pdict["mu"] = c_raw
pdict["mubar"] = PolyLine(
[0, end_damp, end_damp, 1 - end_damp, 1 - end_damp, 1], [
c_crit / c_raw, c_crit / c_raw, 1, 1, c_crit / c_raw,
c_crit / c_raw
])
pdict["tvals"] = np.linspace(tmax * xeval[0], tmax * xeval[1], nt)
pdict["moving_loads_v_norm"] = [
v_raw * np.sqrt(pdict["rho"] / pdict["E"])
]
pdict["file_stem"] = prefix + "DAF_alp{:5.3f}_bet{:5.3f}_n{:d}".format(
alpha, beta, nterms)
a = SpecBeam(**pdict)
a.runme()
# jjj=np.searchsorted(alphas, 0.7)
# if i==0 and j==jjj:
# a.animateme()
w_now = np.max(a.defl[iwindow[0]:iwindow[1], :])
if j == 0:
if numerical_DAF:
w_0 = w_now
else:
lam = (pdict['k1'] / (4 * pdict['E'] * pdict['I']))**0.25
Q = pdict["moving_loads_Fz_norm"][0][0] * pdict['E'] * pdict[
'A']
w_0 = Q * lam / (2 * pdict['k1'])
def test_SpecBeam_const_mat_midpoint_defl_runme_analytical_200():
"""Test SpecBeam for constant mat: close to Ding et al Figure 8, displacement vs time at
beam midpoint (using the runme method) but with k3=0"""
start_time0 = time.time()
ftime = datetime.datetime.fromtimestamp(start_time0).strftime('%Y-%m-%d %H%M%S')
# expected values are digitised from Ding et al 2012.
expected_50terms_t = np.array(
[ 3.511, 3.553, 3.576, 3.605, 3.621, 3.637, 3.651, 3.661,
3.676, 3.693, 3.701, 3.717, 3.733, 3.743, 3.761, 3.777,
3.79 , 3.804, 3.822, 3.833, 3.848, 3.862, 3.877, 3.899,
3.919, 3.94 , 3.956, 3.97 , 3.978, 3.99 , 4.001, 4.014,
4.025, 4.041, 4.052, 4.064, 4.076, 4.086, 4.094, 4.104,
4.112, 4.123, 4.134, 4.146, 4.159, 4.172, 4.18 , 4.192,
4.212, 4.221, 4.234, 4.255, 4.273, 4.292, 4.324, 4.357,
4.373, 4.399, 4.418, 4.445])
#old values for k3~=0
# expected_50terms_displacement = np.array(
# [ -1.30900000e-04, 8.85900000e-05, 2.63900000e-04,
# 3.30200000e-04, 3.30500000e-04, 2.87100000e-04,
# 2.00000000e-04, 9.09500000e-05, -8.36000000e-05,
# -3.01800000e-04, -4.32800000e-04, -6.07300000e-04,
# -7.59900000e-04, -8.90900000e-04, -9.99800000e-04,
# -1.02100000e-03, -9.99100000e-04, -8.67700000e-04,
# -5.61300000e-04, -2.11300000e-04, 2.04300000e-04,
# 7.29200000e-04, 1.42900000e-03, 2.41300000e-03,
# 3.46300000e-03, 4.29400000e-03, 5.08100000e-03,
# 5.62800000e-03, 5.86800000e-03, 6.19600000e-03,
# 6.39300000e-03, 6.52500000e-03, 6.59100000e-03,
# 6.48200000e-03, 6.32900000e-03, 6.02300000e-03,
# 5.69600000e-03, 5.45500000e-03, 5.06200000e-03,
# 4.75600000e-03, 4.40700000e-03, 3.90400000e-03,
# 3.35800000e-03, 2.87800000e-03, 2.35300000e-03,
# 1.82900000e-03, 1.52300000e-03, 9.98700000e-04,
# 5.18300000e-04, 2.12500000e-04, -4.95200000e-05,
# -2.67600000e-04, -3.76500000e-04, -3.76100000e-04,
# -2.00600000e-04, 1.87300000e-05, 1.06500000e-04,
# 1.94500000e-04, 1.94900000e-04, 1.30000000e-04])
expected_50terms_displacement = np.array(
[ -1.74400116e-05, 2.56595529e-04, 3.64963938e-04,
3.96163257e-04, 3.52239419e-04, 2.55908617e-04,
1.36296573e-04, 3.12193756e-05, -1.48035583e-04,
-3.73050108e-04, -4.80427236e-04, -6.84847774e-04,
-8.61705766e-04, -9.44268811e-04, -1.02333177e-03,
-1.00753661e-03, -9.18192599e-04, -7.32771117e-04,
-3.72382730e-04, -7.79760498e-05, 4.06998900e-04,
9.37679667e-04, 1.57072235e-03, 2.58323632e-03,
3.52928135e-03, 4.47726082e-03, 5.12406706e-03,
5.61329890e-03, 5.84231170e-03, 6.13309619e-03,
6.32505191e-03, 6.46203546e-03, 6.49032925e-03,
6.39329339e-03, 6.23960924e-03, 5.99242067e-03,
5.67177967e-03, 5.35598822e-03, 5.07919623e-03,
4.69552191e-03, 4.37030991e-03, 3.90678952e-03,
3.43034780e-03, 2.90774639e-03, 2.35231514e-03,
1.82145021e-03, 1.51724930e-03, 1.09014092e-03,
4.86434682e-04, 2.61200867e-04, -5.02752907e-06,
-2.99906282e-04, -4.26188536e-04, -4.46910518e-04,
-3.09328219e-04, -6.53887601e-05, 4.77786782e-05,
1.84483472e-04, 2.30390682e-04, 2.18090273e-04])
expected_200terms_t = np.array(
[ 3.503, 3.519, 3.539, 3.556, 3.576, 3.595, 3.613, 3.632,
3.651, 3.667, 3.69 , 3.708, 3.727, 3.746, 3.766, 3.782,
3.801, 3.822, 3.84 , 3.856, 3.878, 3.896, 3.915, 3.933,
3.951, 3.97 , 3.99 , 4.009, 4.027, 4.046, 4.067, 4.085,
4.102, 4.122, 4.141, 4.159, 4.178, 4.197, 4.217, 4.234,
4.252, 4.273, 4.291, 4.31 , 4.329, 4.347, 4.368, 4.386,
4.405, 4.423, 4.442, 4.46 , 4.479, 4.495])
expected_200terms_displacement = np.array(
[ 7.04000000e-08, 2.22800000e-05, 2.27000000e-05,
1.23200000e-06, 2.35100000e-05, 2.39300000e-05,
2.46400000e-06, -1.89700000e-05, -6.22700000e-05,
-1.27500000e-04, -1.70700000e-04, -2.57800000e-04,
-3.44800000e-04, -4.53600000e-04, -5.40600000e-04,
-5.84000000e-04, -5.61700000e-04, -4.73800000e-04,
-2.54900000e-04, 1.17100000e-04, 6.85900000e-04,
1.51700000e-03, 2.50100000e-03, 3.70300000e-03,
5.01500000e-03, 6.26200000e-03, 7.20200000e-03,
7.61800000e-03, 7.39900000e-03, 6.74400000e-03,
5.91400000e-03, 5.01800000e-03, 4.10100000e-03,
3.22700000e-03, 2.50600000e-03, 1.85000000e-03,
1.32600000e-03, 9.11400000e-04, 5.84000000e-04,
3.00200000e-04, 1.47600000e-04, 3.87500000e-05,
-4.82900000e-05, -1.13400000e-04, -1.13000000e-04,
-1.34500000e-04, -1.34000000e-04, -1.33600000e-04,
-1.11400000e-04, -6.72600000e-05, -6.68400000e-05,
-6.64500000e-05, -4.41700000e-05, -4.38200000e-05])
t = np.linspace(0, 4.5, 400)
#see Dingetal2012 Table 2 for material properties
pdict = OrderedDict(
E = 6.998*1e9, #Pa
rho = 2373, #kg/m3
L = 160, #m
#v_norm=0.01165,
kf=5.41e-4,
#Fz_norm=1.013e-4,
mu_norm=39.263,
k1_norm=97.552,
# k3_norm=2.497e6,
nterms=200,
BC="SS",
nquad=20,
k1bar=PolyLine([0,0.5],[0.5,1],[1,1],[1,1]),
# k1bar=PolyLine([0,0.5],[0.5,1],[2,1],[2,1]),
moving_loads_x_norm=[[0]],
moving_loads_Fz_norm=[[1.013e-4]],
moving_loads_v_norm=[0.01165,],
tvals=t,
# tvals=np.array([4.0]),
xvals_norm=np.array([0.5]),
use_analytical=True,
implementation="vectorized",
# implementation="fortran",
force_calc=True,
)
a = SpecBeam(**pdict)
a.runme()
# a.calulate_qk(t=t)
#
# yall = a.wofx(x_norm=0.5, normalise_w=False)
ycompare = np.interp(expected_200terms_t, t, a.defl[0,:])
# print(repr(ycompare))
print("n=", pdict['nterms'])
end_time0 = time.time()
elapsed_time = (end_time0 - start_time0); print("Total run time={}".format(str(timedelta(seconds=elapsed_time))))
if DEBUG:
title ='SpecBeam, const mat prop vs Ding et al (2012) \nFigure 8 Displacement at Midpoint of beam but with k3=0'
print(title)
print(' '.join(['{:>9s}']*4).format('t', 'expect', 'calc', 'diff'))
for i, j, k in zip(expected_200terms_t, expected_200terms_displacement, ycompare):
print(' '.join(['{:9.4f}']*4).format(i, j, k, j-k))
print()
fig = plt.figure(figsize=(10,6))
ax = fig.add_subplot("111")
ax.set_xlabel("time, s")
ax.set_ylabel("w, m")
ax.set_xlim(3.5, 4.5)
ax.set_title(title)
ax.plot(expected_50terms_t, expected_50terms_displacement,
label="expect n=50", color='green', marker='o', ls='-')
ax.plot(expected_200terms_t, expected_200terms_displacement,
label="expect n=200", color='black', marker=None, ls='-')
ax.plot(t, a.defl, label="calc n=200")
ax.plot(expected_200terms_t, ycompare, label="calc, n=200 (compare)",
color='red', marker='s', ms=4, ls=':')
leg = ax.legend(loc='upper left')
leg.draggable()
plt.show()
assert_allclose(expected_200terms_displacement, ycompare, atol=2.4e-4)
def test_SpecBeam_const_mat_deflection_shape_stationary_load():
"""static point load at beam centre, analytical vs numerical
properties from moving load case (but with k3=0) in Figure 7 of ding et al"""
# expected values are digitised from Ding et al 2012.
expected_50terms_x = np.array(
[ 70.68 , 71.275, 71.785, 72.189, 72.529, 72.848, 73.209,
73.677, 74.06 , 74.378, 74.74 , 75.122, 75.505, 75.781,
76.079, 76.312, 76.525, 76.716, 76.95 , 77.12 , 77.418,
77.715, 77.907, 78.204, 78.459, 78.778, 79.224, 79.522,
79.883, 80.181, 80.436, 80.606, 80.776, 81.01 , 81.137,
81.307, 81.477, 81.626, 81.902, 82.179, 82.497, 82.774,
82.986, 83.263, 83.539, 84.028, 84.368, 84.623, 84.878,
85.239, 85.728, 86.153, 86.684, 87.386, 87.853, 88.363,
88.81 , 89.341, 89.788])
# this was generated with use_analytical=False
expected_50terms_displacement = np.array(
[ 1.65264432e-04, 2.63028987e-04, 2.72285077e-04,
2.14305202e-04, 1.15107602e-04, -2.68417019e-05,
-1.91982014e-04, -4.49035633e-04, -6.36376878e-04,
-7.29821557e-04, -8.36195689e-04, -7.26860083e-04,
-5.95623829e-04, -3.27010071e-04, 3.04509524e-05,
3.09942290e-04, 6.76583319e-04, 1.05404663e-03,
1.51648858e-03, 1.85245069e-03, 2.52742529e-03,
3.22449986e-03, 3.67513393e-03, 4.31941644e-03,
4.85502315e-03, 5.52505664e-03, 6.09193410e-03,
6.46152111e-03, 6.55576573e-03, 6.55576573e-03,
6.51361055e-03, 6.30277232e-03, 6.09193410e-03,
5.80172148e-03, 5.64421292e-03, 5.34652107e-03,
4.98944993e-03, 4.67648758e-03, 4.09677209e-03,
3.47328742e-03, 2.72692475e-03, 2.07679122e-03,
1.64296844e-03, 1.09554783e-03, 5.50103467e-04,
-9.78991467e-05, -5.05740583e-04, -6.39483464e-04,
-7.26860083e-04, -8.42366564e-04, -6.98673331e-04,
-5.42409810e-04, -2.50752820e-04, 7.72841199e-05,
2.20332813e-04, 2.93525229e-04, 2.50445556e-04,
1.59399796e-04, 3.45668416e-05])
#no longer correct:
expected_200terms_x = np.array(
[ 70.064, 70.404, 70.723, 71.02 , 71.36 , 71.679, 71.955,
72.317, 72.614, 72.976, 73.273, 73.571, 73.911, 74.23 ,
74.527, 74.867, 75.165, 75.505, 75.866, 76.164, 76.483,
76.801, 77.12 , 77.418, 77.779, 78.098, 78.438, 78.693,
79.033, 79.352, 79.671, 79.989, 80.308, 80.648, 80.967,
81.286, 81.583, 81.924, 82.264, 82.582, 82.88 , 83.199,
83.539, 83.815, 84.134, 84.495, 84.793, 85.112, 85.43 ,
85.749, 86.047, 86.429, 86.727, 87.046, 87.365, 87.683,
87.981, 88.342, 88.64 , 88.959, 89.277, 89.617, 89.958])
expected_200terms_displacement = np.array(
[ -2.90800000e-05, -2.90800000e-05, -6.13900000e-05,
-7.75400000e-05, -7.75400000e-05, -1.09900000e-04,
-1.26000000e-04, -1.26000000e-04, -1.26000000e-04,
-1.42200000e-04, -1.09900000e-04, -1.09900000e-04,
-9.37000000e-05, -2.90800000e-05, 3.55400000e-05,
1.64800000e-04, 2.94000000e-04, 4.55600000e-04,
7.30200000e-04, 1.02100000e-03, 1.40900000e-03,
1.86100000e-03, 2.37800000e-03, 2.99200000e-03,
3.68700000e-03, 4.43000000e-03, 5.22100000e-03,
5.96400000e-03, 6.67500000e-03, 7.27300000e-03,
7.58000000e-03, 7.48300000e-03, 6.95000000e-03,
6.06100000e-03, 4.99500000e-03, 3.88000000e-03,
2.83000000e-03, 1.94200000e-03, 1.16600000e-03,
5.20200000e-04, 5.17000000e-05, -2.55300000e-04,
-4.33000000e-04, -5.46000000e-04, -5.78400000e-04,
-5.62200000e-04, -4.81400000e-04, -4.33000000e-04,
-3.19900000e-04, -2.39100000e-04, -1.74500000e-04,
-1.26000000e-04, -4.52300000e-05, -1.29200000e-05,
1.93900000e-05, 1.93900000e-05, 3.55400000e-05,
6.78500000e-05, 3.55400000e-05, 5.17000000e-05,
3.55400000e-05, 1.93900000e-05, 1.93900000e-05])
t = np.linspace(0, 160/2/20, 400)
xvals = np.linspace(0, 160, 200)
#see Dingetal2012 Table 2 for material properties
pdict = OrderedDict(
E = 6.998*1e9, #Pa
rho = 2373, #kg/m3
L = 160, #m
#v_norm=0.01165,
kf=5.41e-4,
#Fz_norm=1.013e-4,
mu_norm=39.263,
k1_norm=97.552,
#k3_norm=2.497e6,
nterms=50,
BC="SS",
nquad=20,
# moving_loads_x_norm=[[0]],
# moving_loads_Fz_norm=[[1.013e-4]],
# moving_loads_v_norm=[0.01165,],
# stationary_loads_x=None,
# stationary_loads_vs_t=None,
# stationary_loads_omega_phase=None,
stationary_loads_x_norm=[0.5],
stationary_loads_vs_t_norm=[PolyLine([0,t[-1]/160*np.sqrt(6.998*1e9/2373.)],[1.013e-4,1.013e-4])],
#self.L * np.sqrt(self.E / self.rho)
# stationary_loads_omega_phase_norm=None,
tvals=t,
xvals=xvals,
use_analytical=False,
implementation="vectorized",
# implementation="fortran",
)
a = SpecBeam(**pdict)
a.runme()
# a = SpecBeam(**pdict)
#
# a.calulate_qk(t=t)
yall = a.defl[:,-1]#a.wofx(x=xvals, tslice=slice(-1, None, None), normalise_w=False)[:,0]
ycompare = np.interp(expected_50terms_x, xvals, yall)
print(repr(ycompare))
if DEBUG:
title ='SpecBeam, stationary load, analytical vs numerical, deflection shape for point load applied at midpoint\n prop from moving load Figure 7 of Ding et al (2012)'
print(title)
print(' '.join(['{:>9s}']*4).format('t', 'expect', 'calc', 'diff'))
for i, j, k in zip(expected_50terms_x, expected_50terms_displacement, ycompare):
print(' '.join(['{:9.4f}']*4).format(i, j, k, j-k))
print()
fig = plt.figure(figsize=(10,6))
ax = fig.add_subplot("111")
ax.set_xlabel("x, m")
ax.set_ylabel("w, m")
ax.set_xlim(70, 90)
ax.set_title(title)
ax.plot(expected_50terms_x, expected_50terms_displacement,
label="expect n=50", color='green', marker='o', ls='-')
ax.plot(expected_200terms_x, expected_200terms_displacement,
label="expect n=200", color='black', marker=None, ls='-')
ax.plot(xvals, yall, label="calc n=50")
ax.plot(expected_50terms_x, ycompare, label="calc, n=50 (compare)",
color='red', marker='s', ms=4, ls=':')
ax.grid()
leg = ax.legend(loc='upper left')
leg.draggable()
plt.show()
assert_allclose(expected_50terms_displacement, ycompare, atol=2.4e-4)
def test_SpecBeam_const_mat_midpoint_defl_runme():
"""Test SpecBeam for constant mat: Figure 8, displacement vs time at
beam midpoint (using the runme method)"""
# expected values are digitised from Ding et al 2012.
expected_50terms_t = np.array(
[ 3.511, 3.553, 3.576, 3.605, 3.621, 3.637, 3.651, 3.661,
3.676, 3.693, 3.701, 3.717, 3.733, 3.743, 3.761, 3.777,
3.79 , 3.804, 3.822, 3.833, 3.848, 3.862, 3.877, 3.899,
3.919, 3.94 , 3.956, 3.97 , 3.978, 3.99 , 4.001, 4.014,
4.025, 4.041, 4.052, 4.064, 4.076, 4.086, 4.094, 4.104,
4.112, 4.123, 4.134, 4.146, 4.159, 4.172, 4.18 , 4.192,
4.212, 4.221, 4.234, 4.255, 4.273, 4.292, 4.324, 4.357,
4.373, 4.399, 4.418, 4.445])
expected_50terms_displacement = np.array(
[ -1.30900000e-04, 8.85900000e-05, 2.63900000e-04,
3.30200000e-04, 3.30500000e-04, 2.87100000e-04,
2.00000000e-04, 9.09500000e-05, -8.36000000e-05,
-3.01800000e-04, -4.32800000e-04, -6.07300000e-04,
-7.59900000e-04, -8.90900000e-04, -9.99800000e-04,
-1.02100000e-03, -9.99100000e-04, -8.67700000e-04,
-5.61300000e-04, -2.11300000e-04, 2.04300000e-04,
7.29200000e-04, 1.42900000e-03, 2.41300000e-03,
3.46300000e-03, 4.29400000e-03, 5.08100000e-03,
5.62800000e-03, 5.86800000e-03, 6.19600000e-03,
6.39300000e-03, 6.52500000e-03, 6.59100000e-03,
6.48200000e-03, 6.32900000e-03, 6.02300000e-03,
5.69600000e-03, 5.45500000e-03, 5.06200000e-03,
4.75600000e-03, 4.40700000e-03, 3.90400000e-03,
3.35800000e-03, 2.87800000e-03, 2.35300000e-03,
1.82900000e-03, 1.52300000e-03, 9.98700000e-04,
5.18300000e-04, 2.12500000e-04, -4.95200000e-05,
-2.67600000e-04, -3.76500000e-04, -3.76100000e-04,
-2.00600000e-04, 1.87300000e-05, 1.06500000e-04,
1.94500000e-04, 1.94900000e-04, 1.30000000e-04])
expected_200terms_t = np.array(
[ 3.503, 3.519, 3.539, 3.556, 3.576, 3.595, 3.613, 3.632,
3.651, 3.667, 3.69 , 3.708, 3.727, 3.746, 3.766, 3.782,
3.801, 3.822, 3.84 , 3.856, 3.878, 3.896, 3.915, 3.933,
3.951, 3.97 , 3.99 , 4.009, 4.027, 4.046, 4.067, 4.085,
4.102, 4.122, 4.141, 4.159, 4.178, 4.197, 4.217, 4.234,
4.252, 4.273, 4.291, 4.31 , 4.329, 4.347, 4.368, 4.386,
4.405, 4.423, 4.442, 4.46 , 4.479, 4.495])
expected_200terms_displacement = np.array(
[ 7.04000000e-08, 2.22800000e-05, 2.27000000e-05,
1.23200000e-06, 2.35100000e-05, 2.39300000e-05,
2.46400000e-06, -1.89700000e-05, -6.22700000e-05,
-1.27500000e-04, -1.70700000e-04, -2.57800000e-04,
-3.44800000e-04, -4.53600000e-04, -5.40600000e-04,
-5.84000000e-04, -5.61700000e-04, -4.73800000e-04,
-2.54900000e-04, 1.17100000e-04, 6.85900000e-04,
1.51700000e-03, 2.50100000e-03, 3.70300000e-03,
5.01500000e-03, 6.26200000e-03, 7.20200000e-03,
7.61800000e-03, 7.39900000e-03, 6.74400000e-03,
5.91400000e-03, 5.01800000e-03, 4.10100000e-03,
3.22700000e-03, 2.50600000e-03, 1.85000000e-03,
1.32600000e-03, 9.11400000e-04, 5.84000000e-04,
3.00200000e-04, 1.47600000e-04, 3.87500000e-05,
-4.82900000e-05, -1.13400000e-04, -1.13000000e-04,
-1.34500000e-04, -1.34000000e-04, -1.33600000e-04,
-1.11400000e-04, -6.72600000e-05, -6.68400000e-05,
-6.64500000e-05, -4.41700000e-05, -4.38200000e-05])
t = np.linspace(0, 4.5, 400)
#see Dingetal2012 Table 2 for material properties
pdict = OrderedDict(
E = 6.998*1e9, #Pa
rho = 2373, #kg/m3
L = 160, #m
#v_norm=0.01165,
kf=5.41e-4,
#Fz_norm=1.013e-4,
mu_norm=39.263,
k1_norm=97.552,
k3_norm=2.497e6,
nterms=50,
BC="SS",
nquad=20,
k1bar=PolyLine([0,0.5],[0.5,1],[1,1],[1,1]),
moving_loads_x_norm=[[0]],
moving_loads_Fz_norm=[[1.013e-4]],
moving_loads_v_norm=[0.01165,],
tvals=t,
xvals_norm=0.5)
a = SpecBeam(**pdict)
a.runme()
# a.calulate_qk(t=t)
#
# yall = a.wofx(x_norm=0.5, normalise_w=False)
ycompare = np.interp(expected_50terms_t, t, a.defl)
if DEBUG:
title ='SpecBeam, const mat prop vs Ding et al (2012) \nFigure 8 Displacement at Midpoint of beam'
print(title)
print(' '.join(['{:>9s}']*4).format('t', 'expect', 'calc', 'diff'))
for i, j, k in zip(expected_50terms_t, expected_50terms_displacement, ycompare):
print(' '.join(['{:9.4f}']*4).format(i, j, k, j-k))
print()
fig = plt.figure(figsize=(10,6))
ax = fig.add_subplot("111")
ax.set_xlabel("time, s")
ax.set_ylabel("w, m")
ax.set_xlim(3.5, 4.5)
ax.set_title(title)
ax.plot(expected_50terms_t, expected_50terms_displacement,
label="expect n=50", color='green', marker='o', ls='-')
ax.plot(expected_200terms_t, expected_200terms_displacement,
label="expect n=200", color='black', marker=None, ls='-')
ax.plot(t, a.defl, label="calc n=50")
ax.plot(expected_50terms_t, ycompare, label="calc, n=50 (compare)",
color='red', marker='s', ms=4, ls=':')
leg = ax.legend(loc='upper left')
leg.draggable()
plt.show()
assert_allclose(expected_50terms_displacement, ycompare, atol=2.4e-4)
def test_SpecBeam_const_mat_deflection_shape_runme():
"""Test SpecBeam for constant mat: Figure 7, deflection with load at midpoint"""
# expected values are digitised from Ding et al 2012.
expected_50terms_x = np.array(
[ 70.68 , 71.275, 71.785, 72.189, 72.529, 72.848, 73.209,
73.677, 74.06 , 74.378, 74.74 , 75.122, 75.505, 75.781,
76.079, 76.312, 76.525, 76.716, 76.95 , 77.12 , 77.418,
77.715, 77.907, 78.204, 78.459, 78.778, 79.224, 79.522,
79.883, 80.181, 80.436, 80.606, 80.776, 81.01 , 81.137,
81.307, 81.477, 81.626, 81.902, 82.179, 82.497, 82.774,
82.986, 83.263, 83.539, 84.028, 84.368, 84.623, 84.878,
85.239, 85.728, 86.153, 86.684, 87.386, 87.853, 88.363,
88.81 , 89.341, 89.788])
expected_50terms_displacement = np.array(
[ 3.23100000e-06, 1.48600000e-04, 1.80900000e-04,
1.64800000e-04, 1.00200000e-04, 1.93900000e-05,
-1.09900000e-04, -2.55300000e-04, -3.52200000e-04,
-3.68300000e-04, -3.19900000e-04, -1.26000000e-04,
1.64800000e-04, 5.04000000e-04, 9.24100000e-04,
1.27900000e-03, 1.66700000e-03, 2.10300000e-03,
2.58800000e-03, 3.00800000e-03, 3.59000000e-03,
4.17100000e-03, 4.70400000e-03, 5.27000000e-03,
5.70600000e-03, 6.17400000e-03, 6.49800000e-03,
6.57800000e-03, 6.44900000e-03, 6.15800000e-03,
5.91600000e-03, 5.64100000e-03, 5.30200000e-03,
4.88200000e-03, 4.51100000e-03, 4.17100000e-03,
3.81600000e-03, 3.38000000e-03, 2.79800000e-03,
2.05500000e-03, 1.42500000e-03, 7.78700000e-04,
3.26300000e-04, -9.37000000e-05, -5.29900000e-04,
-9.01500000e-04, -9.98400000e-04, -1.01500000e-03,
-9.66100000e-04, -8.04500000e-04, -5.29900000e-04,
-2.22900000e-04, 8.40100000e-05, 3.42500000e-04,
3.74800000e-04, 3.10200000e-04, 1.80900000e-04,
1.93900000e-05, -1.26000000e-04])
expected_200terms_x = np.array(
[ 70.064, 70.404, 70.723, 71.02 , 71.36 , 71.679, 71.955,
72.317, 72.614, 72.976, 73.273, 73.571, 73.911, 74.23 ,
74.527, 74.867, 75.165, 75.505, 75.866, 76.164, 76.483,
76.801, 77.12 , 77.418, 77.779, 78.098, 78.438, 78.693,
79.033, 79.352, 79.671, 79.989, 80.308, 80.648, 80.967,
81.286, 81.583, 81.924, 82.264, 82.582, 82.88 , 83.199,
83.539, 83.815, 84.134, 84.495, 84.793, 85.112, 85.43 ,
85.749, 86.047, 86.429, 86.727, 87.046, 87.365, 87.683,
87.981, 88.342, 88.64 , 88.959, 89.277, 89.617, 89.958])
expected_200terms_displacement = np.array(
[ -2.90800000e-05, -2.90800000e-05, -6.13900000e-05,
-7.75400000e-05, -7.75400000e-05, -1.09900000e-04,
-1.26000000e-04, -1.26000000e-04, -1.26000000e-04,
-1.42200000e-04, -1.09900000e-04, -1.09900000e-04,
-9.37000000e-05, -2.90800000e-05, 3.55400000e-05,
1.64800000e-04, 2.94000000e-04, 4.55600000e-04,
7.30200000e-04, 1.02100000e-03, 1.40900000e-03,
1.86100000e-03, 2.37800000e-03, 2.99200000e-03,
3.68700000e-03, 4.43000000e-03, 5.22100000e-03,
5.96400000e-03, 6.67500000e-03, 7.27300000e-03,
7.58000000e-03, 7.48300000e-03, 6.95000000e-03,
6.06100000e-03, 4.99500000e-03, 3.88000000e-03,
2.83000000e-03, 1.94200000e-03, 1.16600000e-03,
5.20200000e-04, 5.17000000e-05, -2.55300000e-04,
-4.33000000e-04, -5.46000000e-04, -5.78400000e-04,
-5.62200000e-04, -4.81400000e-04, -4.33000000e-04,
-3.19900000e-04, -2.39100000e-04, -1.74500000e-04,
-1.26000000e-04, -4.52300000e-05, -1.29200000e-05,
1.93900000e-05, 1.93900000e-05, 3.55400000e-05,
6.78500000e-05, 3.55400000e-05, 5.17000000e-05,
3.55400000e-05, 1.93900000e-05, 1.93900000e-05])
t = np.linspace(0, 160/2/20, 400)
xvals = np.linspace(0, 160, 200)
#see Dingetal2012 Table 2 for material properties
pdict = OrderedDict(
E = 6.998*1e9, #Pa
rho = 2373, #kg/m3
L = 160, #m
#v_norm=0.01165,
kf=5.41e-4,
#Fz_norm=1.013e-4,
mu_norm=39.263,
k1_norm=97.552,
k3_norm=2.497e6,
nterms=50,
BC="SS",
nquad=20,
moving_loads_x_norm=[[0]],
moving_loads_Fz_norm=[[1.013e-4]],
moving_loads_v_norm=[0.01165,],
tvals=t,
xvals=xvals)
a = SpecBeam(**pdict)
a.runme()
# a = SpecBeam(**pdict)
#
# a.calulate_qk(t=t)
yall = a.defl[:,-1]#a.wofx(x=xvals, tslice=slice(-1, None, None), normalise_w=False)[:,0]
ycompare = np.interp(expected_50terms_x, xvals, yall)
if DEBUG:
title ='SpecBeam, const mat prop vs Ding et al (2012) \nFigure 7 deflection when load at Midpoint of beam'
print(title)
print(' '.join(['{:>9s}']*4).format('t', 'expect', 'calc', 'diff'))
for i, j, k in zip(expected_50terms_x, expected_50terms_displacement, ycompare):
print(' '.join(['{:9.4f}']*4).format(i, j, k, j-k))
print()
fig = plt.figure(figsize=(10,6))
ax = fig.add_subplot("111")
ax.set_xlabel("x, m")
ax.set_ylabel("w, m")
ax.set_xlim(70, 90)
ax.set_title(title)
ax.plot(expected_50terms_x, expected_50terms_displacement,
label="expect n=50", color='green', marker='o', ls='-')
ax.plot(expected_200terms_x, expected_200terms_displacement,
label="expect n=200", color='black', marker=None, ls='-')
ax.plot(xvals, yall, label="calc n=50")
ax.plot(expected_50terms_x, ycompare, label="calc, n=50 (compare)",
color='red', marker='s', ms=4, ls=':')
leg = ax.legend(loc='upper left')
leg.draggable()
plt.show()
assert_allclose(expected_50terms_displacement, ycompare, atol=2.4e-4)
else:
if beta==0:
pdict["mu"] = c_crit
pdict["mubar"]=PolyLine([0,end_damp,end_damp,1-end_damp,1-end_damp,1],
[1,1,0,0,1,1])
else:
pdict["mu"]= c_raw
pdict["mubar"]=PolyLine([0,end_damp,end_damp,1-end_damp,1-end_damp,1],
[c_crit/c_raw,c_crit/c_raw,1,1,c_crit/c_raw,c_crit/c_raw])
pdict["tvals"] = np.linspace(tmax*xeval[0],tmax*xeval[1],nt)
pdict["moving_loads_v_norm"]=[v_raw*np.sqrt(pdict["rho"]/pdict["E"])]
pdict["file_stem"] = prefix + "DAF_alp{:5.3f}_bet{:5.3f}_n{:d}".format(alpha,beta,nterms)
a = SpecBeam(**pdict)
a.runme()
# jjj=np.searchsorted(alphas, 0.7)
# if i==0 and j==jjj:
# a.animateme()
w_now = np.max(a.defl[iwindow[0]:iwindow[1],:])
if j==0:
if numerical_DAF:
w_0 = w_now
else:
lam = (pdict['k1'] /(4*pdict['E']*pdict['I']))**0.25
Q = pdict["moving_loads_Fz_norm"][0][0]* pdict['E'] * pdict['A']
w_0 = Q * lam / (2*pdict['k1'])
print("analytical")
def test_SpecBeam_const_mat_deflection_shape_stationary_load():
"""static point load at beam centre, analytical vs numerical
properties from moving load case (but with k3=0) in Figure 7 of ding et al"""
# expected values are digitised from Ding et al 2012.
expected_50terms_x = np.array([
70.68, 71.275, 71.785, 72.189, 72.529, 72.848, 73.209, 73.677, 74.06,
74.378, 74.74, 75.122, 75.505, 75.781, 76.079, 76.312, 76.525, 76.716,
76.95, 77.12, 77.418, 77.715, 77.907, 78.204, 78.459, 78.778, 79.224,
79.522, 79.883, 80.181, 80.436, 80.606, 80.776, 81.01, 81.137, 81.307,
81.477, 81.626, 81.902, 82.179, 82.497, 82.774, 82.986, 83.263, 83.539,
84.028, 84.368, 84.623, 84.878, 85.239, 85.728, 86.153, 86.684, 87.386,
87.853, 88.363, 88.81, 89.341, 89.788
])
# this was generated with use_analytical=False
expected_50terms_displacement = np.array([
1.65264432e-04, 2.63028987e-04, 2.72285077e-04, 2.14305202e-04,
1.15107602e-04, -2.68417019e-05, -1.91982014e-04, -4.49035633e-04,
-6.36376878e-04, -7.29821557e-04, -8.36195689e-04, -7.26860083e-04,
-5.95623829e-04, -3.27010071e-04, 3.04509524e-05, 3.09942290e-04,
6.76583319e-04, 1.05404663e-03, 1.51648858e-03, 1.85245069e-03,
2.52742529e-03, 3.22449986e-03, 3.67513393e-03, 4.31941644e-03,
4.85502315e-03, 5.52505664e-03, 6.09193410e-03, 6.46152111e-03,
6.55576573e-03, 6.55576573e-03, 6.51361055e-03, 6.30277232e-03,
6.09193410e-03, 5.80172148e-03, 5.64421292e-03, 5.34652107e-03,
4.98944993e-03, 4.67648758e-03, 4.09677209e-03, 3.47328742e-03,
2.72692475e-03, 2.07679122e-03, 1.64296844e-03, 1.09554783e-03,
5.50103467e-04, -9.78991467e-05, -5.05740583e-04, -6.39483464e-04,
-7.26860083e-04, -8.42366564e-04, -6.98673331e-04, -5.42409810e-04,
-2.50752820e-04, 7.72841199e-05, 2.20332813e-04, 2.93525229e-04,
2.50445556e-04, 1.59399796e-04, 3.45668416e-05
])
#no longer correct:
expected_200terms_x = np.array([
70.064, 70.404, 70.723, 71.02, 71.36, 71.679, 71.955, 72.317, 72.614,
72.976, 73.273, 73.571, 73.911, 74.23, 74.527, 74.867, 75.165, 75.505,
75.866, 76.164, 76.483, 76.801, 77.12, 77.418, 77.779, 78.098, 78.438,
78.693, 79.033, 79.352, 79.671, 79.989, 80.308, 80.648, 80.967, 81.286,
81.583, 81.924, 82.264, 82.582, 82.88, 83.199, 83.539, 83.815, 84.134,
84.495, 84.793, 85.112, 85.43, 85.749, 86.047, 86.429, 86.727, 87.046,
87.365, 87.683, 87.981, 88.342, 88.64, 88.959, 89.277, 89.617, 89.958
])
expected_200terms_displacement = np.array([
-2.90800000e-05, -2.90800000e-05, -6.13900000e-05, -7.75400000e-05,
-7.75400000e-05, -1.09900000e-04, -1.26000000e-04, -1.26000000e-04,
-1.26000000e-04, -1.42200000e-04, -1.09900000e-04, -1.09900000e-04,
-9.37000000e-05, -2.90800000e-05, 3.55400000e-05, 1.64800000e-04,
2.94000000e-04, 4.55600000e-04, 7.30200000e-04, 1.02100000e-03,
1.40900000e-03, 1.86100000e-03, 2.37800000e-03, 2.99200000e-03,
3.68700000e-03, 4.43000000e-03, 5.22100000e-03, 5.96400000e-03,
6.67500000e-03, 7.27300000e-03, 7.58000000e-03, 7.48300000e-03,
6.95000000e-03, 6.06100000e-03, 4.99500000e-03, 3.88000000e-03,
2.83000000e-03, 1.94200000e-03, 1.16600000e-03, 5.20200000e-04,
5.17000000e-05, -2.55300000e-04, -4.33000000e-04, -5.46000000e-04,
-5.78400000e-04, -5.62200000e-04, -4.81400000e-04, -4.33000000e-04,
-3.19900000e-04, -2.39100000e-04, -1.74500000e-04, -1.26000000e-04,
-4.52300000e-05, -1.29200000e-05, 1.93900000e-05, 1.93900000e-05,
3.55400000e-05, 6.78500000e-05, 3.55400000e-05, 5.17000000e-05,
3.55400000e-05, 1.93900000e-05, 1.93900000e-05
])
t = np.linspace(0, 160 / 2 / 20, 400)
xvals = np.linspace(0, 160, 200)
#see Dingetal2012 Table 2 for material properties
pdict = OrderedDict(
E=6.998 * 1e9, #Pa
rho=2373, #kg/m3
L=160, #m
#v_norm=0.01165,
kf=5.41e-4,
#Fz_norm=1.013e-4,
mu_norm=39.263,
k1_norm=97.552,
#k3_norm=2.497e6,
nterms=50,
BC="SS",
nquad=20,
# moving_loads_x_norm=[[0]],
# moving_loads_Fz_norm=[[1.013e-4]],
# moving_loads_v_norm=[0.01165,],
# stationary_loads_x=None,
# stationary_loads_vs_t=None,
# stationary_loads_omega_phase=None,
stationary_loads_x_norm=[0.5],
stationary_loads_vs_t_norm=[
PolyLine([0, t[-1] / 160 * np.sqrt(6.998 * 1e9 / 2373.)],
[1.013e-4, 1.013e-4])
],
#self.L * np.sqrt(self.E / self.rho)
# stationary_loads_omega_phase_norm=None,
tvals=t,
xvals=xvals,
use_analytical=False,
implementation="vectorized",
# implementation="fortran",
)
a = SpecBeam(**pdict)
a.runme()
# a = SpecBeam(**pdict)
#
# a.calulate_qk(t=t)
yall = a.defl[:,
-1] #a.wofx(x=xvals, tslice=slice(-1, None, None), normalise_w=False)[:,0]
ycompare = np.interp(expected_50terms_x, xvals, yall)
print(repr(ycompare))
if DEBUG:
title = 'SpecBeam, stationary load, analytical vs numerical, deflection shape for point load applied at midpoint\n prop from moving load Figure 7 of Ding et al (2012)'
print(title)
print(' '.join(['{:>9s}'] * 4).format('t', 'expect', 'calc', 'diff'))
for i, j, k in zip(expected_50terms_x, expected_50terms_displacement,
ycompare):
print(' '.join(['{:9.4f}'] * 4).format(i, j, k, j - k))
print()
fig = plt.figure(figsize=(10, 6))
ax = fig.add_subplot("111")
ax.set_xlabel("x, m")
ax.set_ylabel("w, m")
ax.set_xlim(70, 90)
ax.set_title(title)
ax.plot(expected_50terms_x,
expected_50terms_displacement,
label="expect n=50",
color='green',
marker='o',
ls='-')
ax.plot(expected_200terms_x,
expected_200terms_displacement,
label="expect n=200",
color='black',
marker=None,
ls='-')
ax.plot(xvals, yall, label="calc n=50")
ax.plot(expected_50terms_x,
ycompare,
label="calc, n=50 (compare)",
color='red',
marker='s',
ms=4,
ls=':')
ax.grid()
leg = ax.legend(loc='upper left')
leg.draggable()
plt.show()
assert_allclose(expected_50terms_displacement, ycompare, atol=2.4e-4)
def test_SpecBeam_const_mat_midpoint_defl_runme_analytical_200():
"""Test SpecBeam for constant mat: close to Ding et al Figure 8, displacement vs time at
beam midpoint (using the runme method) but with k3=0"""
start_time0 = time.time()
ftime = datetime.datetime.fromtimestamp(start_time0).strftime(
'%Y-%m-%d %H%M%S')
# expected values are digitised from Ding et al 2012.
expected_50terms_t = np.array([
3.511, 3.553, 3.576, 3.605, 3.621, 3.637, 3.651, 3.661, 3.676, 3.693,
3.701, 3.717, 3.733, 3.743, 3.761, 3.777, 3.79, 3.804, 3.822, 3.833,
3.848, 3.862, 3.877, 3.899, 3.919, 3.94, 3.956, 3.97, 3.978, 3.99,
4.001, 4.014, 4.025, 4.041, 4.052, 4.064, 4.076, 4.086, 4.094, 4.104,
4.112, 4.123, 4.134, 4.146, 4.159, 4.172, 4.18, 4.192, 4.212, 4.221,
4.234, 4.255, 4.273, 4.292, 4.324, 4.357, 4.373, 4.399, 4.418, 4.445
])
#old values for k3~=0
# expected_50terms_displacement = np.array(
# [ -1.30900000e-04, 8.85900000e-05, 2.63900000e-04,
# 3.30200000e-04, 3.30500000e-04, 2.87100000e-04,
# 2.00000000e-04, 9.09500000e-05, -8.36000000e-05,
# -3.01800000e-04, -4.32800000e-04, -6.07300000e-04,
# -7.59900000e-04, -8.90900000e-04, -9.99800000e-04,
# -1.02100000e-03, -9.99100000e-04, -8.67700000e-04,
# -5.61300000e-04, -2.11300000e-04, 2.04300000e-04,
# 7.29200000e-04, 1.42900000e-03, 2.41300000e-03,
# 3.46300000e-03, 4.29400000e-03, 5.08100000e-03,
# 5.62800000e-03, 5.86800000e-03, 6.19600000e-03,
# 6.39300000e-03, 6.52500000e-03, 6.59100000e-03,
# 6.48200000e-03, 6.32900000e-03, 6.02300000e-03,
# 5.69600000e-03, 5.45500000e-03, 5.06200000e-03,
# 4.75600000e-03, 4.40700000e-03, 3.90400000e-03,
# 3.35800000e-03, 2.87800000e-03, 2.35300000e-03,
# 1.82900000e-03, 1.52300000e-03, 9.98700000e-04,
# 5.18300000e-04, 2.12500000e-04, -4.95200000e-05,
# -2.67600000e-04, -3.76500000e-04, -3.76100000e-04,
# -2.00600000e-04, 1.87300000e-05, 1.06500000e-04,
# 1.94500000e-04, 1.94900000e-04, 1.30000000e-04])
expected_50terms_displacement = np.array([
-1.74400116e-05, 2.56595529e-04, 3.64963938e-04, 3.96163257e-04,
3.52239419e-04, 2.55908617e-04, 1.36296573e-04, 3.12193756e-05,
-1.48035583e-04, -3.73050108e-04, -4.80427236e-04, -6.84847774e-04,
-8.61705766e-04, -9.44268811e-04, -1.02333177e-03, -1.00753661e-03,
-9.18192599e-04, -7.32771117e-04, -3.72382730e-04, -7.79760498e-05,
4.06998900e-04, 9.37679667e-04, 1.57072235e-03, 2.58323632e-03,
3.52928135e-03, 4.47726082e-03, 5.12406706e-03, 5.61329890e-03,
5.84231170e-03, 6.13309619e-03, 6.32505191e-03, 6.46203546e-03,
6.49032925e-03, 6.39329339e-03, 6.23960924e-03, 5.99242067e-03,
5.67177967e-03, 5.35598822e-03, 5.07919623e-03, 4.69552191e-03,
4.37030991e-03, 3.90678952e-03, 3.43034780e-03, 2.90774639e-03,
2.35231514e-03, 1.82145021e-03, 1.51724930e-03, 1.09014092e-03,
4.86434682e-04, 2.61200867e-04, -5.02752907e-06, -2.99906282e-04,
-4.26188536e-04, -4.46910518e-04, -3.09328219e-04, -6.53887601e-05,
4.77786782e-05, 1.84483472e-04, 2.30390682e-04, 2.18090273e-04
])
expected_200terms_t = np.array([
3.503, 3.519, 3.539, 3.556, 3.576, 3.595, 3.613, 3.632, 3.651, 3.667,
3.69, 3.708, 3.727, 3.746, 3.766, 3.782, 3.801, 3.822, 3.84, 3.856,
3.878, 3.896, 3.915, 3.933, 3.951, 3.97, 3.99, 4.009, 4.027, 4.046,
4.067, 4.085, 4.102, 4.122, 4.141, 4.159, 4.178, 4.197, 4.217, 4.234,
4.252, 4.273, 4.291, 4.31, 4.329, 4.347, 4.368, 4.386, 4.405, 4.423,
4.442, 4.46, 4.479, 4.495
])
expected_200terms_displacement = np.array([
7.04000000e-08, 2.22800000e-05, 2.27000000e-05, 1.23200000e-06,
2.35100000e-05, 2.39300000e-05, 2.46400000e-06, -1.89700000e-05,
-6.22700000e-05, -1.27500000e-04, -1.70700000e-04, -2.57800000e-04,
-3.44800000e-04, -4.53600000e-04, -5.40600000e-04, -5.84000000e-04,
-5.61700000e-04, -4.73800000e-04, -2.54900000e-04, 1.17100000e-04,
6.85900000e-04, 1.51700000e-03, 2.50100000e-03, 3.70300000e-03,
5.01500000e-03, 6.26200000e-03, 7.20200000e-03, 7.61800000e-03,
7.39900000e-03, 6.74400000e-03, 5.91400000e-03, 5.01800000e-03,
4.10100000e-03, 3.22700000e-03, 2.50600000e-03, 1.85000000e-03,
1.32600000e-03, 9.11400000e-04, 5.84000000e-04, 3.00200000e-04,
1.47600000e-04, 3.87500000e-05, -4.82900000e-05, -1.13400000e-04,
-1.13000000e-04, -1.34500000e-04, -1.34000000e-04, -1.33600000e-04,
-1.11400000e-04, -6.72600000e-05, -6.68400000e-05, -6.64500000e-05,
-4.41700000e-05, -4.38200000e-05
])
t = np.linspace(0, 4.5, 400)
#see Dingetal2012 Table 2 for material properties
pdict = OrderedDict(
E=6.998 * 1e9, #Pa
rho=2373, #kg/m3
L=160, #m
#v_norm=0.01165,
kf=5.41e-4,
#Fz_norm=1.013e-4,
mu_norm=39.263,
k1_norm=97.552,
# k3_norm=2.497e6,
nterms=200,
BC="SS",
nquad=20,
k1bar=PolyLine([0, 0.5], [0.5, 1], [1, 1], [1, 1]),
# k1bar=PolyLine([0,0.5],[0.5,1],[2,1],[2,1]),
moving_loads_x_norm=[[0]],
moving_loads_Fz_norm=[[1.013e-4]],
moving_loads_v_norm=[
0.01165,
],
tvals=t,
# tvals=np.array([4.0]),
xvals_norm=np.array([0.5]),
use_analytical=True,
implementation="vectorized",
# implementation="fortran",
force_calc=True,
)
a = SpecBeam(**pdict)
a.runme()
# a.calulate_qk(t=t)
#
# yall = a.wofx(x_norm=0.5, normalise_w=False)
ycompare = np.interp(expected_200terms_t, t, a.defl[0, :])
# print(repr(ycompare))
print("n=", pdict['nterms'])
end_time0 = time.time()
elapsed_time = (end_time0 - start_time0)
print("Total run time={}".format(str(timedelta(seconds=elapsed_time))))
if DEBUG:
title = 'SpecBeam, const mat prop vs Ding et al (2012) \nFigure 8 Displacement at Midpoint of beam but with k3=0'
print(title)
print(' '.join(['{:>9s}'] * 4).format('t', 'expect', 'calc', 'diff'))
for i, j, k in zip(expected_200terms_t, expected_200terms_displacement,
ycompare):
print(' '.join(['{:9.4f}'] * 4).format(i, j, k, j - k))
print()
fig = plt.figure(figsize=(10, 6))
ax = fig.add_subplot("111")
ax.set_xlabel("time, s")
ax.set_ylabel("w, m")
ax.set_xlim(3.5, 4.5)
ax.set_title(title)
ax.plot(expected_50terms_t,
expected_50terms_displacement,
label="expect n=50",
color='green',
marker='o',
ls='-')
ax.plot(expected_200terms_t,
expected_200terms_displacement,
label="expect n=200",
color='black',
marker=None,
ls='-')
ax.plot(t, a.defl, label="calc n=200")
ax.plot(expected_200terms_t,
ycompare,
label="calc, n=200 (compare)",
color='red',
marker='s',
ms=4,
ls=':')
leg = ax.legend(loc='upper left')
leg.draggable()
plt.show()
assert_allclose(expected_200terms_displacement, ycompare, atol=2.4e-4)
def test_SpecBeam_const_mat_deflection_shape_runme():
"""Test SpecBeam for constant mat: Figure 7, deflection with load at midpoint"""
# expected values are digitised from Ding et al 2012.
expected_50terms_x = np.array([
70.68, 71.275, 71.785, 72.189, 72.529, 72.848, 73.209, 73.677, 74.06,
74.378, 74.74, 75.122, 75.505, 75.781, 76.079, 76.312, 76.525, 76.716,
76.95, 77.12, 77.418, 77.715, 77.907, 78.204, 78.459, 78.778, 79.224,
79.522, 79.883, 80.181, 80.436, 80.606, 80.776, 81.01, 81.137, 81.307,
81.477, 81.626, 81.902, 82.179, 82.497, 82.774, 82.986, 83.263, 83.539,
84.028, 84.368, 84.623, 84.878, 85.239, 85.728, 86.153, 86.684, 87.386,
87.853, 88.363, 88.81, 89.341, 89.788
])
expected_50terms_displacement = np.array([
3.23100000e-06, 1.48600000e-04, 1.80900000e-04, 1.64800000e-04,
1.00200000e-04, 1.93900000e-05, -1.09900000e-04, -2.55300000e-04,
-3.52200000e-04, -3.68300000e-04, -3.19900000e-04, -1.26000000e-04,
1.64800000e-04, 5.04000000e-04, 9.24100000e-04, 1.27900000e-03,
1.66700000e-03, 2.10300000e-03, 2.58800000e-03, 3.00800000e-03,
3.59000000e-03, 4.17100000e-03, 4.70400000e-03, 5.27000000e-03,
5.70600000e-03, 6.17400000e-03, 6.49800000e-03, 6.57800000e-03,
6.44900000e-03, 6.15800000e-03, 5.91600000e-03, 5.64100000e-03,
5.30200000e-03, 4.88200000e-03, 4.51100000e-03, 4.17100000e-03,
3.81600000e-03, 3.38000000e-03, 2.79800000e-03, 2.05500000e-03,
1.42500000e-03, 7.78700000e-04, 3.26300000e-04, -9.37000000e-05,
-5.29900000e-04, -9.01500000e-04, -9.98400000e-04, -1.01500000e-03,
-9.66100000e-04, -8.04500000e-04, -5.29900000e-04, -2.22900000e-04,
8.40100000e-05, 3.42500000e-04, 3.74800000e-04, 3.10200000e-04,
1.80900000e-04, 1.93900000e-05, -1.26000000e-04
])
expected_200terms_x = np.array([
70.064, 70.404, 70.723, 71.02, 71.36, 71.679, 71.955, 72.317, 72.614,
72.976, 73.273, 73.571, 73.911, 74.23, 74.527, 74.867, 75.165, 75.505,
75.866, 76.164, 76.483, 76.801, 77.12, 77.418, 77.779, 78.098, 78.438,
78.693, 79.033, 79.352, 79.671, 79.989, 80.308, 80.648, 80.967, 81.286,
81.583, 81.924, 82.264, 82.582, 82.88, 83.199, 83.539, 83.815, 84.134,
84.495, 84.793, 85.112, 85.43, 85.749, 86.047, 86.429, 86.727, 87.046,
87.365, 87.683, 87.981, 88.342, 88.64, 88.959, 89.277, 89.617, 89.958
])
expected_200terms_displacement = np.array([
-2.90800000e-05, -2.90800000e-05, -6.13900000e-05, -7.75400000e-05,
-7.75400000e-05, -1.09900000e-04, -1.26000000e-04, -1.26000000e-04,
-1.26000000e-04, -1.42200000e-04, -1.09900000e-04, -1.09900000e-04,
-9.37000000e-05, -2.90800000e-05, 3.55400000e-05, 1.64800000e-04,
2.94000000e-04, 4.55600000e-04, 7.30200000e-04, 1.02100000e-03,
1.40900000e-03, 1.86100000e-03, 2.37800000e-03, 2.99200000e-03,
3.68700000e-03, 4.43000000e-03, 5.22100000e-03, 5.96400000e-03,
6.67500000e-03, 7.27300000e-03, 7.58000000e-03, 7.48300000e-03,
6.95000000e-03, 6.06100000e-03, 4.99500000e-03, 3.88000000e-03,
2.83000000e-03, 1.94200000e-03, 1.16600000e-03, 5.20200000e-04,
5.17000000e-05, -2.55300000e-04, -4.33000000e-04, -5.46000000e-04,
-5.78400000e-04, -5.62200000e-04, -4.81400000e-04, -4.33000000e-04,
-3.19900000e-04, -2.39100000e-04, -1.74500000e-04, -1.26000000e-04,
-4.52300000e-05, -1.29200000e-05, 1.93900000e-05, 1.93900000e-05,
3.55400000e-05, 6.78500000e-05, 3.55400000e-05, 5.17000000e-05,
3.55400000e-05, 1.93900000e-05, 1.93900000e-05
])
t = np.linspace(0, 160 / 2 / 20, 400)
xvals = np.linspace(0, 160, 200)
#see Dingetal2012 Table 2 for material properties
pdict = OrderedDict(
E=6.998 * 1e9, #Pa
rho=2373, #kg/m3
L=160, #m
#v_norm=0.01165,
kf=5.41e-4,
#Fz_norm=1.013e-4,
mu_norm=39.263,
k1_norm=97.552,
k3_norm=2.497e6,
nterms=50,
BC="SS",
nquad=20,
moving_loads_x_norm=[[0]],
moving_loads_Fz_norm=[[1.013e-4]],
moving_loads_v_norm=[
0.01165,
],
tvals=t,
xvals=xvals)
a = SpecBeam(**pdict)
a.runme()
# a = SpecBeam(**pdict)
#
# a.calulate_qk(t=t)
yall = a.defl[:,
-1] #a.wofx(x=xvals, tslice=slice(-1, None, None), normalise_w=False)[:,0]
ycompare = np.interp(expected_50terms_x, xvals, yall)
if DEBUG:
title = 'SpecBeam, const mat prop vs Ding et al (2012) \nFigure 7 deflection when load at Midpoint of beam'
print(title)
print(' '.join(['{:>9s}'] * 4).format('t', 'expect', 'calc', 'diff'))
for i, j, k in zip(expected_50terms_x, expected_50terms_displacement,
ycompare):
print(' '.join(['{:9.4f}'] * 4).format(i, j, k, j - k))
print()
fig = plt.figure(figsize=(10, 6))
ax = fig.add_subplot("111")
ax.set_xlabel("x, m")
ax.set_ylabel("w, m")
ax.set_xlim(70, 90)
ax.set_title(title)
ax.plot(expected_50terms_x,
expected_50terms_displacement,
label="expect n=50",
color='green',
marker='o',
ls='-')
ax.plot(expected_200terms_x,
expected_200terms_displacement,
label="expect n=200",
color='black',
marker=None,
ls='-')
ax.plot(xvals, yall, label="calc n=50")
ax.plot(expected_50terms_x,
ycompare,
label="calc, n=50 (compare)",
color='red',
marker='s',
ms=4,
ls=':')
leg = ax.legend(loc='upper left')
leg.draggable()
plt.show()
assert_allclose(expected_50terms_displacement, ycompare, atol=2.4e-4)
def test_SpecBeam_const_mat_midpoint_defl_runme():
"""Test SpecBeam for constant mat: Figure 8, displacement vs time at
beam midpoint (using the runme method)"""
# expected values are digitised from Ding et al 2012.
expected_50terms_t = np.array([
3.511, 3.553, 3.576, 3.605, 3.621, 3.637, 3.651, 3.661, 3.676, 3.693,
3.701, 3.717, 3.733, 3.743, 3.761, 3.777, 3.79, 3.804, 3.822, 3.833,
3.848, 3.862, 3.877, 3.899, 3.919, 3.94, 3.956, 3.97, 3.978, 3.99,
4.001, 4.014, 4.025, 4.041, 4.052, 4.064, 4.076, 4.086, 4.094, 4.104,
4.112, 4.123, 4.134, 4.146, 4.159, 4.172, 4.18, 4.192, 4.212, 4.221,
4.234, 4.255, 4.273, 4.292, 4.324, 4.357, 4.373, 4.399, 4.418, 4.445
])
expected_50terms_displacement = np.array([
-1.30900000e-04, 8.85900000e-05, 2.63900000e-04, 3.30200000e-04,
3.30500000e-04, 2.87100000e-04, 2.00000000e-04, 9.09500000e-05,
-8.36000000e-05, -3.01800000e-04, -4.32800000e-04, -6.07300000e-04,
-7.59900000e-04, -8.90900000e-04, -9.99800000e-04, -1.02100000e-03,
-9.99100000e-04, -8.67700000e-04, -5.61300000e-04, -2.11300000e-04,
2.04300000e-04, 7.29200000e-04, 1.42900000e-03, 2.41300000e-03,
3.46300000e-03, 4.29400000e-03, 5.08100000e-03, 5.62800000e-03,
5.86800000e-03, 6.19600000e-03, 6.39300000e-03, 6.52500000e-03,
6.59100000e-03, 6.48200000e-03, 6.32900000e-03, 6.02300000e-03,
5.69600000e-03, 5.45500000e-03, 5.06200000e-03, 4.75600000e-03,
4.40700000e-03, 3.90400000e-03, 3.35800000e-03, 2.87800000e-03,
2.35300000e-03, 1.82900000e-03, 1.52300000e-03, 9.98700000e-04,
5.18300000e-04, 2.12500000e-04, -4.95200000e-05, -2.67600000e-04,
-3.76500000e-04, -3.76100000e-04, -2.00600000e-04, 1.87300000e-05,
1.06500000e-04, 1.94500000e-04, 1.94900000e-04, 1.30000000e-04
])
expected_200terms_t = np.array([
3.503, 3.519, 3.539, 3.556, 3.576, 3.595, 3.613, 3.632, 3.651, 3.667,
3.69, 3.708, 3.727, 3.746, 3.766, 3.782, 3.801, 3.822, 3.84, 3.856,
3.878, 3.896, 3.915, 3.933, 3.951, 3.97, 3.99, 4.009, 4.027, 4.046,
4.067, 4.085, 4.102, 4.122, 4.141, 4.159, 4.178, 4.197, 4.217, 4.234,
4.252, 4.273, 4.291, 4.31, 4.329, 4.347, 4.368, 4.386, 4.405, 4.423,
4.442, 4.46, 4.479, 4.495
])
expected_200terms_displacement = np.array([
7.04000000e-08, 2.22800000e-05, 2.27000000e-05, 1.23200000e-06,
2.35100000e-05, 2.39300000e-05, 2.46400000e-06, -1.89700000e-05,
-6.22700000e-05, -1.27500000e-04, -1.70700000e-04, -2.57800000e-04,
-3.44800000e-04, -4.53600000e-04, -5.40600000e-04, -5.84000000e-04,
-5.61700000e-04, -4.73800000e-04, -2.54900000e-04, 1.17100000e-04,
6.85900000e-04, 1.51700000e-03, 2.50100000e-03, 3.70300000e-03,
5.01500000e-03, 6.26200000e-03, 7.20200000e-03, 7.61800000e-03,
7.39900000e-03, 6.74400000e-03, 5.91400000e-03, 5.01800000e-03,
4.10100000e-03, 3.22700000e-03, 2.50600000e-03, 1.85000000e-03,
1.32600000e-03, 9.11400000e-04, 5.84000000e-04, 3.00200000e-04,
1.47600000e-04, 3.87500000e-05, -4.82900000e-05, -1.13400000e-04,
-1.13000000e-04, -1.34500000e-04, -1.34000000e-04, -1.33600000e-04,
-1.11400000e-04, -6.72600000e-05, -6.68400000e-05, -6.64500000e-05,
-4.41700000e-05, -4.38200000e-05
])
t = np.linspace(0, 4.5, 400)
#see Dingetal2012 Table 2 for material properties
pdict = OrderedDict(
E=6.998 * 1e9, #Pa
rho=2373, #kg/m3
L=160, #m
#v_norm=0.01165,
kf=5.41e-4,
#Fz_norm=1.013e-4,
mu_norm=39.263,
k1_norm=97.552,
k3_norm=2.497e6,
nterms=50,
BC="SS",
nquad=20,
k1bar=PolyLine([0, 0.5], [0.5, 1], [1, 1], [1, 1]),
moving_loads_x_norm=[[0]],
moving_loads_Fz_norm=[[1.013e-4]],
moving_loads_v_norm=[
0.01165,
],
tvals=t,
xvals_norm=0.5)
a = SpecBeam(**pdict)
a.runme()
# a.calulate_qk(t=t)
#
# yall = a.wofx(x_norm=0.5, normalise_w=False)
ycompare = np.interp(expected_50terms_t, t, a.defl)
if DEBUG:
title = 'SpecBeam, const mat prop vs Ding et al (2012) \nFigure 8 Displacement at Midpoint of beam'
print(title)
print(' '.join(['{:>9s}'] * 4).format('t', 'expect', 'calc', 'diff'))
for i, j, k in zip(expected_50terms_t, expected_50terms_displacement,
ycompare):
print(' '.join(['{:9.4f}'] * 4).format(i, j, k, j - k))
print()
fig = plt.figure(figsize=(10, 6))
ax = fig.add_subplot("111")
ax.set_xlabel("time, s")
ax.set_ylabel("w, m")
ax.set_xlim(3.5, 4.5)
ax.set_title(title)
ax.plot(expected_50terms_t,
expected_50terms_displacement,
label="expect n=50",
color='green',
marker='o',
ls='-')
ax.plot(expected_200terms_t,
expected_200terms_displacement,
label="expect n=200",
color='black',
marker=None,
ls='-')
ax.plot(t, a.defl, label="calc n=50")
ax.plot(expected_50terms_t,
ycompare,
label="calc, n=50 (compare)",
color='red',
marker='s',
ms=4,
ls=':')
leg = ax.legend(loc='upper left')
leg.draggable()
plt.show()
assert_allclose(expected_50terms_displacement, ycompare, atol=2.4e-4)