 0, -1)
b.apply_load(80, 0, -2)
b.apply_load(20, 4, -1)
b.bc_slope = [(0, 0)]
b.bc_deflection = [(0, 0)]
assert b.length == 4
assert b.second_moment == Piecewise((1.5*I, x <= 2), (I, x <= 4))
assert b.slope().subs(x, 4) == 120.0/(E*I)
assert b.slope().subs(x, 2) == 80.0/(E*I)
assert int(b.deflection().subs(x, 4).args[0]) == 302 # Coefficient of 1/(E*I)
l = symbols('l', positive=True)
R1, M1, R2, R3, P = symbols('R1 M1 R2 R3 P')
b1 = Beam(2*l, E, I)
b2 = Beam(2*l, E, I)
b = b1.join(b2,"hinge")
b.apply_load(M1, 0, -2)
b.apply_load(R1, 0, -1)
b.apply_load(R2, l, -1)
b.apply_load(R3, 4*l, -1)
b.apply_load(P, 3*l, -1)
b.bc_slope = [(0, 0)]
b.bc_deflection = [(0, 0), (l, 0), (4*l, 0)]
b.solve_for_reaction_loads(M1, R1, R2, R3)
assert b.reaction_loads == {R3: -P/2, R2: -5*P/4, M1: -P*l/4, R1: 3*P/4}
assert b.slope().subs(x, 3*l) == -7*P*l**2/(48*E*I)
assert b.deflection().subs(x, 2*l) == 7*P*l**3/(24*E*I)
assert b.deflection().subs(x, 3*l) == 5*P*l**3/(16*E*I)示例2: test_point_cflexure
def test_point_cflexure():
E = Symbol('E')
I = Symbol('I')
b = Beam(10, E, I)
b.apply_load(-4, 0, -1)
b.apply_load(-46, 6, -1)
b.apply_load(10, 2, -1)
b.apply_load(20, 4, -1)
b.apply_load(3, 6, 0)
assert b.point_cflexure() == [S(10)/3]示例3: test_composite_beam
def test_composite_beam():
E = Symbol('E')
I = Symbol('I')
b1 = Beam(2, E, 1.5*I)
b2 = Beam(2, E, I)
b = b1.join(b2, "fixed")
b.apply_load(-20, 0, -1)
b.apply_load(80, 0, -2)
b.apply_load(20, 4, -1)
b.bc_slope = [(0, 0)]
b.bc_deflection = [(0, 0)]
assert b.length == 4
assert b.second_moment == Piecewise((1.5*I, x <= 2), (I, x <= 4))
assert b.slope().subs(x, 4) == 120.0/(E*I)
assert b.slope().subs(x, 2) == 80.0/(E*I)
assert int(b.deflection().subs(x, 4).args[0]) == 302 # Coefficient of 1/(E*I)
l = symbols('l', positive=True)
R1, M1, R2, R3, P = symbols('R1 M1 R2 R3 P')
b1 = Beam(2*l, E, I)
b2 = Beam(2*l, E, I)
b = b1.join(b2,"hinge")
b.apply_load(M1, 0, -2)
b.apply_load(R1, 0, -1)
b.apply_load(R2, l, -1)
b.apply_load(R3, 4*l, -1)
b.apply_load(P, 3*l, -1)
b.bc_slope = [(0, 0)]
b.bc_deflection = [(0, 0), (l, 0), (4*l, 0)]
b.solve_for_reaction_loads(M1, R1, R2, R3)
assert b.reaction_loads == {R3: -P/2, R2: -5*P/4, M1: -P*l/4, R1: 3*P/4}
assert b.slope().subs(x, 3*l) == -7*P*l**2/(48*E*I)
assert b.deflection().subs(x, 2*l) == 7*P*l**3/(24*E*I)
assert b.deflection().subs(x, 3*l) == 5*P*l**3/(16*E*I)
# When beams having same second moment are joined.
b1 = Beam(2, 500, 10)
b2 = Beam(2, 500, 10)
b = b1.join(b2, "fixed")
b.apply_load(M1, 0, -2)
b.apply_load(R1, 0, -1)
b.apply_load(R2, 1, -1)
b.apply_load(R3, 4, -1)
b.apply_load(10, 3, -1)
b.bc_slope = [(0, 0)]
b.bc_deflection = [(0, 0), (1, 0), (4, 0)]
b.solve_for_reaction_loads(M1, R1, R2, R3)
assert b.slope() == -2*SingularityFunction(x, 0, 1)/5625 + SingularityFunction(x, 0, 2)/1875\
- 133*SingularityFunction(x, 1, 2)/135000 + SingularityFunction(x, 3, 2)/1000\
- 37*SingularityFunction(x, 4, 2)/67500
assert b.deflection() == -SingularityFunction(x, 0, 2)/5625 + SingularityFunction(x, 0, 3)/5625\
- 133*SingularityFunction(x, 1, 3)/405000 + SingularityFunction(x, 3, 3)/3000\
- 37*SingularityFunction(x, 4, 3)/202500示例4: test_Beam
def test_Beam():
E = Symbol("E")
E_1 = Symbol("E_1")
I = Symbol("I")
I_1 = Symbol("I_1")
b = Beam(1, E, I)
assert b.length == 1
assert b.elastic_modulus == E
assert b.second_moment == I
assert b.variable == x
# Test the length setter
b.length = 4
assert b.length == 4
# Test the E setter
b.elastic_modulus = E_1
assert b.elastic_modulus == E_1
# Test the I setter
b.second_moment = I_1
assert b.second_moment is I_1
# Test the variable setter
b.variable = y
assert b.variable is y
# Test for all boundary conditions.
b.bc_deflection = [(0, 2)]
b.bc_slope = [(0, 1)]
assert b.boundary_conditions == {"deflection": [(0, 2)], "slope": [(0, 1)]}
# Test for slope boundary condition method
b.bc_slope.extend([(4, 3), (5, 0)])
s_bcs = b.bc_slope
assert s_bcs == [(0, 1), (4, 3), (5, 0)]
# Test for deflection boundary condition method
b.bc_deflection.extend([(4, 3), (5, 0)])
d_bcs = b.bc_deflection
assert d_bcs == [(0, 2), (4, 3), (5, 0)]
# Test for updated boundary conditions
bcs_new = b.boundary_conditions
assert bcs_new == {"deflection": [(0, 2), (4, 3), (5, 0)], "slope": [(0, 1), (4, 3), (5, 0)]}
b1 = Beam(30, E, I)
b1.apply_load(-8, 0, -1)
b1.apply_load(R1, 10, -1)
b1.apply_load(R2, 30, -1)
b1.apply_load(120, 30, -2)
b1.bc_deflection = [(10, 0), (30, 0)]
b1.solve_for_reaction_loads(R1, R2)
# Test for finding reaction forces
p = b1.reaction_loads
q = {R1: 6, R2: 2}
assert p == q
# Test for load distribution function.
p = b1.load
q = (
-8 * SingularityFunction(x, 0, -1)
+ 6 * SingularityFunction(x, 10, -1)
+ 120 * SingularityFunction(x, 30, -2)
+ 2 * SingularityFunction(x, 30, -1)
)
assert p == q
# Test for shear force distribution function
p = b1.shear_force()
q = (
-8 * SingularityFunction(x, 0, 0)
+ 6 * SingularityFunction(x, 10, 0)
+ 120 * SingularityFunction(x, 30, -1)
+ 2 * SingularityFunction(x, 30, 0)
)
assert p == q
# Test for bending moment distribution function
p = b1.bending_moment()
q = (
-8 * SingularityFunction(x, 0, 1)
+ 6 * SingularityFunction(x, 10, 1)
+ 120 * SingularityFunction(x, 30, 0)
+ 2 * SingularityFunction(x, 30, 1)
)
assert p == q
# Test for slope distribution function
p = b1.slope()
q = (
-4 * SingularityFunction(x, 0, 2)
+ 3 * SingularityFunction(x, 10, 2)
+ 120 * SingularityFunction(x, 30, 1)
+ SingularityFunction(x, 30, 2)
+ 4000 / 3
)
assert p == q / (E * I)
#.........这里部分代码省略.........
示例5: test_remove_load
def test_remove_load():
E = Symbol('E')
I = Symbol('I')
b = Beam(4, E, I)
try:
b.remove_load(2, 1, -1)
# As no load is applied on beam, ValueError should be returned.
except ValueError:
assert True
else:
assert False
b.apply_load(-3, 0, -2)
b.apply_load(4, 2, -1)
b.apply_load(-2, 2, 2, end = 3)
b.remove_load(-2, 2, 2, end = 3)
assert b.load == -3*SingularityFunction(x, 0, -2) + 4*SingularityFunction(x, 2, -1)
assert b.applied_loads == [(-3, 0, -2, None), (4, 2, -1, None)]
try:
b.remove_load(1, 2, -1)
# As load of this magnitude was never applied at
# this position, method should return a ValueError.
except ValueError:
assert True
else:
assert False
b.remove_load(-3, 0, -2)
b.remove_load(4, 2, -1)
assert b.load == 0
assert b.applied_loads == []示例6: test_max_deflection
def test_max_deflection():
E, I, l, F = symbols('E, I, l, F', positive=True)
b = Beam(l, E, I)
b.bc_deflection = [(0, 0),(l, 0)]
b.bc_slope = [(0, 0),(l, 0)]
b.apply_load(F/2, 0, -1)
b.apply_load(-F*l/8, 0, -2)
b.apply_load(F/2, l, -1)
b.apply_load(F*l/8, l, -2)
b.apply_load(-F, l/2, -1)
assert b.max_deflection() == (l/2, F*l**3/(192*E*I))示例7: test_apply_support
def test_apply_support():
E = Symbol('E')
I = Symbol('I')
b = Beam(4, E, I)
b.apply_support(0, "cantilever")
b.apply_load(20, 4, -1)
M_0, R_0 = symbols('M_0, R_0')
b.solve_for_reaction_loads(R_0, M_0)
assert b.slope() == (80*SingularityFunction(x, 0, 1) - 10*SingularityFunction(x, 0, 2)
+ 10*SingularityFunction(x, 4, 2))/(E*I)
assert b.deflection() == (40*SingularityFunction(x, 0, 2) - 10*SingularityFunction(x, 0, 3)/3
+ 10*SingularityFunction(x, 4, 3)/3)/(E*I)
b = Beam(30, E, I)
b.apply_support(10, "pin")
b.apply_support(30, "roller")
b.apply_load(-8, 0, -1)
b.apply_load(120, 30, -2)
R_10, R_30 = symbols('R_10, R_30')
b.solve_for_reaction_loads(R_10, R_30)
assert b.slope() == (-4*SingularityFunction(x, 0, 2) + 3*SingularityFunction(x, 10, 2)
+ 120*SingularityFunction(x, 30, 1) + SingularityFunction(x, 30, 2) + 4000/3)/(E*I)
assert b.deflection() == (4000*x/3 - 4*SingularityFunction(x, 0, 3)/3 + SingularityFunction(x, 10, 3)
+ 60*SingularityFunction(x, 30, 2) + SingularityFunction(x, 30, 3)/3 - 12000)/(E*I)示例8: test_parabolic_loads
def test_parabolic_loads():
E, I, L = symbols('E, I, L', positive=True, real=True)
R, M, P = symbols('R, M, P', real=True)
# cantilever beam fixed at x=0 and parabolic distributed loading across
# length of beam
beam = Beam(L, E, I)
beam.bc_deflection.append((0, 0))
beam.bc_slope.append((0, 0))
beam.apply_load(R, 0, -1)
beam.apply_load(M, 0, -2)
# parabolic load
beam.apply_load(1, 0, 2)
beam.solve_for_reaction_loads(R, M)
assert beam.reaction_loads[R] == -L**3 / 3
# cantilever beam fixed at x=0 and parabolic distributed loading across
# first half of beam
beam = Beam(2 * L, E, I)
beam.bc_deflection.append((0, 0))
beam.bc_slope.append((0, 0))
beam.apply_load(R, 0, -1)
beam.apply_load(M, 0, -2)
# parabolic load from x=0 to x=L
beam.apply_load(1, 0, 2, end=L)
beam.solve_for_reaction_loads(R, M)
# result should be the same as the prior example
assert beam.reaction_loads[R] == -L**3 / 3
# check constant load
beam = Beam(2 * L, E, I)
beam.apply_load(P, 0, 0, end=L)
loading = beam.load.xreplace({L: 10, E: 20, I: 30, P: 40})
assert loading.xreplace({x: 5}) == 40
assert loading.xreplace({x: 15}) == 0
# check ramp load
beam = Beam(2 * L, E, I)
beam.apply_load(P, 0, 1, end=L)
assert beam.load == (P*SingularityFunction(x, 0, 1) -
P*SingularityFunction(x, L, 1) -
P*L*SingularityFunction(x, L, 0))
# check higher order load: x**8 load from x=0 to x=L
beam = Beam(2 * L, E, I)
beam.apply_load(P, 0, 8, end=L)
loading = beam.load.xreplace({L: 10, E: 20, I: 30, P: 40})
assert loading.xreplace({x: 5}) == 40 * 5**8
assert loading.xreplace({x: 15}) == 0示例9: test_max_bmoment
def test_max_bmoment():
E = Symbol('E')
I = Symbol('I')
l, P = symbols('l, P', positive=True)
b = Beam(l, E, I)
R1, R2 = symbols('R1, R2')
b.apply_load(R1, 0, -1)
b.apply_load(R2, l, -1)
b.apply_load(P, l/2, -1)
b.solve_for_reaction_loads(R1, R2)
b.reaction_loads
assert b.max_bmoment() == (l/2, P*l/4)
b = Beam(l, E, I)
R1, R2 = symbols('R1, R2')
b.apply_load(R1, 0, -1)
b.apply_load(R2, l, -1)
b.apply_load(P, 0, 0, end=l)
b.solve_for_reaction_loads(R1, R2)
assert b.max_bmoment() == (l/2, P*l**2/8)示例10: max_shear_force
def max_shear_force(self):
E = Symbol('E')
I = Symbol('I')
b = Beam(3, E, I)
R, M = symbols('R, M')
b.apply_load(R, 0, -1)
b.apply_load(M, 0, -2)
b.apply_load(2, 3, -1)
b.apply_load(4, 2, -1)
b.apply_load(2, 2, 0, end=3)
b.solve_for_reaction_loads(R, M)
assert b.max_shear_force() == (Interval(0, 2), 8)
l = symbols('l', positive=True)
P = Symbol('P')
b = Beam(l, E, I)
R1, R2 = symbols('R1, R2')
b.apply_load(R1, 0, -1)
b.apply_load(R2, l, -1)
b.apply_load(P, 0, 0, end=l)
b.solve_for_reaction_loads(R1, R2)
assert b.max_shear_force() == (0, l*Abs(P)/2)示例11: test_apply_support
def test_apply_support():
E = Symbol('E')
I = Symbol('I')
b = Beam(4, E, I)
b.apply_support(0, "cantilever")
b.apply_load(20, 4, -1)
M_0, R_0 = symbols('M_0, R_0')
b.solve_for_reaction_loads(R_0, M_0)
assert b.slope() == (80*SingularityFunction(x, 0, 1) - 10*SingularityFunction(x, 0, 2)
+ 10*SingularityFunction(x, 4, 2))/(E*I)
assert b.deflection() == (40*SingularityFunction(x, 0, 2) - 10*SingularityFunction(x, 0, 3)/3
+ 10*SingularityFunction(x, 4, 3)/3)/(E*I)
b = Beam(30, E, I)
b.apply_support(10, "pin")
b.apply_support(30, "roller")
b.apply_load(-8, 0, -1)
b.apply_load(120, 30, -2)
R_10, R_30 = symbols('R_10, R_30')
b.solve_for_reaction_loads(R_10, R_30)
assert b.slope() == (-4*SingularityFunction(x, 0, 2) + 3*SingularityFunction(x, 10, 2)
+ 120*SingularityFunction(x, 30, 1) + SingularityFunction(x, 30, 2) + S(4000)/3)/(E*I)
assert b.deflection() == (4000*x/3 - 4*SingularityFunction(x, 0, 3)/3 + SingularityFunction(x, 10, 3)
+ 60*SingularityFunction(x, 30, 2) + SingularityFunction(x, 30, 3)/3 - 12000)/(E*I)
P = Symbol('P', positive=True)
L = Symbol('L', positive=True)
b = Beam(L, E, I)
b.apply_support(0, type='fixed')
b.apply_support(L, type='fixed')
b.apply_load(-P, L/2, -1)
R_0, R_L, M_0, M_L = symbols('R_0, R_L, M_0, M_L')
b.solve_for_reaction_loads(R_0, R_L, M_0, M_L)
assert b.reaction_loads == {R_0: P/2, R_L: P/2, M_0: -L*P/8, M_L: L*P/8}示例12: test_variable_moment
def test_variable_moment():
E = Symbol('E')
I = Symbol('I')
b = Beam(4, E, 2*(4 - x))
b.apply_load(20, 4, -1)
R, M = symbols('R, M')
b.apply_load(R, 0, -1)
b.apply_load(M, 0, -2)
b.bc_deflection = [(0, 0)]
b.bc_slope = [(0, 0)]
b.solve_for_reaction_loads(R, M)
assert b.slope().expand() == ((10*x*SingularityFunction(x, 0, 0)
- 10*(x - 4)*SingularityFunction(x, 4, 0))/E).expand()
assert b.deflection().expand() == ((5*x**2*SingularityFunction(x, 0, 0)
- 10*Piecewise((0, Abs(x)/4 < 1), (16*meijerg(((3, 1), ()), ((), (2, 0)), x/4), True))
+ 40*SingularityFunction(x, 4, 1))/E).expand()
b = Beam(4, E - x, I)
b.apply_load(20, 4, -1)
R, M = symbols('R, M')
b.apply_load(R, 0, -1)
b.apply_load(M, 0, -2)
b.bc_deflection = [(0, 0)]
b.bc_slope = [(0, 0)]
b.solve_for_reaction_loads(R, M)
assert b.slope().expand() == ((-80*(-log(-E) + log(-E + x))*SingularityFunction(x, 0, 0)
+ 80*(-log(-E + 4) + log(-E + x))*SingularityFunction(x, 4, 0) + 20*(-E*log(-E)
+ E*log(-E + x) + x)*SingularityFunction(x, 0, 0) - 20*(-E*log(-E + 4) + E*log(-E + x)
+ x - 4)*SingularityFunction(x, 4, 0))/I).expand()示例13: test_beam_units
def test_beam_units():
E = Symbol('E')
I = Symbol('I')
R1, R2 = symbols('R1, R2')
b = Beam(8*meter, 200*giga*newton/meter**2, 400*1000000*(milli*meter)**4)
b.apply_load(5*kilo*newton, 2*meter, -1)
b.apply_load(R1, 0*meter, -1)
b.apply_load(R2, 8*meter, -1)
b.apply_load(10*kilo*newton/meter, 4*meter, 0, end=8*meter)
b.bc_deflection = [(0*meter, 0*meter), (8*meter, 0*meter)]
b.solve_for_reaction_loads(R1, R2)
assert b.reaction_loads == {R1: -13750*newton, R2: -31250*newton}
b = Beam(3*meter, E*newton/meter**2, I*meter**4)
b.apply_load(8*kilo*newton, 1*meter, -1)
b.apply_load(R1, 0*meter, -1)
b.apply_load(R2, 3*meter, -1)
b.apply_load(12*kilo*newton*meter, 2*meter, -2)
b.bc_deflection = [(0*meter, 0*meter), (3*meter, 0*meter)]
b.solve_for_reaction_loads(R1, R2)
assert b.reaction_loads == {R1: -28000*newton/3, R2: 4000*newton/3}
assert b.deflection().subs(x, 1*meter) == 62000*meter/(9*E*I)示例14: test_statically_indeterminate
def test_statically_indeterminate():
E = Symbol('E')
I = Symbol('I')
M1, M2 = symbols('M1, M2')
F = Symbol('F')
l = Symbol('l', positive=True)
b5 = Beam(l, E, I)
b5.bc_deflection = [(0, 0),(l, 0)]
b5.bc_slope = [(0, 0),(l, 0)]
b5.apply_load(R1, 0, -1)
b5.apply_load(M1, 0, -2)
b5.apply_load(R2, l, -1)
b5.apply_load(M2, l, -2)
b5.apply_load(-F, l/2, -1)
b5.solve_for_reaction_loads(R1, R2, M1, M2)
p = b5.reaction_loads
q = {R1: F/2, R2: F/2, M1: -F*l/8, M2: F*l/8}
assert p == q示例15: test_insufficient_bconditions
def test_insufficient_bconditions():
# Test cases when required number of boundary conditions
# are not provided to solve the integration constants.
L = symbols('L', positive=True)
E, I, P, a3, a4 = symbols('E I P a3 a4')
b = Beam(L, E, I, base_char='a')
b.apply_load(R2, L, -1)
b.apply_load(R1, 0, -1)
b.apply_load(-P, L/2, -1)
b.solve_for_reaction_loads(R1, R2)
p = b.slope()
q = P*SingularityFunction(x, 0, 2)/4 - P*SingularityFunction(x, L/2, 2)/2 + P*SingularityFunction(x, L, 2)/4
assert p == q/(E*I) + a3
p = b.deflection()
q = P*SingularityFunction(x, 0, 3)/12 - P*SingularityFunction(x, L/2, 3)/6 + P*SingularityFunction(x, L, 3)/12
assert p == q/(E*I) + a3*x + a4
b.bc_deflection = [(0, 0)]
p = b.deflection()
q = a3*x + P*SingularityFunction(x, 0, 3)/12 - P*SingularityFunction(x, L/2, 3)/6 + P*SingularityFunction(x, L, 3)/12
assert p == q/(E*I)
b.bc_deflection = [(0, 0), (L, 0)]
p = b.deflection()
q = -L**2*P*x/16 + P*SingularityFunction(x, 0, 3)/12 - P*SingularityFunction(x, L/2, 3)/6 + P*SingularityFunction(x, L, 3)/12
assert p == q/(E*I)