StressPost¶

class sectionproperties.post.stress_post.StressPost(section: Section)[source]¶

Bases: object

Class for post-processing finite element stress results.

A StressPost object is created when a stress analysis is carried out and is returned as an object to allow post-processing of the results. The StressPost object creates a deepcopy of the MaterialGroup s within the cross-section to allow the calculation of stresses for each material. Methods for post-processing the calculated stresses are provided.

Variables:

section (Section) – Cross-section object for stress calculation
material_groups (MaterialGroup) – A deep copy of the Section material_groups

Methods

`get_stress`	Returns the stresses within each material.
`plot_mohrs_circles`	Plots Mohr's circles of the 3D stress state at position (`x`, `y`).
`plot_stress`	Plots filled stress contours over the finite element mesh.
`plot_stress_vector`	Plots stress vectors over the finite element mesh.

__init__(section: Section) → None[source]¶

Inits the StressPost class.

Parameters:: section (Section) – Cross-section object for stress calculation

plot_stress(stress: str, title: str | None = None, cmap: str = 'coolwarm', stress_limits: tuple[float, float] | None = None, normalize: bool = True, fmt: str = '{x:.4e}', colorbar_label: str = 'Stress', alpha: float = 0.5, material_list: list[Material] | None = None, **kwargs: Any) → matplotlib.axes.Axes[source]¶

Plots filled stress contours over the finite element mesh.

Parameters:

stress (str) – Type of stress to plot, see below for allowable values
title (str | None) – Plot title, if None uses default plot title for selected stress. Defaults to None.
cmap (str) – Matplotlib color map, see https://matplotlib.org/stable/tutorials/colors/colormaps.html for more detail. Defaults to "coolwarm".
stress_limits (tuple[float, float] | None) – Custom colorbar stress limits (sig_min, sig_max), values outside these limits will appear as white. Defaults to None.
normalize (bool) – If set to True, CenteredNorm is used to scale the colormap, if set to False, the default linear scaling is used. Defaults to True.
fmt (str) – Number formatting string, see https://docs.python.org/3/library/string.html. Defaults to "{x:.4e}".
colorbar_label (str) – Colorbar label. Defaults to "Stress".
alpha (float) – Transparency of the mesh outlines: \(0 \leq \alpha \leq 1\). Defaults to 0.5.
material_list (list[Material] | None) – If specified, only plots materials present in the list. If set to None, plots all materials. Defaults to None.
kwargs (Any) – Passed to plotting_context()

Raises:

RuntimeError – If the plot failed to be generated

Returns:

Matplotlib axes object

Return type:

matplotlib.axes.Axes

Stress contour plotting options

In general the stresses are described by an action followed by a stress direction (action)_(stress-direction), e.g. mzz_zx represents the shear stress in the zx direction caused by the torsion mzz.

Below is a list of the acceptable values for stress:

stress="n_zz" - normal stress \(\sigma_{zz,N}\) resulting from the axial load \(N\)
stress="mxx_zz" - normal stress \(\sigma_{zz,Mxx}\) resulting from the bending moment \(M_{xx}\)
stress="myy_zz" - normal stress \(\sigma_{zz,Myy}\) resulting from the bending moment \(M_{yy}\)
stress="m11_zz" - normal stress \(\sigma_{zz,M11}\) resulting from the bending moment \(M_{11}\)
stress="m22_zz" - normal stress \(\sigma_{zz,M22}\) resulting from the bending moment \(M_{22}\)
stress="m_zz" - normal stress \(\sigma_{zz,\Sigma M}\) resulting from all bending moments \(M_{xx} + M_{yy} + M_{11} + M_{22}\)
stress="mzz_zx" - x component of the shear stress \(\sigma_{zx,Mzz}\) resulting from the torsion moment \(M_{zz}\)
stress="mzz_zy" - y component of the shear stress \(\sigma_{zy,Mzz}\) resulting from the torsion moment \(M_{zz}\)
stress="mzz_zxy" - resultant shear stress \(\sigma_{zxy,Mzz}\) resulting from the torsion moment \(M_{zz}\)
stress="vx_zx" - x component of the shear stress \(\sigma_{zx,Vx}\) resulting from the shear force \(V_{x}\)
stress="vx_zy" - y component of the shear stress \(\sigma_{zy,Vx}\) resulting from the shear force \(V_{x}\)
stress="vx_zxy" - resultant shear stress \(\sigma_{zxy,Vx}\) resulting from the shear force \(V_{x}\)
stress="vy_zx" - x component of the shear stress \(\sigma_{zx,Vy}\) resulting from the shear force \(V_{y}\)
stress="vy_zy" - y component of the shear stress \(\sigma_{zy,Vy}\) resulting from the shear force \(V_{y}\)
stress="vy_zxy" - resultant shear stress \(\sigma_{zxy,Vy}\) resulting from the shear force \(V_{y}\)
stress="v_zx" - x component of the shear stress \(\sigma_{zx,\Sigma V}\) resulting from the sum of the applied shear forces \(V_{x} + V_{y}\).
stress="v_zy" - y component of the shear stress \(\sigma_{zy,\Sigma V}\) resulting from the sum of the applied shear forces \(V_{x} + V_{y}\).
stress="v_zxy" - resultant shear stress \(\sigma_{zxy,\Sigma V}\) resulting from the sum of the applied shear forces \(V_{x} + V_{y}\)
stress="zz" - combined normal stress \(\sigma_{zz}\) resulting from all actions
stress="zx" - x component of the shear stress \(\sigma_{zx}\) resulting from all actions
stress="zy" - y component of the shear stress \(\sigma_{zy}\) resulting from all actions
stress="zxy" - resultant shear stress \(\sigma_{zxy}\) resulting from all actions
stress="11" - major principal stress \(\sigma_{11}\) resulting from all actions
stress="33" - minor principal stress \(\sigma_{33}\) resulting from all actions
stress="vm" - von Mises stress \(\sigma_{vM}\) resulting from all actions

plot_stress_vector(stress: str, title: str | None = None, cmap: str = 'YlOrBr', normalize: bool = False, fmt: str = '{x:.4e}', colorbar_label: str = 'Stress', alpha: float = 0.2, **kwargs: Any) → Axes[source]¶

Plots stress vectors over the finite element mesh.

Parameters:

stress (str) – Type of stress to plot, see below for allowable values
title (str | None) – Plot title, if None uses default plot title for selected stress. Defaults to None.
cmap (str) – Matplotlib color map, see https://matplotlib.org/stable/tutorials/colors/colormaps.html for more detail. Defaults to "YlOrBr".
normalize (bool) – If set to True, CenteredNorm is used to scale the colormap, if set to False, the default linear scaling is used. Defaults to True.
fmt (str) – Number formatting string, see https://docs.python.org/3/library/string.html. Defaults to "{x:.4e}".
colorbar_label (str) – Colorbar label. Defaults to "Stress".
alpha (float) – Transparency of the mesh outlines: \(0 \leq \alpha \leq 1\). Defaults to 0.2.
kwargs (Any) – Passed to plotting_context()

Raises:

RuntimeError – If the plot failed to be generated

Returns:

Matplotlib axes object

Return type:

Axes

Stress vector plotting options

Below is a list of the acceptable values for stress:

stress="mzz_zxy" - resultant shear stress \(\sigma_{zxy,Mzz}\) resulting from the torsion moment \(M_{zz}\)
stress="vx_zxy" - resultant shear stress \(\sigma_{zxy,Vx}\) resulting from the shear force \(V_{x}\)
stress="vy_zxy" - resultant shear stress \(\sigma_{zxy,Vy}\) resulting from the shear force \(V_{y}\)
stress="v_zxy" - resultant shear stress \(\sigma_{zxy,\Sigma V}\) resulting from the sum of the applied shear forces \(V_{x} + V_{y}\)
stress="zxy" - resultant shear stress \(\sigma_{zxy}\) resulting from all actions

get_stress() → list[dict[str, str | ndarray[tuple[Any, ...], dtype[float64]]]][source]¶

Returns the stresses within each material.

Returns:: A list of dictionaries containing the cross-section stresses at each node for each material
Return type:: list[dict[str, str | ndarray[tuple[Any, …], dtype[float64]]]]

Note

Each list of stresses in the dictionary contains the stresses at every node (order from node 0 to node n) in the entire mesh. As a result, when the current material does not exist at a node, a value of zero will be reported.

Dictionary keys and values

Below is a list of the returned dictionary keys and values:

"material" - material name
"sig_zz_n" - normal stress \(\sigma_{zz,N}\) resulting from the axial load \(N\)
"sig_zz_mxx" - normal stress \(\sigma_{zz,Mxx}\) resulting from the bending moment \(M_{xx}\)
"sig_zz_myy" - normal stress \(\sigma_{zz,Myy}\) resulting from the bending moment \(M_{yy}\)
"sig_zz_m11" - normal stress \(\sigma_{zz,M11}\) resulting from the bending moment \(M_{11}\)
"sig_zz_m22" - normal stress \(\sigma_{zz,M22}\) resulting from the bending moment \(M_{22}\)
"sig_zz_m" - normal stress \(\sigma_{zz,\Sigma M}\) resulting from all bending moments \(M_{xx} + M_{yy} + M_{11} + M_{22}\)
"sig_zx_mzz" - x component of the shear stress \(\sigma_{zx,Mzz}\) resulting from the torsion moment \(M_{zz}\)
"sig_zy_mzz" - y component of the shear stress \(\sigma_{zy,Mzz}\) resulting from the torsion moment \(M_{zz}\)
"sig_zxy_mzz" - resultant shear stress \(\sigma_{zxy,Mzz}\) resulting from the torsion moment \(M_{zz}\)
"sig_zx_vx" - x component of the shear stress \(\sigma_{zx,Vx}\) resulting from the shear force \(V_{x}\)
"sig_zy_vx" - y component of the shear stress \(\sigma_{zy,Vx}\) resulting from the shear force \(V_{x}\)
"sig_zxy_vx" - resultant shear stress \(\sigma_{zxy,Vx}\) resulting from the shear force \(V_{x}\)
"sig_zx_vy" - x component of the shear stress \(\sigma_{zx,Vy}\) resulting from the shear force \(V_{y}\)
"sig_zy_vy" - y component of the shear stress \(\sigma_{zy,Vy}\) resulting from the shear force \(V_{y}\)
"sig_zxy_vy" - resultant shear stress \(\sigma_{zxy,Vy}\) resulting from the shear force \(V_{y}\)
"sig_zx_v" - x component of the shear stress \(\sigma_{zx,\Sigma V}\) resulting from the sum of the applied shear forces \(V_{x} + V_{y}\).
"sig_zy_v" - y component of the shear stress \(\sigma_{zy,\Sigma V}\) resulting from the sum of the applied shear forces \(V_{x} + V_{y}\).
"sig_zxy_v" - resultant shear stress \(\sigma_{zxy,\Sigma V}\) resulting from the sum of the applied shear forces \(V_{x} + V_{y}\)
"sig_zz" - combined normal stress \(\sigma_{zz}\) resulting from all actions
"sig_zx" - x component of the shear stress \(\sigma_{zx}\) resulting from all actions
"sig_zy" - y component of the shear stress \(\sigma_{zy}\) resulting from all actions
"sig_zxy" - resultant shear stress \(\sigma_{zxy}\) resulting from all actions
"sig_11" - major principal stress \(\sigma_{11}\) resulting from all actions
"sig_33" - minor principal stress \(\sigma_{33}\) resulting from all actions
"sig_vm" - von Mises stress \(\sigma_{vM}\) resulting from all actions

plot_mohrs_circles(x: float, y: float, title: str | None = None, **kwargs: Any) → Axes[source]¶

Plots Mohr’s circles of the 3D stress state at position (x, y).

Parameters:

x (float) – x-coordinate of the point to draw Mohr’s Circle
y (float) – y-coordinate of the point to draw Mohr’s Circle
title (str | None) – Plot title, if None uses default plot title “Mohr’s Circles for 3D Stress State at {pt}”. Defaults to None.
kwargs (Any) – Passed to plotting_context()

Raises:

ValueError – If the point (x, y) is not within the mesh
RuntimeError – If the plot failed to be generated

Returns:

Matplotlib axes object

Return type:

Axes

Example

The following example plots the Mohr’s circles for the 3D stress state within a 150x90x12 UA section at the point x=10, y=88.9 resulting from the following actions:

\(N = 50\) kN
\(M_{xx} = -5\) kN.m
\(M_{22} = 2.5\) kN.m
\(M_{zz} = 1.5\) kN.m
\(V_{x} = 10\) kN
\(V_{y} = 5\) kN

from sectionproperties.pre.library import angle_section
from sectionproperties.analysis import Section

# create geometry and section
geom = angle_section(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
geom.create_mesh(mesh_sizes=[0])
sec = Section(geometry=geom)

# perform analysis
sec.calculate_geometric_properties()
sec.calculate_warping_properties()
post = sec.calculate_stress(
    n=50e3, mxx=-5e6, m22=2.5e6, mzz=0.5e6, vx=10e3, vy=5e3
)

# plot mohr's circle
post.plot_mohrs_circles(x=10, y=88.9)

(Source code, png, hires.png, pdf)

../_images/sectionproperties-post-stress_post-StressPost-1.png — Mohr’s circles for a 150x90x12 UA¶