Fiber Section Mesh

Section mesh class

This is a main class for creating fiber section triangular mesh.

class opstool.pre.section.FiberSecMesh(sec_name='My Section')

A class to mesh the cross-section with triangular fibers.

Parameters

sec_namestr

Assign a name to the section.

add_patch_group(patches)

Add the patches.

Parameters

patchesdict|patch|List[patch]

A dict of name as a key, Geometry as value.

Returns

SecMesh instance

get_patch_group()

Return the group dict for each geometry obj.

Returns

group : dict[str, any]

set_mesh_size(mesh_size)

Assign the mesh size dict for each mesh.

Parameters

mesh_sizedict[str, float] | list[float] | float

The mesh sizes describe the maximum mesh element size to be used in the finite-element mesh for each Geometry object.

• If dict, name as the key, mesh size as value.

• If floated, all geoms will use the same meshsize.

• If list or tuple, the length must be the same as the geoms.

Returns

instance

set_ops_mat_tag(mat_tag)

Assign the opensees mat tag for each mesh.

Parameters

mat_tagdict[str, int] | list[int] | int

• If dict, name as a key, OpenSees matTag previously defined as value.

• If list or tuple, the length must be the same as the geom patches.

• If int, all patches will use the same matTag.

Returns

instance

set_mesh_color(colors)

Assign the color to plot the section.

Parameters

colorsdict[str, str] | list[str|list|tuple] | str

If dict, the patch name as a key, color as value.

mesh()

Mesh the section.

If set_mesh_size has not been invoked, the mesh size of each Geometry will be calculated by its area / 100.

Returns

None

get_fiber_data()

Return fiber data.

Returns

Tuple(dict, dict)

fiber center dict, fiber area dict

get_section()

Return the section object.

Returns

section: Section

add_rebar_points(points, dia, ops_mat_tag=None, color='black', group_name='Rebar')

Add rebars by coord points.

Parameters

points: list[list[float, float]]

A list of rebar coords, [(x1, y1), (x2, y2),…,(xn, yn)], in which each element represents a rebar point.

dia: float

Rebar diameter.

ops_mat_tag: int

OpenSees mat Tag for rebar previously defined.

color: str or rgb tuple.

Color to plot rebar.

group_name: str, default=’Rebar’

Assign rebar group name

Returns

None

add_rebar_line(points, dia, gap=0.1, n=None, closure=False, ops_mat_tag=None, color='black', group_name='Rebar')

Add rebar along a line, can be a line or polygon.

Parameters

points: list[list[float, float]]

A list of rebar coords, [(x1, y1), (x2, y2),…,(xn, yn)], in which each element represents a corner point, and every two corner points are divided by the arg gap.

dia: float

Rebar diameter.

gap: float, default=0.1

Rebar space.

n: int, default=None

The number of rebars, if not None, update the Arg gap according to n. This means that if you know the number of rebars, you don’t need to input gap or set gap to any number.

closure: bool, default=False

If True, the rebar line is a closed loop.

ops_mat_tag: int

OpenSees mat Tag for rebar previously defined.

color: str or rgb tuple.

Color to plot rebar.

group_name: str, default=’Rebar’

Assign rebar group name

Returns

None

add_rebar_circle(xo, radius, dia, gap=0.1, n=None, angles=(0.0, 360), ops_mat_tag=None, color='black', group_name='Rebar')

Add the rebars along a circle.

Parameters

xo: list[float, float]

Center coords of circle, [(xc, yc)].

radius: float

Radius of circle.

dia: float

rebar dia.

gap: float, default=0.1

Rebar space.

n: int, default=None

The number of rebars, if not None, update the Arg gap according to n. This means that if you know the number of rebars, you don’t need to input gap or set gap to any number.

angles: Union[list, tuple], default=[0.0, 360]

The start angle and end angle, degree.

ops_mat_tag: int, defaultt=None

OpenSees material matTag for rebar previously defined.

color: str or rgb tuple.

Color to plot rebar.

group_name: str, default=’Rebar’

Assign rebar group name.

Returns

None

get_rebars_num()

Returns the number of rebars.

Returns

nums: int, number of rebars.

get_rebars_area()

Returns the total area of rebars.

Returns

area: float, total area of rebars.

get_centroid()

Return the centroid.

Returns

centroid: list[float, float], [xc, yc]

get_area()

Return section area. For a single-material section, it is the geometric area, and for a composite section, it is the equivalent area.

Returns

area: float, section area.

get_geom_area()

Return the total geometric area of a section.

Returns

area: float, section area.

get_iy()

Return Moment of inertia of the section around the y-axis.

Returns

iy: float, Moment of inertia of the section around the y-axis.

get_iz()

Return Moment of inertia of the section around the z-axis.

Returns

iz: float, Moment of inertia of the section around the z-axis.

get_j()

Return section torsion constant.

Returns

j: float, section torsion constant.

get_dist_from_centroid()

Return the distance from section edge to the centroid.

Returns

list, [ztop, zbot, yright, yleft]

z axis top, z axis bottom, y-axis right, y-axis left

get_sec_props(Eref=1.0, display_results=False, fmt='8.3E', plot_centroids=False)

Solving Section Geometry Properties by Finite Element Method, by sectionproperties pacakge. See sectionproperties results

This command may be slower. If you don’t need features such as shear area, you can use method get_frame_props().

Parameters

Eref: float, default=1.0

Reference modulus of elasticity, it is important to analyze the composite section. If it is not a composite section, please ignore this parameter.

display_resultsbool, default=True

whether to display the results.

fmtstr, optional

Number formatting string when display_results=True.

plot_centroidsbool, default=False

whether to plot centroids.

Returns

sec_props: dict

section props dict, including:

• Cross-sectional area (A)

• Shear area (Asy, Asz)

• Elastic centroid (centroid)

• Second moments of area about the centroidal axis (Iy, Iz, Iyz)

• Elastic section moduli about the centroidal axis with respect to the top and bottom fibres (Wyt, Wyb, Wzt, Wzb)

• Torsion constant (J)

• Principal axis angle (phi)

• Section mass (mass), only true if material density is defined, otherwise geometric area (mass density is 1)

• ratio of reinforcement (rho_rebar)

Note

If it is not a composite section, please ignore the Eref parameter; Otherwise, please use the Eref parameter, all section properties will be transformed according to the reference material, and the mechanical properties of the reference material are then used in the practical analysis.

Note that according to the OpenSees convention, the x-axis refers to the normal direction of the section, the y-axis refers to the abscissa, and the z-axis refers to the ordinate direction.

get_frame_props(Eref=1.0, display_results=False, fmt='8.3E')

Calculates and returns the properties required for a frame analysis. See sectionproperties frame_properties

This method is fast, but cannot calculate the shear area compared to the method get_sec_props().

Parameters

Eref: float, default=1.0

Reference modulus of elasticity, it is important to analyze the composite section. If it is not a composite section, please ignore this parameter. See https://sectionproperties.readthedocs.io/en/latest/user_guide/results.html#label-material-affects-results

display_resultsbool, default=True

whether to display the results.

fmtstr, optional

Number formatting string when display_results=True.

Returns

sec_props: dict

section props dict, including:

• Cross-sectional area (A)

• Elastic centroid (centroid)

• Second moments of area about the centroidal axis (Iy, Iz, Iyz)

• Elastic section moduli about the centroidal axis with respect to the top and bottom fibers (Wyt, Wyb, Wzt, Wzb)

• Torsion constant (J)

• Principal axis angle (phi)

• Section mass (mass), only true if material density is defined, otherwise geometric area (mass density is 1)

• ratio of reinforcement (rho_rebar)

Note

If it is not a composite section, please ignore the Eref parameter; Otherwise, please use the Eref parameter, all section properties will be transformed according to the reference material, and the mechanical properties of the reference material are then used in the practical analysis.

Note that according to the OpenSees convention, the x-axis refers to the normal direction of the section, the y-axis refers to the abscissa, and the z-axis refers to the ordinate direction.

display_all_results(Eref=1.0, fmt='8.6e')

Prints all results that have been calculated by sectionproperties to the terminal.

Parameters

Eref: float, default=1.0

Reference modulus of elasticity, it is important to analyze the composite section. If it is not a composite section, please ignore this parameter. See sectionproperties document

fmtstr, optional

Number formatting string.

get_stress(N=0, Vy=0, Vz=0, Myy=0, Mzz=0, Mxx=0, plot_stress='all', cmap='YlOrBr', normalize=False, fmt='{x:.4e}', colorbar_label='Stress', alpha=0.75, **kargs)

Calculates the cross-section stress resulting from design actions and returns a list of dictionaries containing the cross-section stresses for each region by method assign_group().

Note

This function is only available for elastic stress analysis, and reinforcement is ignored. The stresses are realistic only if you specify the correct material for each geometry region.

Parameters

Nfloat, optional

Axial force, by default 0

Vyfloat, optional

Shear force acting in the y-direction, by default 0

Vzfloat, optional

Shear force acting in the z-direction, by default 0

Myyfloat, optional

Bending moment about the centroidal yy-axis, by default 0

Mzzfloat, optional

Bending moment about the centroidal zz-axis, by default 0

Mxxfloat, optional

Torsion moment about the centroidal xx-axis, by default 0

plot_stressstr, optional

plot the various cross-section stresses, by default None. Note that according to the OpenSees convention, the x-axis refers to the normal direction of the section, the y-axis refers to the abscissa, and the z-axis refers to the ordinate direction. Optional as follows (if plot_stress=”all”, will plot all stress types):

• Combined Stress Plots:

  • “xx”–combined normal stress resulting from all actions;

  • “xy”–y-component of the shear stress resulting from all actions;

  • “xz”– z-component of the shear stress resulting from all actions;

  • “xyz”–resultant shear stress resulting from all actions;

  • “p1”–major principal stress resulting from all actions;

  • “p3”– Minor principal stress resulting from all actions;

  • “vm”–von Mises stress resulting from all actions;

• Primary Stress Plots:

  • “n_xx”–normal stress resulting from the axial load N;

  • “myy_xx”–normal stress resulting from the bending moment Myy;

  • “mzz_xx”–normal stress resulting from the bending moment Mzz;

  • “m_xx”–normal stress resulting from all bending moments Myy+Mzz;

  • “mxx_xy”–y-component of the shear stress resulting from the torsion moment Mxx;

  • “mxx_xz”–z-component of the shear stress resulting from the torsion moment Mxx;

  • “mxx_xyz”–resultant shear stress resulting from the torsion moment Mxx;

  • “vy_xy”–y-component of the shear stress resulting from the shear force Vy;

  • “vy_xz”–z-component of the shear stress resulting from the shear force Vy;

  • “vy_xyz”–resultant shear stress resulting from the shear force Vy;

  • “vz_xy”–y-component of the shear stress resulting from the shear force Vz;

  • “vz_xz”–z-component of the shear stress resulting from the shear force Vz;

  • “vz_xyz”–resultant shear stress resulting from the shear force Vz;

  • “v_xy”–y-component of the shear stress resulting from the sum of the applied shear forces Vy+Vz;

  • “v_xz”–z-component of the shear stress resulting from the sum of the applied shear forces Vy+Vz;

  • “v_xyz”–resultant shear stress resulting from the sum of the applied shear forces Vy+Vz;

cmapstr, optional

Matplotlib color map, by default ‘coolwarm’

normalizebool, optional

If set to true, the CenteredNorm is used to scale the colormap. If set to false, the default linear scaling is used., by default True

fmt: str

Number formatting string, see here

colorbar_label: str, default=’Stress’

Colorbar label

alpha: float, default=0.75

Transparency of the mesh outlines

Returns

list[dict]:

A list of dictionaries containing the cross-section stresses for each region by method assign_group().

centring()

Move the section centroid to (0, 0).

Returns

None

rotate(theta=0)

Rotate the section clockwise.

Parameters

thetafloat, default=0

Rotation angle, unit: degree.

Returns

None

to_opspy_cmds(secTag, GJ=None, G=None)

Generate openseespy fiber section command.

Parameters

secTagint

The section tag assigned in OpenSees.

GJ: float, default = None

Torsion stiffness. Note that at least one of GJ and G needs to be specified, and if both, it will be calculated by GJ.

G: float, default = None

Shear modulus. The program automatically calculates the torsion constant. Note that at least one of GJ and G needs to be specified, and if both, it will be calculated by GJ.

Returns

None

to_file(output_path, secTag, GJ=None, G=None, fmt=':.6E')

Output the opensees fiber code to file.

Parameters

output_pathstr

The filepath to save, e.g., r “my_dir/my_section.py”

Note

Notes that output_path must be endswith .py or .tcl, function will create the file by the right style.

secTagint

The section tag assigned in OpenSees.

GJ: float, default = None

Torsion stiffness. Note that at least one of GJ and G needs to be specified, and if both, it will be calculated by GJ.

G: float, default = None

Shear modulus. The program automatically calculates the torsion constant. Note that at least one of GJ and G needs to be specified, and if both, it will be calculated by GJ.

fmtstr, default = “:.6E”

Formatting style for floating point numbers.

Returns

None

view(fill=True, show_legend=True, ax=None)

Display the section mesh.

Parameters

fillbool, default=True

Whether to fill the trangles.

show_legend: bool, default=True

Whether to show the legend.

axmatplotlib.axes.Axes, optional

The axes to plot the section mesh.

Returns

None

opstool.pre.section.SecMesh

alias of FiberSecMesh

Utility functions for creating geometry and materials

opstool.pre.section.create_material(name='default', elastic_modulus=1.0, poissons_ratio=0.0, yield_strength=1.0, density=1.0, color='w')

Create a meterial object of sectionproperties material.

Parameters

namestr, default=’default’

meterial name.

elastic_modulusfloat, default==1

elastic_modulus.

poissons_ratiofloat, default=0

poissons_ratio

yield_strengthfloat, default==1

yield_strength

densityfloat, default=1

mass density

color: str, default=’w’

plot color by sectionproperties.

Returns

sectionproperties material

opstool.pre.section.create_polygon_patch(outline, holes=None, material=None)

Add a polygon plane geom object.

Parameters

outlinelist[list[float, float]]

The coords list of polygon points, [(x1, y1), (x2, y2),…,(xn, yn)]

holes: list[list[list[float, float]]].

Hole of the section, a list of multiple hole coords, [hole1, hole2,…holeN], holeN=[(x1, y1), (x2, y2),…,(xn, yn)].

material: material obj

The instance from opstool.pre.section.create_material()

Returns

geometry:

Geometry in

sectionproperties.

opstool.pre.section.create_circle_patch(xo, radius, holes=None, angle1=0.0, angle2=360, n_sub=40, material=None)

Add the circle geom obj.

Parameters

xolist[float, float]

Center coords, [(xc, yc)].

radius: float

radius.

holes: list[list[list[float, float]]].

Hole of the section, a list of multiple hole coords, [hole1, hole2,…holeN], holeN=[(x1, y1), (x2, y2),…,(xn, yn)].

angle1float

The start angle, degree

angle2float

The end angle, deree

n_sub: int

The partition number of the perimeter.

material: material obj

The instance from opstool.pre.section.create_material().

Returns

geometry:

Geometry in

sectionproperties.

opstool.pre.section.create_patch_from_dxf(filepath, spline_delta=0.1, degrees_per_segment=1)

An interface for the creation of Geometry objects from CAD .dxf files. See sectionproperties docs.

Parameters

filepath: str|path

A path-like object for the dxf file.

spline_delta: float, default = 0.1

Splines are not supported in shapely, so they are approximated as polylines, this argument affects the spline sampling rate.

degrees_per_segment: float, default = 1

The number of degrees discretized as a single line segment.

Returns

geometry:

Geometry in

sectionproperties.

opstool.pre.section.create_polygon_points(start=(0.0, 0.0), incrs=None, close=False)

Create a polygon points.

Parameters

startlist[float, float]

The start point, [x0, y0].

incrslist[list[float, float]], default=None

The increment points, [[dx1, dy1], [dx2, dy2],…,[dxn, dyn]].

closebool, default=False

Close the polygon or not.

Returns

points: list[list[float, float]]

coord points on the polygon line.

opstool.pre.section.create_circle_points(xo, radius, angles=(0.0, 360), n_sub=40)

Add the circle geom obj.

Parameters

xolist[float, float]

Center coords, [(xc, yc)].

radius: float

radius.

anglesUnion[list, tuple], default=(0.0, 360)

The start angle and the end angle, deree

n_sub: int, default=40

The partition number of the perimeter.

Returns

points: list[list[float, float]]

coord points on arc line.

opstool.pre.section.offset(points, d)

Offsets closed polygons.

Parameters

pointslist[list[float, float]]

A list containing the coordinate points, [(x1, y1),(x2, y2),…,(xn.yn)].

dfloat

Offsets closed polygons, positive values offset inwards, negative values outwards.

Returns

coords: list[[float, float]], new offset points.

Examples

>>> import opstool as opst
>>> outlines1 = [[0, 0], [0, 1], [1, 1]]
>>> outlines2 = opst.pre.section.offset(outlines1, d=0.1)
>>> outlines3 = [[0, 0], [0, 1], [1, 1], [1, 0]]
>>> outlines4 = opst.pre.section.offset(outlines3, d=0.1)

opstool.pre.section.line_offset(points, d)

Offset a distance from a non-closed line ring on its right or its left side.

Parameters

pointslist[list[float, float]]

A list containing the coordinate points, [(x1, y1),(x2, y2),…,(xn.yn)].

dfloat

Offsets non-closed line ring, negative for left side offset, positive for right side offset.

Returns

coords: list[[float, float]]

Examples

>>> import opstool as opst
>>> lines = [[0, 0], [0, 1]]
>>> lines2 = opst.pre.section.line_offset(lines, d=0.1)
>>> lines = [[0, 0], [0, 1], [1, 1]]
>>> lines3 = opst.pre.section.line_offset(lines, d=0.1)
>>> lines = [[0, 0], [0, 1], [1, 0]]
>>> lines4 = opst.pre.section.line_offset(lines, d=0.1)

opstool.pre.section.poly_offset(points, d)

Offsets closed polygons, same as opstool.pre.section.offset()

Parameters

pointslist[list[float, float]]

A list containing the coordinate points, [(x1, y1),(x2, y2),…,(xn.yn)].

dfloat

Offsets closed polygons, positive values offset inwards, negative values outwards.

Returns

coords: list[[float, float]]

opstool.pre.section.set_patch_material(geom, material=Material(name='default', elastic_modulus=1, poissons_ratio=0, yield_strength=1, density=1, color='w'))

Assign material to a geom patch.

Parameters

geom: geom obj | list[geom obj]

The geometry object.

material: material obj | list[material obj]

The material object of opstool.pre.section.create_material().

opstool.pre.section.vis_fiber_sec_real(ele_tag, sec_num=1, color=None, show_matTag=False, highlight_matTag=None, highlight_color='k', ax=None)

Visualizing the actual fiber section data, where only the fiber center coordinates and areas are demonstrated, represents the data used in analysis.

Note

This is applicable for 3D only and not for 2D!

Parameters

ele_tagint

The element ID to which the section belongs, for display purposes.

sec_numint

The section at which Gauss points to display, numbered starting from 1, from i to segment j.

color: str, optional

Defaults to gradient colors, varying based on the distance to the section’s center point.

show_matTagbool, optional

Whether to show the material tag on the fiber. Defaults to False.

highlight_matTagfloat or list of floats

The material tag to highlight, if any. Defaults to None. If listed, then highlight all the materials in the list.

highlight_colorstr or array-like, optional

Color for highlight_matTag. Defaults to gradient colors, varying based on the distance to the section’s center point.

axmatplotlib.axes.Axes, optional

The axes to plot the section. Defaults to None.

Wrapper for OpenSeesPy section commands

The following commands wrap the fiber section-related commands in OpenSeesPy. These commands retain the same functionality as the original commands but additionally save the user-provided input data for purposes such as visualization.

opstool.pre.section.section(*args)

args see section command

opstool.pre.section.fiber(*args)

args see fiber command

opstool.pre.section.patch(*args)

args see patch command

opstool.pre.section.layer(*args)

args see layer command

opstool.pre.section.plot_fiber_sec_cmds(sec_tag, title='My Section', label_size=18, tick_size=15, title_size=20)

Plot the fiber section by section tag.

Parameters

sec_tagint

section tag in the OpenSeesPy domain.

titlestr, optional

Title of plot, by default “My Section”

label_sizeint, optional

Axis label size, by default 18

tick_sizeint, optional

Axis tick size, by default 15

title_sizeint, optional

Title size, by default 20

Example

import numpy as np
import openseespy.opensees as ops
import opstool as opst

ops.wipe()
ops.model("basic", "-ndm", 3, "-ndf", 6)
ops.uniaxialMaterial("Elastic", 1, 1000)

The following commands, like those in OpenSeesPy, create objects in the domain.

sectag = 1
opst.pre.section.section("Fiber", sectag, "-GJ", 1.0e6)
opst.pre.section.patch("circ", 1, 40, 1, 0, 0, 1.9, 2, 0, 360, color="blue", opacity=0.75)
opst.pre.section.patch("circ", 1, 40, 5, 0, 0, 1, 1.9, 0, 360, color="green", opacity=0.35)
opst.pre.section.layer("circ", 1, 40, np.pi * 0.016**2, 0, 0, 1.9 - 0.016, 0.0, 360.0, color="red")
# plot
opst.pre.section.plot_fiber_sec_cmds(sec_tag=1)

Let’s look at another example.

sectag = 2
opst.pre.section.section("Fiber", sectag, "-GJ", 1.0e6)
opst.pre.section.patch("quad", 1, 20, 20, -1, -1, 1, -1, 2, 3, -2, 3, color="blue", opacity=0.25)
opst.pre.section.layer(
    "straight", 1, 20, np.pi * 0.02**2, *[-0.9, -0.9], *[1.9, 2.9], color="black"
)
opst.pre.section.fiber(0, 1, np.pi * 0.05**2, 1, color="red")
# plot
opst.pre.section.plot_fiber_sec_cmds(sec_tag=2)