def test_cvepet3(): # {{{1
"""3-point bending CVEPET3 panel"""
L = 200 # mm
B = 50 # mm
h = 26 # mm
t = 2.5 # mm
E = 43820 # MPa
G = 8 * 1.5 # MPa, schuim met siktsels
P = -150 # N
H = h + 2 * t
Ix = B * (H**3 - h**3) / 12
A = B * h
results = bm.solve(L, (0, L), bm.Load(force=P, pos=L / 2),
np.ones(L + 1) * E * Ix,
np.ones(L + 1) * G * A,
np.ones(L + 1) * H / 2, -np.ones(L + 1) * H / 2, False)
bending_bm = results.y[int(L / 2)]
bending_formula = P * L**3 / (48 * E * Ix)
results = bm.solve(L, (0, L), bm.Load(force=P, pos=L / 2),
np.ones(L + 1) * E * Ix,
np.ones(L + 1) * G * A,
np.ones(L + 1) * H / 2, -np.ones(L + 1) * H / 2, True)
total_bm = results.y[int(L / 2)]
total_formula = bending_formula + (1.5 * P / 2 * L / 2) / (G * A)
reldiff = abs((bending_bm - bending_formula) / bending_formula)
assert reldiff < 0.005
reldifft = abs((total_bm - total_formula) / total_formula)
assert reldifft < 0.02
def test_cvepet3(): # {{{1
"""3-point bending CVEPET3 panel"""
L = 200 # mm
B = 50 # mm
h = 26 # mm
t = 2.5 # mm
E = 43820 # MPa
G = 8 * 1.5 # MPa, schuim met siktsels
P = -150 # N
H = h + 2 * t
Ix = B * (H**3 - h**3) / 12
A = B * h
problem = {
'length': L,
'EI': np.ones(L + 1) * E * Ix,
'GA': np.ones(L + 1) * G * A,
'top': np.ones(L + 1) * H / 2,
'bot': -np.ones(L + 1) * H / 2,
'supports': (0, L),
'shear': False,
'loads': bm.Load(force=P, pos=L / 2)
}
bm.solve(problem)
bending_bm = problem['y'][int(L / 2)]
bending_formula = P * L**3 / (48 * E * Ix)
problem["shear"] = True
bm.solve(problem)
total_bm = problem['y'][int(L / 2)]
total_formula = bending_formula + (1.5 * P / 2 * L / 2) / (G * A)
reldiff = abs((bending_bm - bending_formula) / bending_formula)
assert reldiff < 0.005
reldifft = abs((total_bm - total_formula) / total_formula)
assert reldifft < 0.02
def test_supported_pointloads(): # {{{1
"""Ends supported beam with three equidistant point loads"""
problem = {
'length':
L,
'EI':
np.ones(L + 1) * E * Ix,
'GA':
np.ones(L + 1) * G * A,
'top':
np.ones(L + 1) * H / 2,
'bot':
-np.ones(L + 1) * H / 2,
'supports': (0, L),
'shear':
False,
'loads': [
bm.Load(force=P, pos=L / 4),
bm.Load(force=P, pos=L / 2),
bm.Load(force=P, pos=3 * L / 4)
]
}
bm.solve(problem)
deflection_bm = problem['y'][int(L / 2)]
deflection_formula = 19 * P * L**3 / (384 * E * Ix)
reldiff = abs((deflection_bm - deflection_formula) / deflection_formula)
assert reldiff < 0.005
def test_supported_triangl(): # {{{1
"""Ends supported beam with triangle load"""
problem = {'length': L, 'EI': np.ones(L+1)*E*I, 'GA': np.ones(L+1)*G*A,
'top': np.ones(L+1)*H/2, 'bot': -np.ones(L+1)*H/2,
'supports': (0, L), 'shear': False,
'loads': bm.TriangleLoad(force=P, start=0, end=L)}
bm.solve(problem)
deflection_bm = problem['y'][int(0.519*L)]
deflection_formula = 0.01304*P*L**3/(E*I)
reldiff = abs((deflection_bm-deflection_formula)/deflection_formula)
assert reldiff < 0.005
def test_supported_central_pointload(): # {{{1
"""Ends supported beam with central point load"""
problem = {'length': L, 'EI': np.ones(L+1)*E*I, 'GA': np.ones(L+1)*G*A,
'top': np.ones(L+1)*H/2, 'bot': -np.ones(L+1)*H/2,
'supports': (0, L), 'shear': False,
'loads': bm.Load(force=P, pos=L/2)}
bm.solve(problem)
deflection_bm = problem['y'][L/2]
deflection_formula = P*L**3/(48*E*I)
reldiff = abs((deflection_bm-deflection_formula)/deflection_formula)
assert reldiff < 0.005
def test_supported_distributed(): # {{{1
"""Ends supported beam with distributed load"""
problem = {'length': L, 'EI': np.ones(L+1)*E*I, 'GA': np.ones(L+1)*G*A,
'top': np.ones(L+1)*H/2, 'bot': -np.ones(L+1)*H/2,
'supports': (0, L), 'shear': False,
'loads': bm.DistLoad(force=P, start=0, end=L)}
bm.solve(problem)
deflection_bm = problem['y'][L/2]
deflection_formula = 5*P*L**3/(384*E*I)
reldiff = abs((deflection_bm-deflection_formula)/deflection_formula)
assert reldiff < 0.005
def test_clamped_pointload(): # {{{1
"""Clamped beam with point load at end"""
problem = {'length': L, 'EI': np.ones(L+1)*E*I, 'GA': np.ones(L+1)*G*A,
'top': np.ones(L+1)*H/2, 'bot': -np.ones(L+1)*H/2,
'shear': False, 'supports': None,
'loads': bm.Load(force=P, pos=L)}
bm.solve(problem)
deflection_bm = problem['y'][L]
deflection_formula = P*L**3/(3*E*I)
reldiff = abs((deflection_bm-deflection_formula)/deflection_formula)
assert reldiff < 0.005
def test_clamped_moment_end():
"""Begin clamped, moment load at end."""
M = 500 * 1000
problem = {
'length': L,
'EI': np.ones(L + 1) * E * Ix,
'GA': np.ones(L + 1) * G * A,
'top': np.ones(L + 1) * H / 2,
'bot': -np.ones(L + 1) * H / 2,
'shear': False,
'supports': None,
'loads': bm.MomentLoad(M, pos=L)
}
bm.solve(problem)
deflection_bm = problem['y'][L]
deflection_formula = M * L**2 / (2 * E * Ix)
reldiff = abs((deflection_bm - deflection_formula) / deflection_formula)
assert reldiff < 0.005
def test_clamped_pointload(): # {{{1
"""Clamped beam with point load at end"""
results = bm.solve(L, None, bm.Load(force=P, pos=L),
np.ones(L + 1) * E * Ix,
np.ones(L + 1) * G * A,
np.ones(L + 1) * H / 2, -np.ones(L + 1) * H / 2, False)
deflection_bm = results.y[L]
deflection_formula = P * L**3 / (3 * E * Ix)
reldiff = abs((deflection_bm - deflection_formula) / deflection_formula)
assert reldiff < 0.005
def test_supported_moment_begin():
"""Ends supported beam with moment load at begin."""
M = 500 * 1000
x = 422
problem = {
'length': L,
'EI': np.ones(L + 1) * E * Ix,
'GA': np.ones(L + 1) * G * A,
'top': np.ones(L + 1) * H / 2,
'bot': -np.ones(L + 1) * H / 2,
'supports': (0, L),
'shear': False,
'loads': bm.MomentLoad(M, 0)
}
bm.solve(problem)
deflection_bm = problem['y'][x]
deflection_formula = 0.0642 * M * L**2 / (E * Ix)
reldiff = abs((deflection_bm - deflection_formula) / deflection_formula)
assert reldiff < 0.005
def test_supported_moment_both():
"""Ends supported beam with moment load at both ends."""
M = 500 * 1000 / 2
problem = {
'length': L,
'EI': np.ones(L + 1) * E * Ix,
'GA': np.ones(L + 1) * G * A,
'top': np.ones(L + 1) * H / 2,
'bot': -np.ones(L + 1) * H / 2,
'supports': (0, L),
'shear': False,
'loads': [bm.MomentLoad(M, 0),
bm.MomentLoad(-M, L)]
}
bm.solve(problem)
deflection_bm = problem['y'][int(L / 2)]
deflection_formula = 6 * M * L**2 / (48 * E * Ix)
reldiff = abs((deflection_bm - deflection_formula) / deflection_formula)
assert reldiff < 0.005
def test_supported_triangl(): # {{{1
"""Ends supported beam with triangle load"""
results = bm.solve(L, (0, L), bm.TriangleLoad(force=P, start=0, end=L),
np.ones(L + 1) * E * Ix,
np.ones(L + 1) * G * A,
np.ones(L + 1) * H / 2, -np.ones(L + 1) * H / 2, False)
deflection_bm = results.y[int(0.519 * L)]
deflection_formula = 0.01304 * P * L**3 / (E * Ix)
reldiff = abs((deflection_bm - deflection_formula) / deflection_formula)
assert reldiff < 0.005
def test_supported_distributed(): # {{{1
"""Ends supported beam with distributed load"""
results = bm.solve(L, (0, L), bm.DistLoad(force=P, start=0, end=L),
np.ones(L + 1) * E * Ix,
np.ones(L + 1) * G * A,
np.ones(L + 1) * H / 2, -np.ones(L + 1) * H / 2, False)
deflection_bm = results.y[int(L / 2)]
deflection_formula = 5 * P * L**3 / (384 * E * Ix)
reldiff = abs((deflection_bm - deflection_formula) / deflection_formula)
assert reldiff < 0.005
def test_supported_central_pointload(): # {{{1
"""Ends supported beam with central point load"""
results = bm.solve(L, (0, L), bm.Load(force=P, pos=L / 2),
np.ones(L + 1) * E * Ix,
np.ones(L + 1) * G * A,
np.ones(L + 1) * H / 2, -np.ones(L + 1) * H / 2, False)
deflection_bm = results.y[int(L / 2)]
deflection_formula = P * L**3 / (48 * E * Ix)
reldiff = abs((deflection_bm - deflection_formula) / deflection_formula)
assert reldiff < 0.005
def test_clamped_distributed(): # {{{1
"""Clamped beam with distributed load"""
results = bm.solve(L, None, bm.DistLoad(force=P, start=0, end=L),
np.ones(L + 1) * E * Ix,
np.ones(L + 1) * G * A,
np.ones(L + 1) * H / 2, -np.ones(L + 1) * H / 2, False)
deflection_bm = results.y[L]
deflection_formula = P * L**3 / (8 * E * Ix)
reldiff = abs((deflection_bm - deflection_formula) / deflection_formula)
assert reldiff < 0.005
def test_clamped_moment_end():
"""Begin clamped, moment load at end."""
M = 500 * 1000
results = bm.solve(L, None, bm.MomentLoad(M, pos=L),
np.ones(L + 1) * E * Ix,
np.ones(L + 1) * G * A,
np.ones(L + 1) * H / 2, -np.ones(L + 1) * H / 2, False)
deflection_bm = results.y[L]
deflection_formula = M * L**2 / (2 * E * Ix)
reldiff = abs((deflection_bm - deflection_formula) / deflection_formula)
assert reldiff < 0.005
def test_supported_moment_begin():
"""Ends supported beam with moment load at begin."""
M = 500 * 1000
x = 422
results = bm.solve(L, (0, L), bm.MomentLoad(M, 0),
np.ones(L + 1) * E * Ix,
np.ones(L + 1) * G * A,
np.ones(L + 1) * H / 2, -np.ones(L + 1) * H / 2, False)
deflection_bm = results.y[x]
deflection_formula = 0.0642 * M * L**2 / (E * Ix)
reldiff = abs((deflection_bm - deflection_formula) / deflection_formula)
assert reldiff < 0.005
def test_supported_moment_both():
"""Ends supported beam with moment load at both ends."""
M = 500 * 1000 / 2
results = bm.solve(
L, (0, L),
[bm.MomentLoad(M, 0), bm.MomentLoad(-M, L)],
np.ones(L + 1) * E * Ix,
np.ones(L + 1) * G * A,
np.ones(L + 1) * H / 2, -np.ones(L + 1) * H / 2, False)
deflection_bm = results.y[int(L / 2)]
deflection_formula = 6 * M * L**2 / (48 * E * Ix)
reldiff = abs((deflection_bm - deflection_formula) / deflection_formula)
assert reldiff < 0.005
def test_supported_pointloads(): # {{{1
"""Ends supported beam with three equidistant point loads"""
results = bm.solve(L, (0, L), [
bm.Load(force=P, pos=L / 4),
bm.Load(force=P, pos=L / 2),
bm.Load(force=P, pos=3 * L / 4)
],
np.ones(L + 1) * E * Ix,
np.ones(L + 1) * G * A,
np.ones(L + 1) * H / 2, -np.ones(L + 1) * H / 2, False)
deflection_bm = results.y[int(L / 2)]
deflection_formula = 19 * P * L**3 / (384 * E * Ix)
reldiff = abs((deflection_bm - deflection_formula) / deflection_formula)
assert reldiff < 0.005
