๐Ÿ“ Mesh๏ƒ

Mesh๏ƒ

../_images/mesh.png
class fibermat.mesh.Mesh(*args, **kwargs)๏ƒ

A class inherited from pandas.DataFrame to represent a mesh structure for a set of discontinuous fibers.

It defines:

  • the beam elements (intra-fiber connections).

  • the constraint elements (inter-fiber connections).

Parameters๏ƒ

netpandas.DataFrame, optional

Fiber network represented by a Net object.

Other Parameters๏ƒ

kwargs :

Additional keyword arguments ignored by the function.

Note

The constructor calls init() method if the object is instantiated with parameters. Otherwise, initialization is performed with the pandas.DataFrame constructor.

Use:
>>> # Generate a set of fibers
>>> mat = Mat(100)
>>> # Build the fiber network
>>> net = Net(mat)
>>> # Create the fiber mesh
>>> mesh = Mesh(net)
>>> mesh
      fiber          s          x          y          z  beam  constraint
0         0 -12.500000  -1.176401  -3.074404 -24.338157     1           0
1         0 -11.222534  -0.806746  -1.851590 -24.338157     2         752
2         0 -10.466114  -0.587864  -1.127531 -24.338157     3         123
3         0 -10.009779  -0.455816  -0.690719 -24.338157     4        1519
4         0  -5.432013   0.868835   3.691203 -24.338157     5         706
...     ...        ...        ...        ...        ...   ...         ...
1729     99   6.159453 -21.379789  -8.424815  24.516947  1730        1094
1730     99   6.740970 -21.060169  -8.910618  24.516947  1731         157
1731     99   7.284437 -20.761462  -9.364634  24.516947  1732        1294
1732     99  11.270660 -18.570503 -12.694751  24.516947  1733        1585
1733     99  12.500000 -17.894817 -13.721749  24.516947  1716        1733

[1734 rows x 7 columns]

Data๏ƒ

  • indexpandas.Index

    Node label. Each label refers to a unique node.

  • Node:
    • fiberpandas.Series

      Label of the fiber to which the node belongs

    • spandas.Series

      Node curvilinear abscissa along the fiber (mm).

  • Node position:
    • xpandas.Series

      X-coordinate of the node (mm).

    • ypandas.Series

      Y-coordinate of the node (mm).

    • zpandas.Series

      Z-coordinate of the node (mm).

  • Elements:
    • constraintpandas.Series

      Index of the connected node. It defines a constraint on the relative node positions.

    • beampandas.Series

      Index of the next node along the fiber. It defines a mechanical beam element.

Attributes๏ƒ

attrs :

Global attributes of DataFrame.

Methods๏ƒ

init() :

Create a discontinuous fiber mesh.

check() :

Check that a Mesh object is defined correctly.

property attrs๏ƒ
Global attributes of DataFrame:
  • nint

    Number of fibers. By default, it is empty (n = 0).

  • sizefloat

    Box dimensions (mm). By default, the domain is a 50 mm square cube.

  • periodicbool

    Boundary periodicity. By default, the domain is periodic.

  • thresholdfloat, optional

    Threshold distance value for proximity detection (mm).

check()๏ƒ

Check that a Mesh object is defined correctly.

This method is called when a Mesh object is initialized.

Raises๏ƒ

KeyError

If any keys are missing from the columns of Mesh object.

AttributeError

If any attributes are missing from the dictionary attrs.

IndexError
If row indices are incorrectly defined:

  • Row indices are not unique in [0,โ€ฆ, m-1] where m is the number of nodes.

  • Node labels are not sorted.

TypeError

If labels are not integers.

ValueError

If fibers, beams or constraints are ill-defined, improperly connected or not sorted.

Returns๏ƒ

bool

Indicates whether the object can be instantiated as Mesh.

Tip

  • If self is None, it returns an empty Mesh object.

  • If a โ€œskip_checkโ€ flag is True in attrs, the check is passed.

static init(net=None, **kwargs)๏ƒ

Create a discontinuous fiber mesh.

Parameters๏ƒ

netpandas.DataFrame, optional

Fiber network represented by a Net object.

Returns๏ƒ

meshpandas.DataFrame

Initialized Mesh object.

Other Parameters๏ƒ

kwargs :

Additional keyword arguments ignored by the function.

Example๏ƒ

from fibermat import *

# Generate a set of fibers
mat = Mat(100)
# Build the fiber network
net = Net(mat)
# Create the fiber mesh
mesh = Mesh(net)

# Check data
Mesh.check(mesh)  # or `mesh.check()`
# -> returns True if correct, otherwise it raises an error.

# Figure
fig, ax = plt.subplots(subplot_kw=dict(projection='3d', aspect='equal',
                                       xlabel="X", ylabel="Y", zlabel="Z"))
ax.view_init(azim=45, elev=30, roll=0)
if len(mesh):
    # Draw elements
    for i, j, k in tqdm(zip(mesh.index, mesh.beam, mesh.constraint),
                        total=len(mesh), desc="Draw mesh"):
        # Get element data
        a, b, c = mesh.iloc[[i, j, k]][[*"xyz"]].values
        if mesh.iloc[i].s < mesh.iloc[j].s:
            # Draw intra-fiber connection
            plt.plot(*np.c_[a, b],
                     c=plt.cm.tab10(mesh.fiber.iloc[i] % 10))
        if mesh.iloc[i].z < mesh.iloc[k].z:
            # Draw inter-fiber connection
            plt.plot(*np.c_[a, c], '--ok',
                     lw=1, mfc='none', ms=3, alpha=0.2)
        if mesh.iloc[i].fiber == mesh.iloc[k].fiber:
            # Draw fiber end nodes
            plt.plot(*np.c_[a, c], '+k', ms=3, alpha=0.2)
# Set drawing box dimensions
ax.set_xlim(-0.5 * mesh.attrs["size"], 0.5 * mesh.attrs["size"])
ax.set_ylim(-0.5 * mesh.attrs["size"], 0.5 * mesh.attrs["size"])
plt.show()
../_images/mesh.png