Shell element Response¶

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

✅ ShellMITC4
✅ ShellMITC9
✅ ShellDKGQ
✅ ShellDKGT
✅ ShellNLDKGQ
✅ ShellNLDKGT
✅ ShellNL
✅ ASDShellQ4
✅ ASDShellT3

[1]:

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

import opstool as opst

[2]:

opst.load_ops_examples("Shell3D")  # or your model code here

# add beam loads
ops.timeSeries("Linear", 1)
ops.pattern("Plain", 1, 1)
_ = opst.pre.gen_grav_load(direction="z", factor=-9810)


# plot
opst.vis.pyvista.set_plot_props(notebook=True)
fig = opst.vis.pyvista.plot_model(show_nodal_loads=True, show_ele_loads=True)
fig.show(jupyter_backend="static")

The original Tcl file comes from http://www.dinochen.com/, and the Python version is converted by opstool.tcl2py().

../../_images/src_post_shell_resp_3_1.png

Result Saving¶

[3]:

ops.system("BandGeneral")
# Create the constraint handler, the transformation method
ops.constraints("Transformation")
# Create the DOF numberer, the reverse Cuthill-McKee algorithm
ops.numberer("RCM")
# Create the convergence test, the norm of the residual with a tolerance of
# 1e-12 and a max number of iterations of 10
ops.test("NormDispIncr", 1.0e-12, 10, 3)
# Create the solution algorithm, a Newton-Raphson algorithm
ops.algorithm("Newton")
# Create the integration scheme, the LoadControl scheme using steps of 0.1
ops.integrator("LoadControl", 0.1)
# Create the analysis object
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.

project_gauss_to_nodes is used to project the Gauss point results to the nodes.

“copy”: The response of each node is copied from the Gaussian point closest to it.
“average”: The response of each node is equal to the weighted average of the responses of all Gaussian points of the element, with the weight being the integration point weight.
“extrapolate”: The nodal responses are obtained by extrapolating the element shape functions.

[4]:

ODB = opst.post.CreateODB(
    odb_tag=1,
    project_gauss_to_nodes="copy",  # "extrapolate", "copy", "average"
)
for i in range(10):
    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="Shell" is used to specify extracting the response of shell elements.

[5]:

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

OPSTOOL ::  Loading Shell 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.

[6]:

all_resp.data_vars

[6]:

Data variables:
    sectionForces               (time, eleTags, GaussPoints, secDOFs) float32 141kB ...
    sectionDeformations         (time, eleTags, GaussPoints, secDOFs) float32 141kB ...
    Stresses                    (time, eleTags, GaussPoints, fiberPoints, stressDOFs) float32 440kB ...
    Strains                     (time, eleTags, GaussPoints, fiberPoints, stressDOFs) float32 440kB ...
    sectionForcesAtNodes        (time, nodeTags, secDOFs) float32 43kB 0.0 .....
    sectionDeformationsAtNodes  (time, nodeTags, secDOFs) float32 43kB 0.0 .....
    StressesAtNodes             (time, nodeTags, fiberPoints, stressDOFs) float32 133kB ...
    StrainsAtNodes              (time, nodeTags, fiberPoints, stressDOFs) float32 133kB ...

section forces and deformations at Gauss points are supported, representing the shell section response per unit length.

Stresses and Strains refer to the fiber stress and strain at the Gauss points. fiberPoints represents the fiber No. on each section at the Gauss point, typically counted from the bottom. Stress and strain have five components, because sigma33 (the normal stress along the local z-axis) is zero and omitted. The remaining components represent stresses along the local directions.

[7]:

all_resp.attrs  # attributes

[7]:

{'FXX,FYY,FXY': 'Membrane (in-plane) forces or deformations.',
 'MXX,MYY,MXY': 'Bending moments or rotations (out-plane) of plate.',
 'VXZ,VYZ': 'Shear forces or deformations.',
 'sigma11, sigma22': 'Normal stress (strain) along local x, y',
 'sigma12, sigma23, sigma13': 'Shear stress (strain).'}

Shell element Response¶

Result Saving¶

Result Reading¶

Section response¶

Stresses and Strains¶