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

  • cmap (str) – Matplotlib color map, see https://matplotlib.org/stable/tutorials/colors/colormaps.html for more detail

  • stress_limits (tuple[float, float] | None) – Custom colorbar stress limits (sig_min, sig_max), values outside these limits will appear as white

  • normalize (bool) – If set to True, CenteredNorm is used to scale the colormap, if set to False, the default linear scaling is used

  • fmt (str) – Number formatting string, see https://docs.python.org/3/library/string.html

  • colorbar_label (str) – Colorbar label

  • alpha (float) – Transparency of the mesh outlines: \(0 \leq \alpha \leq 1\)

  • material_list (list[Material] | None) – If specified, only plots materials present in the list. If set to None, plots all materials.

  • 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:
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, object]][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, object]]

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

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 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}”

  • 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#