14.7.3. Statics of a 3d 3-element cantilever beam (ops_vis)ΒΆ
Example .py
file can be downloaded here
:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 | import openseespy.opensees as ops
import openseespy.postprocessing.ops_vis as opsv
# import opensees as ops # local compilation
# import ops_vis as opsv # local
import matplotlib.pyplot as plt
ops.wipe()
ops.model('basic', '-ndm', 3, '-ndf', 6)
b = 0.2
h = 0.4
A, Iz, Iy, J = 0.04, 0.0010667, 0.0002667, 0.01172
E = 25.0e6
G = 9615384.6
# Lx, Ly, Lz = 4., 3., 5.
Lx, Ly, Lz = 4., 4., 4.
ops.node(1, 0., 0., 0.)
ops.node(2, 0., 0., Lz)
ops.node(3, Lx, 0., Lz)
ops.node(4, Lx, Ly, Lz)
ops.fix(1, 1, 1, 1, 1, 1, 1)
lmass = 200.
ops.mass(2, lmass, lmass, lmass, 0.001, 0.001, 0.001)
ops.mass(3, lmass, lmass, lmass, 0.001, 0.001, 0.001)
ops.mass(4, lmass, lmass, lmass, 0.001, 0.001, 0.001)
gTTagz = 1
gTTagx = 2
gTTagy = 3
coordTransf = 'Linear'
ops.geomTransf(coordTransf, gTTagz, 0., -1., 0.)
ops.geomTransf(coordTransf, gTTagx, 0., -1., 0.)
ops.geomTransf(coordTransf, gTTagy, 1., 0., 0.)
ops.element('elasticBeamColumn', 1, 1, 2, A, E, G, J, Iy, Iz, gTTagz)
ops.element('elasticBeamColumn', 2, 2, 3, A, E, G, J, Iy, Iz, gTTagx)
ops.element('elasticBeamColumn', 3, 3, 4, A, E, G, J, Iy, Iz, gTTagy)
Ew = {}
Px = -4.e1
Py = -2.5e1
Pz = -3.e1
ops.timeSeries('Constant', 1)
ops.pattern('Plain', 1, 1)
ops.load(4, Px, Py, Pz, 0., 0., 0.)
ops.constraints('Transformation')
ops.numberer('RCM')
ops.system('BandGeneral')
ops.test('NormDispIncr', 1.0e-6, 6, 2)
ops.algorithm('Linear')
ops.integrator('LoadControl', 1)
ops.analysis('Static')
ops.analyze(1)
opsv.plot_model()
sfac = 2.0e0
# fig_wi_he = 22., 14.
fig_wi_he = 30., 20.
# - 1
nep = 9
opsv.plot_defo(sfac, nep, fmt_interp='b-', az_el=(-68., 39.),
fig_wi_he=fig_wi_he, endDispFlag=0)
plt.title('3d 3-element cantilever beam')
# - 2
opsv.plot_defo(sfac, 19, fmt_interp='b-', az_el=(6., 30.),
fig_wi_he=fig_wi_he)
plt.title('3d 3-element cantilever beam')
# - 3
nfreq = 6
eigValues = ops.eigen(nfreq)
modeNo = 6
sfac = 2.0e1
opsv.plot_mode_shape(modeNo, sfac, 19, fmt_interp='b-', az_el=(106., 46.),
fig_wi_he=fig_wi_he)
plt.title(f'Mode {modeNo}')
sfacN = 1.e-2
sfacVy = 5.e-2
sfacVz = 1.e-2
sfacMy = 1.e-2
sfacMz = 1.e-2
sfacT = 1.e-2
# plt.figure()
minY, maxY = opsv.section_force_diagram_3d('N', Ew, sfacN)
plt.title(f'Axial force N, max = {maxY:.2f}, min = {minY:.2f}')
minY, maxY = opsv.section_force_diagram_3d('Vy', Ew, sfacVy)
plt.title(f'Transverse force Vy, max = {maxY:.2f}, min = {minY:.2f}')
minY, maxY = opsv.section_force_diagram_3d('Vz', Ew, sfacVz)
plt.title(f'Transverse force Vz, max = {maxY:.2f}, min = {minY:.2f}')
minY, maxY = opsv.section_force_diagram_3d('My', Ew, sfacMy)
plt.title(f'Bending moments My, max = {maxY:.2f}, min = {minY:.2f}')
minY, maxY = opsv.section_force_diagram_3d('Mz', Ew, sfacMz)
plt.title(f'Bending moments Mz, max = {maxY:.2f}, min = {minY:.2f}')
minY, maxY = opsv.section_force_diagram_3d('T', Ew, sfacT)
plt.title(f'Torsional moment T, max = {maxY:.2f}, min = {minY:.2f}')
# just for demonstration,
# the section data below does not match the data in OpenSees model above
# For now it can be source of inconsistency because OpenSees has
# not got functions to return section dimensions.
# A workaround is to have own Python helper functions to reuse data
# specified once
ele_shapes = {1: ['circ', [h]],
2: ['rect', [b, h]],
3: ['I', [b, h, b/10., h/6.]]}
opsv.plot_extruded_shapes_3d(ele_shapes, fig_wi_he=fig_wi_he)
plt.show()
exit()
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