Statics of a 3d 3-element cantilever beam

Example .py file can be downloaded here:

_images/demo_cantilever_3el_3d_model.png _images/demo_cantilever_3el_3d_extruded_members.png _images/demo_cantilever_3el_3d_defo.png _images/demo_cantilever_3el_3d_Mz.png _images/demo_cantilever_3el_3d_My.png _images/demo_cantilever_3el_3d_Vz.png _images/demo_cantilever_3el_3d_Vy.png _images/demo_cantilever_3el_3d_T.png 
  1import openseespy.opensees as ops
  2import opsvis as opsv
  3
  4import matplotlib.pyplot as plt
  5
  6ops.wipe()
  7
  8ops.model('basic', '-ndm', 3, '-ndf', 6)
  9
 10b = 0.2
 11h = 0.4
 12
 13A, Iz, Iy, J = 0.04, 0.0010667, 0.0002667, 0.01172
 14
 15E = 25.0e6
 16G = 9615384.6
 17
 18# Lx, Ly, Lz = 4., 3., 5.
 19Lx, Ly, Lz = 4., 4., 4.
 20
 21ops.node(1, 0., 0., 0.)
 22ops.node(2, 0., 0., Lz)
 23ops.node(3, Lx, 0., Lz)
 24ops.node(4, Lx, Ly, Lz)
 25
 26ops.fix(1, 1, 1, 1, 1, 1, 1)
 27
 28lmass = 200.
 29
 30ops.mass(2, lmass, lmass, lmass, 0.001, 0.001, 0.001)
 31ops.mass(3, lmass, lmass, lmass, 0.001, 0.001, 0.001)
 32ops.mass(4, lmass, lmass, lmass, 0.001, 0.001, 0.001)
 33
 34gTTagz = 1
 35gTTagx = 2
 36gTTagy = 3
 37
 38coordTransf = 'Linear'
 39ops.geomTransf(coordTransf, gTTagz, 0., -1., 0.)
 40ops.geomTransf(coordTransf, gTTagx, 0., -1., 0.)
 41ops.geomTransf(coordTransf, gTTagy, 1., 0., 0.)
 42
 43ops.element('elasticBeamColumn', 1, 1, 2, A, E, G, J, Iy, Iz, gTTagz)
 44ops.element('elasticBeamColumn', 2, 2, 3, A, E, G, J, Iy, Iz, gTTagx)
 45ops.element('elasticBeamColumn', 3, 3, 4, A, E, G, J, Iy, Iz, gTTagy)
 46
 47Ew = {}
 48
 49Px = -4.e1
 50Py = -2.5e1
 51Pz = -3.e1
 52
 53ops.timeSeries('Constant', 1)
 54ops.pattern('Plain', 1, 1)
 55ops.load(4, Px, Py, Pz, 0., 0., 0.)
 56
 57ops.constraints('Transformation')
 58ops.numberer('RCM')
 59ops.system('BandGeneral')
 60ops.test('NormDispIncr', 1.0e-6, 6, 2)
 61ops.algorithm('Linear')
 62ops.integrator('LoadControl', 1)
 63ops.analysis('Static')
 64ops.analyze(1)
 65
 66
 67opsv.plot_model()
 68
 69sfac = 2.0e0
 70
 71# fig_wi_he = 22., 14.
 72fig_wi_he = 30., 20.
 73
 74# - 1
 75nep = 9
 76opsv.plot_defo(sfac, nep, az_el=(-68., 39.),
 77               fig_wi_he=fig_wi_he, endDispFlag=0)
 78
 79plt.title('3d 3-element cantilever beam')
 80
 81# - 2
 82opsv.plot_defo(sfac, 19, az_el=(6., 30.), fig_wi_he=fig_wi_he)
 83
 84plt.title('3d 3-element cantilever beam')
 85
 86# - 3
 87nfreq = 6
 88eigValues = ops.eigen(nfreq)
 89
 90modeNo = 6
 91
 92sfac = 2.0e1
 93opsv.plot_mode_shape(modeNo, sfac, 19, az_el=(106., 46.),
 94                     fig_wi_he=fig_wi_he)
 95plt.title(f'Mode {modeNo}')
 96
 97sfacN = 1.e-2
 98sfacVy = 5.e-2
 99sfacVz = 1.e-2
100sfacMy = 1.e-2
101sfacMz = 1.e-2
102sfacT = 1.e-2
103
104# plt.figure()
105opsv.section_force_diagram_3d('N', sfacN)
106plt.title('Axial force N')
107
108opsv.section_force_diagram_3d('Vy', sfacVy)
109plt.title('Transverse force Vy')
110
111opsv.section_force_diagram_3d('Vz', sfacVz)
112plt.title('Transverse force Vz')
113
114opsv.section_force_diagram_3d('My', sfacMy)
115plt.title('Bending moments My')
116
117opsv.section_force_diagram_3d('Mz', sfacMz)
118plt.title('Bending moments Mz')
119
120opsv.section_force_diagram_3d('T', sfacT)
121plt.title('Torsional moment T')
122
123# just for demonstration,
124# the section data below does not match the data in OpenSees model above
125# For now it can be source of inconsistency because OpenSees has
126# not got functions to return section dimensions.
127# A workaround is to have own Python helper functions to reuse data
128# specified once
129ele_shapes = {1: ['circ', [h]],
130              2: ['rect', [b, h]],
131              3: ['I', [b, h, b/10., h/6.]]}
132opsv.plot_extruded_shapes_3d(ele_shapes, fig_wi_he=fig_wi_he)
133
134plt.show()
135
136exit()