Truss element Response

Supported truss elements include most truss elements in OpenSees, including:

• ✅ Truss

• ✅ TrussSection

• ✅ corotTruss

• ✅ corotTrussSection

import matplotlib.pyplot as plt
import openseespy.opensees as ops

import opstool as opst

%matplotlib inline

ops.wipe()
ops.model("basic", "-ndm", 2, "-ndf", 2)
# variables
A = 4.0
E = 29000.0
alpha = 0.05
sY = 36.0
udisp = 2.5
Nsteps = 1000
Px = 160.0
Py = 0.0
# create nodes
ops.node(1, 0.0, 0.0)
ops.node(2, 72.0, 0.0)
ops.node(3, 168.0, 0.0)
ops.node(4, 48.0, 144.0)
# set boundary condition
ops.fix(1, 1, 1)
ops.fix(2, 1, 1)
ops.fix(3, 1, 1)
# define materials
ops.uniaxialMaterial("Hardening", 1, E, sY, 0.0, alpha / (1 - alpha) * E)
# define elements
ops.element("Truss", 1, 1, 4, A, 1)
ops.element("Truss", 2, 2, 4, A, 1)
ops.element("Truss", 3, 3, 4, A, 1)
# create TimeSeries
ops.timeSeries("Linear", 1)
# create a plain load pattern
ops.pattern("Plain", 1, 1)
# Create the nodal load
ops.load(4, Px, Py)

# plot
opst.vis.pyvista.set_plot_props(notebook=True)  # Set notebook mode for PyVista
fig = opst.vis.pyvista.plot_model(show_nodal_loads=True, load_scale=3, bc_scale=5)
fig.show(jupyter_backend="static")  # or None

Result Saving

ops.system("BandGeneral")
ops.constraints("Transformation")
ops.numberer("RCM")
ops.test("NormDispIncr", 1.0e-12, 10, 3)
ops.algorithm("Newton")
ops.integrator("LoadControl", 1.0 / Nsteps)
ops.analysis("Static")

opstool allows us to save the data at each step of the analysis! First, we create a database class using opstool.post.CreateODB, and then, during each step of the analysis, we call its method .fetch_response_step to retrieve the data for the current step. Once all the analysis steps are completed, we use the .save_response method to save the data in one go.

ODB = opst.post.CreateODB(odb_tag=1)
for i in range(Nsteps):
    ops.analyze(1)
    ODB.fetch_response_step()
ODB.save_response()

OPSTOOL ::  All responses data with _odb_tag = 1 saved in .opstool.output/RespStepData-1.nc!

Result Reading

The provided function opstool.post.get_element_responses() make it easy to read element responses.

ele_type="Truss" is used to specify extracting the response of frame elements.

all_resp = opst.post.get_element_responses(odb_tag=1, ele_type="Truss")

OPSTOOL ::  Loading Truss response data from .opstool.output/RespStepData-1.nc ...

The result is an xarray DataSet object, and we can access the associated DataArray objects through .data_vars.

all_resp.data_vars

Data variables:
    axialForce  (time, eleTags) float32 12kB 0.0 0.0 0.0 ... 162.8 -30.63 -161.7
    axialDefo   (time, eleTags) float32 12kB 0.0 0.0 0.0 ... -0.03855 -0.8036
    Stress      (time, eleTags) float32 12kB 0.0 0.0 0.0 ... 40.69 -7.658 -40.42
    Strain      (time, eleTags) float32 12kB 0.0 0.0 ... -0.0002641 -0.004287

The variable names, along with their dimensions and coordinates, are displayed above. The first two represent the axial force and deformation of the truss element, while the latter refers to the stress and strain of the material in its cross-section.

all_resp["axialForce"]

<xarray.DataArray 'axialForce' (time: 1001, eleTags: 3)> Size: 12kB
array([[ 0.0000000e+00,  0.0000000e+00,  0.0000000e+00],
       [ 1.5702428e-01, -2.0976454e-02, -1.6697697e-01],
       [ 3.1404856e-01, -4.1952908e-02, -3.3395395e-01],
       ...,
       [ 1.6241649e+02, -3.0538671e+01, -1.6135800e+02],
       [ 1.6258820e+02, -3.0584375e+01, -1.6151137e+02],
       [ 1.6275992e+02, -3.0630081e+01, -1.6166473e+02]], dtype=float32)
Coordinates:
  * time     (time) float32 4kB 0.0 0.001 0.002 0.003 ... 0.997 0.998 0.999 1.0
  * eleTags  (eleTags) int32 12B 1 2 3

xarray.DataArray

'axialForce'

• time: 1001
• eleTags: 3

• 0.0 0.0 0.0 0.157 -0.02098 ... -30.58 -161.5 162.8 -30.63 -161.7

  array([[ 0.0000000e+00,  0.0000000e+00,  0.0000000e+00],
         [ 1.5702428e-01, -2.0976454e-02, -1.6697697e-01],
         [ 3.1404856e-01, -4.1952908e-02, -3.3395395e-01],
         ...,
         [ 1.6241649e+02, -3.0538671e+01, -1.6135800e+02],
         [ 1.6258820e+02, -3.0584375e+01, -1.6151137e+02],
         [ 1.6275992e+02, -3.0630081e+01, -1.6166473e+02]], dtype=float32)

• Coordinates: (2)
  • time
    (time)
    float32
    0.0 0.001 0.002 ... 0.998 0.999 1.0

    array([0.   , 0.001, 0.002, ..., 0.998, 0.999, 1.   ], dtype=float32)

  • eleTags
    (eleTags)
    int32
    1 2 3

    array([1, 2, 3])

• Indexes: (2)
  • time
    PandasIndex

    PandasIndex(Index([                  0.0, 0.0010000000474974513, 0.0020000000949949026,
            0.003000000026077032,  0.004000000189989805,  0.004999999888241291,
            0.006000000052154064,  0.007000000216066837,   0.00800000037997961,
            0.008999999612569809,
           ...
              0.9909999966621399,    0.9919999837875366,    0.9929999709129333,
              0.9940000176429749,    0.9950000047683716,    0.9959999918937683,
               0.996999979019165,    0.9980000257492065,    0.9990000128746033,
                             1.0],
          dtype='float32', name='time', length=1001))

  • eleTags
    PandasIndex

    PandasIndex(Index([1, 2, 3], dtype='int32', name='eleTags'))

• Attributes: (0)

axialForce = all_resp["axialForce"]
ts = axialForce.time

for etag in axialForce.coords["eleTags"].data:
    plt.plot(ts, axialForce.sel(eleTags=etag).data, label=f"Ele {etag}")

plt.legend()
plt.title("All Elements Axial Forces")
plt.show()

strain = all_resp["Strain"]
ts = axialForce.time

for etag in strain.coords["eleTags"].data:
    plt.plot(ts, strain.sel(eleTags=etag).data, label=f"Ele {etag}")

plt.legend()
plt.title("All Elements Strain")
plt.show()

axialForce = opst.post.get_element_responses(odb_tag=1, ele_type="Truss", resp_type="axialForce")
axialDefo = opst.post.get_element_responses(odb_tag=1, ele_type="Truss", resp_type="axialDefo")

plt.plot(axialDefo.sel(eleTags=1), axialForce.sel(eleTags=1))
plt.title("Element 1 Axial Force vs. Deformation")
plt.xlabel("Deformation")
plt.ylabel("Axial Force")
plt.show()

OPSTOOL ::  Loading Truss axialForce response data from .opstool.output/RespStepData-1.nc ...

OPSTOOL ::  Loading Truss axialDefo response data from .opstool.output/RespStepData-1.nc ...