Python Beam.apply_load方法代码示例

# 需要导入模块: from sympy.physics.continuum_mechanics.beam import Beam [as 别名]
# 或者: from sympy.physics.continuum_mechanics.beam.Beam import apply_load [as 别名]
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)

# 需要导入模块: from sympy.physics.continuum_mechanics.beam import Beam [as 别名]
# 或者: from sympy.physics.continuum_mechanics.beam.Beam import apply_load [as 别名]
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))

# 需要导入模块: from sympy.physics.continuum_mechanics.beam import Beam [as 别名]
# 或者: from sympy.physics.continuum_mechanics.beam.Beam import apply_load [as 别名]
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}

# 需要导入模块: from sympy.physics.continuum_mechanics.beam import Beam [as 别名]
# 或者: from sympy.physics.continuum_mechanics.beam.Beam import apply_load [as 别名]
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()

# 需要导入模块: from sympy.physics.continuum_mechanics.beam import Beam [as 别名]
# 或者: from sympy.physics.continuum_mechanics.beam.Beam import apply_load [as 别名]
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]

# 需要导入模块: from sympy.physics.continuum_mechanics.beam import Beam [as 别名]
# 或者: from sympy.physics.continuum_mechanics.beam.Beam import apply_load [as 别名]
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 == []

# 需要导入模块: from sympy.physics.continuum_mechanics.beam import Beam [as 别名]
# 或者: from sympy.physics.continuum_mechanics.beam.Beam import apply_load [as 别名]
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)

# 需要导入模块: from sympy.physics.continuum_mechanics.beam import Beam [as 别名]
# 或者: from sympy.physics.continuum_mechanics.beam.Beam import apply_load [as 别名]
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)

# 需要导入模块: from sympy.physics.continuum_mechanics.beam import Beam [as 别名]
# 或者: from sympy.physics.continuum_mechanics.beam.Beam import apply_load [as 别名]
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)

# 需要导入模块: from sympy.physics.continuum_mechanics.beam import Beam [as 别名]
# 或者: from sympy.physics.continuum_mechanics.beam.Beam import apply_load [as 别名]
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

# 需要导入模块: from sympy.physics.continuum_mechanics.beam import Beam [as 别名]
# 或者: from sympy.physics.continuum_mechanics.beam.Beam import apply_load [as 别名]
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.........

# 需要导入模块: from sympy.physics.continuum_mechanics.beam import Beam [as 别名]
# 或者: from sympy.physics.continuum_mechanics.beam.Beam import apply_load [as 别名]
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

# 需要导入模块: from sympy.physics.continuum_mechanics.beam import Beam [as 别名]
# 或者: from sympy.physics.continuum_mechanics.beam.Beam import apply_load [as 别名]
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)

# 需要导入模块: from sympy.physics.continuum_mechanics.beam import Beam [as 别名]
# 或者: from sympy.physics.continuum_mechanics.beam.Beam import apply_load [as 别名]
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) + S(4000)/3
    assert p == q/(E*I)

    # Test for deflection distribution function
    p = b1.deflection()
    q = 4000*x/3 - 4*SingularityFunction(x, 0, 3)/3 + SingularityFunction(x, 10, 3) + 60*SingularityFunction(x, 30, 2) + SingularityFunction(x, 30, 3)/3 - 12000
    assert p == q/(E*I)

    # Test using symbols
    l = Symbol('l')
    w0 = Symbol('w0')
    w2 = Symbol('w2')
    a1 = Symbol('a1')
    c = Symbol('c')
    c1 = Symbol('c1')
    d = Symbol('d')
    e = Symbol('e')
    f = Symbol('f')

    b2 = Beam(l, E, I)

    b2.apply_load(w0, a1, 1)
#.........这里部分代码省略.........