Base class for multidomain#

Multi-Domain semi-analytical method (panels.multidomain)#

class panels.multidomain.MultiDomain(panels, conn=None)#

Class for multi-domain semi-analytical approach

This class has some useful methods that will help plotting output for different panel groups within the multi-domain and so forth.

For more details about the theory involved, see Castro and Donadon (2017) [castro2017Multidomain] .

Parameters:
panelsiterable

A list, tuple etc of Shell objects.

conndict

A connectivity dictionary.

Methods

calc_damaged_stiffness(dmg_index, k_i)

Calculate the reduced stiffness given the damage index

calc_kC([conn, c, silent, finalize, inc])

Calculate the constitutive stiffness matrix of the assembly --- this is kP (made by diagonally assemblying kP_i from the MD paper)

calc_kG([c, silent, finalize])

Calculate the geometric stiffness matrix of the assembly

calc_k_dmg(c, pA, pB, nr_x_gauss, ...[, ...])

Calculate the damaged k_tsl and the damage index

calc_results(c[, group, vec, gridx, gridy, ...])

Contour plot for a Ritz constants vector.

calc_separation(res_pan_top, res_pan_bot)

Calculates the separation between two panels

calc_traction_stiffness(kw_tsl, ...)

Calculates traction for the approach where SB_TSL connection is used

force(c, group, eval_panel[, x_cte_force, ...])

Calculate the force along a line (xcte or ycte)

get_kC_conn([conn, finalize, c, kw_tsl])

Stiffness matrix due to the multidomain connectivities

get_size()

Size of K of a single panel

plot([c, group, invert_y, vec, filename, ...])

Contour plot for a Ritz constants vector.

strain(c, group[, gridx, gridy, NLterms, ...])

Calculate the strain field

stress(c, group[, gridx, gridy, NLterms, ...])

Calculate the stress field

update_TSL_history(curr_max_dmg_index)

Used to update the maximum del_d (over all loading histories) - this prevents exisiting damage from vanishing when the updated separation predicts there is less separation than what was present earlier (as badly modelled self-healing materials aren't part of this thesis :) )

uvw(c, group[, gridx, gridy, nr_x_gauss, ...])

Calculate the displacement field

calc_fext

calc_fint

calc_kM

calc_kT

force_out_plane

force_out_plane_damage

Notes

Concerning the conn dictionary, the key ‘func’ stands for the connection function that builds the compatibility relations between the panels.

The connections functions available are:

  • ‘SSycte’ : defines a skin-skin connection for const x and calls the following functions fkCSSycte11, fkCSSycte12, fkCSSycte22

  • ‘SSxcte’ : defines a skin-skin connection for const y and calls the following functions fkCSSxcte11, fkCSSxcte12, fkCSSxcte22

  • ‘SB’ : defines a skin-base connection and calls the following functions fkCBFycte11, fkCBFycte12, fkCBFycte22

  • ‘BFycte’: defines a base-flange connection and calls the following functions fkCBFycte11, fkCBFycte12, fkCBFycte22

Explanations about the connetion functions are found in connections module.

Examples

>>> panel_1 = Shell(*args)
>>> panel_2 = Shell(*args)
>>> panel_3 = Shell(*args)
>>> panels = [panel_1, panel_2]
>>> conn = [
        dict(p1=panel_1, p2=panel_2, func='SSxcte', xcte1=0, xcte2=panel_2.a),
        dict(p1=panel_2, p2=panel_3, func='SSycte', ycte1=0, ycte2=panel_3.b)
        ] # A list of dictionary that indicates two connections: (panel_1-panel_2) and (panel_2-panel_3)

xcte1 = location (x const) in panel 1 which connects to panel 2 xcte2 = ……………………… 2 ………………….. 2

>>> md = MultiDomain(panels, conn)

Point or distributed forces or displacements can be easily added by using one of the methods:

With this, calculating the stiffness matrix, external force vector and solving the systems becomes straightforward:

>>> kC = md.calc_kC()
>>> fext = md.calc_fext()

Solving with the Python module structsolve:

>>> from structsolve import static
>>>
>>> incs, cs = static(k0, fext, silent=True)

And plotting the results for the group named 'skin'.

>>> md.plot(cs[0], 'skin', filename='tmp_cylinder_compression_lb_Nxx_cte.png')

The group name attribute belongs to each domain, and is passed while instantiating the :class:.Shell object. Furthermore, it is important to pass the correct relative position of each domain within the group for generating consistent plots. For examples on how to create complex multidomains, see create_cylinder() and create_cylinder_blade_stiffened().

calc_damaged_stiffness(dmg_index, k_i)#

Calculate the reduced stiffness given the damage index

Parameters:
dmg_indexTYPE

DESCRIPTION.

k_iTYPE, optional

DESCRIPTION. The default is None.

Returns:
None.
calc_kC(conn=None, c=None, silent=True, finalize=True, inc=1.0)#

Calculate the constitutive stiffness matrix of the assembly — this is kP (made by diagonally assemblying kP_i from the MD paper)

Parameters:
conndict, optional

A connectivity dictionary. Optional if already defined for the assembly.

carray-like or None, optional

This must be the result of a static analysis, used to compute non-linear terms based on the actual displacement field.

silentbool, optional

A boolean to tell whether the log messages should be printed.

finalizebool, optional

Asserts validity of output data and makes the output matrix symmetric, should be False when assemblying.

incfloat, optional

Dummy argument needed for non-linear analyses.

calc_kG(c=None, silent=False, finalize=True)#

Calculate the geometric stiffness matrix of the assembly

Parameters:
carray-like or None, optional

This must be the result of a static analysis, used to compute non-linear terms based on the actual displacement field.

silentbool, optional

A boolean to tell whether the log messages should be printed.

finalizebool, optional

Asserts validity of output data and makes the output matrix symmetric, should be False when assemblying.

calc_k_dmg(c, pA, pB, nr_x_gauss, nr_y_gauss, tsl_type, prev_max_dmg_index, k_i=None, tau_o=None, G1c=None)#

Calculate the damaged k_tsl and the damage index

Input:

prev_max_dmg_index = Max damage index per integration point for the previous converged NR iteration

NOTE: Currently this only works for 1 contact region bec of the way del_d is being stored in the

MD object. To ensure that it works for multiple connected domamins, it needs to be stored with the shell object instead and modify the rest accordingly

calc_results(c, group=None, vec='w', gridx=50, gridy=50, nr_x_gauss=None, nr_y_gauss=None, eval_panel=None, x_cte_force=None, y_cte_force=None)#

Contour plot for a Ritz constants vector.

Parameters:
cnp.ndarray

The Ritz constants that will be used to compute the field contour.

groupstr

A group to plot. Each panel in panels should contain an attribute group, which is used to identify which entities should be plotted together.

vecstr, optional

Variable that needs to be calculated Can be one of the components:

  • Displacement: 'u', 'v', 'w', 'phix', 'phiy'

  • Strain: 'exx', 'eyy', 'gxy', 'kxx', 'kyy', 'kxy', 'gyz', 'gxz'

  • Stress: 'Nxx', 'Nyy', 'Nxy', 'Mxx', 'Myy', 'Mxy', 'Qy', 'Qx'

gridxint, optional

Number of points along the \(x\) axis where to calculate the displacement field.

gridyint, optional

Number of points along the \(y\) where to calculate the displacement field.

use_gauss_pointsbool, optional

Uses the gauss integration points (x_gauss and y_gauss) to evaluate the fields

nr_x_gauss, nr_y_gaussArray

Number of gauss sampling points along x and y respectively where the displacement field is to be calculated Either one of nr_x_gauss and nr_y_gauss needs to be specified or both When specified, stress_gauss_points and strain_gauss points are called instead

eval_panelShell object

Used to evaluate results for a single panel (that is passed) instead of an entire group of panels

x_cte_force or y_cte_forcefloat

Constant \(x\) or \(y\) coordinate of a line at which the force is to be calculated. Coordinates are relative to specific panel, i.e. \(0 \le x \le a\), \(0 \le y \le b\).

calc_separation(res_pan_top, res_pan_bot)#

Calculates the separation between two panels

INPUT ARGUMENTS:

res_pan_A,B

!!!!!! PANEL TOP NEEDS TO BE THE ONE ON THE TOP !!!!!!!

calc_traction_stiffness(kw_tsl, corrected_max_del_d)#

Calculates traction for the approach where SB_TSL connection is used

force(c, group, eval_panel, x_cte_force=None, y_cte_force=None, gridx=50, gridy=50, NLterms=True, nr_x_gauss=None, nr_y_gauss=None)#

Calculate the force along a line (xcte or ycte)

Parameters:
cfloat

The full set of Ritz constants

groupstr
Dummy variable in this function - just used to avoid changing the stress

function when results for a single panel need to be evaluated

A group to plot. Each panel in panels should contain an

attribute group, which is used to identify which entities should be plotted together.

eval_panelShell object

Used to evaluate results for a single panel (that is passed) instead of an entire group of panels

x_cte_force or y_cte_forcefloat

Constant \(x\) or \(y\) coordinate of a line at which the force is to be calculated. Coordinates are relative to specific panel, i.e. \(0 \le x \le a\), \(0 \le y \le b\).

gridxint, optional

Number of points along the \(x\) axis where to calculate the displacement field.

gridyint, optional

Number of points along the \(y\) where to calculate the displacement field.

NLtermsbool

Flag to indicate whether non-linear strain components should be considered.

nr_x_gauss, nr_y_gaussint

Number of gauss sampling points along \(x\) and \(y\), respectively. The displacement field is to be calculated along either one of nr_x_gauss or nr_y_gauss.

Returns:
outdict

A dict containing many np.ndarrays, with the keys: (Fxx, Fyy, Fxy).

get_kC_conn(conn=None, finalize=True, c=None, kw_tsl=None)#

Stiffness matrix due to the multidomain connectivities

These are based on penalty stiffnesses, as detailed in Castro and Donadon (2017) [castro2017Multidomain] .

conn = List of dicts

Each elem of the list = dict for a single connection pair Each dict contains info of that specific with connection pair

Example: conn = [dict(p1=top1, p2=top2, func=’SSxcte’, xcte1=top1.a, xcte2=0)]

For func, possible options are:

‘SSxcte’ and ‘SSycte’ = between 2 skins along an edge ‘BFxcte’ and ‘BFycte’ = between stiffener base and flange ‘SB’ = btwn 2 skins connected over an area ‘SB_TSL’ = btwn 2 skins connected over an area with a TSL introduced

at the interface

Required param:

tsl_type, nr_x_gauss, nr_x_gauss

get_size()#

Size of K of a single panel

plot(c=None, group=None, invert_y=False, vec='w', filename='', ax=None, figsize=(3.5, 2.0), save=True, title='', identify=False, show_boundaries=False, boundary_line='--k', boundary_linewidth=1.0, colorbar=False, cbar_nticks=10, cbar_format=None, cbar_title='', cbar_fontsize=7, colormap='jet', aspect='equal', clean=True, dpi=400, texts=[], xs=None, ys=None, gridx=50, gridy=50, num_levels=400, vecmin=None, vecmax=None, nr_x_gauss=None, nr_y_gauss=None, res=None, silent=True, display_zero=False, flip_plot=False, eval_panel=None)#

Contour plot for a Ritz constants vector.

Parameters:
cnp.ndarray or None

The Ritz constants that will be used to compute the field contour.

groupstr or None

A group to plot. Each panel in panels should contain an attribute group, which is used to identify which entities should be plotted together.

vecstr, optional

Can be one of the components:

  • Displacement: 'u', 'v', 'w', 'phix', 'phiy'

  • Strain: 'exx', 'eyy', 'gxy', 'kxx', 'kyy', 'kxy', 'gyz', 'gxz'

  • Stress: 'Nxx', 'Nyy', 'Nxy', 'Mxx', 'Myy', 'Mxy', 'Qy', 'Qx'

invert_ybool, optional

Inverts the \(y\) axis of the plot.

savebool, optional

Flag telling whether the contour should be saved to an image file.

dpiint, optional

Resolution of the saved file in dots per inch.

filenamestr, optional

The file name for the generated image file. If no value is given, the \(name\) parameter of the Shell object will be used.

axAxesSubplot, optional

When ax is given, the contour plot will be created inside it.

figsizetuple, optional

The figure size given by (width, height).

titlestr, optional

If any string is given a title is added to the contour plot.

indentifybool, optional

If domains should be identified. If yes, the name of each panel is used.

show_boundariesbool, optional

If boundaries between domains should be drawn.

boundary_linestr, optional

Matplotlib string to define line type and color.

boundary_linewidthfloat, optional

Matplotlib float to define line width.

colorbarbool, optional

If a colorbar should be added to the contour plot.

cbar_nticksint, optional

Number of ticks added to the colorbar.

cbar_format[ None | format string | Formatter object ], optional

See the matplotlib.pyplot.colorbar documentation.

cbar_titlestr, optional

Colorbar title. If cbar_title == '' no title is added.

cbar_fontsizeint, optional

Fontsize of the colorbar labels.

colormapstring, optional

Name of a matplotlib available colormap.

aspectstr, optional

String that will be passed to the AxesSubplot.set_aspect() method.

cleanbool, optional

Clean axes ticks, grids, spines etc.

xsnp.ndarray, optional

The \(x\) positions where to calculate the displacement field. Default is None and the method _default_field is used.

ysnp.ndarray, optional

The y positions where to calculate the displacement field. Default is None and the method _default_field is used.

gridxint, optional

Number of points along the \(x\) axis where to calculate the displacement field.

gridyint, optional

Number of points along the \(y\) where to calculate the displacement field.

num_levelsint, optional

Number of contour levels (higher values make the contour smoother).

vecminfloat, optional

Minimum value for the contour scale (useful to compare with other results). If not specified it will be taken from the calculated field.

vecmaxfloat, optional

Maximum value for the contour scale.

calc_data_onlybool, optional

If only calculated data should be returned.

nr_x_gauss, nr_y_gaussint

Number of gauss sampling points along x and y respectively where the displacement field is to be calculated Either one of nr_x_gauss and nr_y_gauss needs to be specified or both When specified, uvw_gauss_points, stress_gauss_points and strain_gauss points are called instead

calc_res_field_onlybool, optional

Only calcuates the result fields and returns it back

reswhatever data the stress, strain and uvw functions output, optional

Contains the results of a previous run. If results already exist, then they’re not computed again

silentbool, optional

True = doesnt print any messages

display_zerobool, optional

Decides whether 0 should be displayed as a tick in the colour bar or not

flip_plotbool, optional

Flips plot so that x axis is now horizontal

Returns:
axmatplotlib.axes.Axes

The Matplotlib object that can be used to modify the current plot if needed.

datadict

Data calculated during the plotting procedure.

strain(c, group, gridx=50, gridy=50, NLterms=True, nr_x_gauss=None, nr_y_gauss=None, eval_panel=None)#

Calculate the strain field

The strain field consists of in-plane strains (\(\varepsilon_{xx}\), \(\varepsilon_{yy}\), \(\gamma_{xy}\)) and curvatures (\(\kappa_{xx}\), \(\kappa_{yy}\), \(\kappa_{xy}\)) at each point over the grid of interest. The size of the grid is defined using gridx and gridy. In the multidomain assembly, each domain will have a corresponding grid defined by this amount of points.

Parameters:
cfloat

The full set of Ritz constants

groupstr

A group to plot. Each panel in panels should contain an attribute group, which is used to identify which entities that should be plotted together.

gridxint, optional

Number of points along the \(x\) axis, where the strain field is calculated.

gridyint, optional

Number of points along the \(y\) axis, where the strain field is calculated.

NLtermsbool

Flag to indicate whether non-linear strain components should be considered.

nr_x_gauss, nr_y_gaussint

Number of gauss sampling points along x and y respectively where the field is to be calculated. Either one of nr_x_gauss or nr_y_gauss needs to be specified, or both. They can be different.

eval_panelShell object

Used to evaluate results for a single panel (that is passed) instead of an entire group of panels.

Returns:
outdict

A dictionary of np.ndarrays with the keys: (x, y, exx, eyy, gxy, kxx, kyy, kxy). Each has the shape: (no_panels_in_group) x gridx x gridy

stress(c, group, gridx=50, gridy=50, NLterms=True, nr_x_gauss=None, nr_y_gauss=None, eval_panel=None, x_cte_force=None, y_cte_force=None)#

Calculate the stress field

The stress field consists of in-plane distributed forces (Nxx, Nyy, Nxy) and distributed moments (Mxx, Myy, Mxy) at each point over the grid of interest. The size of the grid is defined using gridx and gridy. In the multidomain assembly, each domain will have a corresponding grid defined by this amount of points.

Parameters:
cfloat

The full set of Ritz constants

groupstr

A group to plot. Each panel in panels should contain an attribute group, which is used to identify which entities should be plotted together.

gridxint, optional

Number of points along the \(x\) axis where to calculate the displacement field.

gridyint, optional

Number of points along the \(y\) where to calculate the displacement field.

NLtermsbool

Flag to indicate whether non-linear strain components should be considered.

nr_x_gauss, nr_y_gaussint

Number of gauss sampling points along x and y respectively where the displacement field is to be calculated Either one of nr_x_gauss and nr_y_gauss needs to be specified or both Both can be different

eval_panelShell object

Used to evaluate results for a single panel (that is passed) instead of an entire group of panels

Returns:
outdict

A dict containing many np.ndarrays, with the keys: (x, y, Nxx, Nyy, Nxy, Mxx, Myy, Mxy).

update_TSL_history(curr_max_dmg_index)#

Used to update the maximum del_d (over all loading histories) - this prevents exisiting damage from vanishing when the updated separation predicts there is less separation than what was present earlier (as badly modelled self-healing materials aren’t part of this thesis :) )

uvw(c, group, gridx=50, gridy=50, nr_x_gauss=None, nr_y_gauss=None, eval_panel=None)#

Calculate the displacement field

For a given full set of Ritz constants c, the displacement field is calculated and stored in the parameters u, v, w, phix, phiy of the Shell object.

Parameters:
cfloat

The full set of Ritz constants

groupstr

A group to plot. Each panel in panels should contain an attribute group, which is used to identify which entities should be plotted together.

gridxint, optional

Number of points along the \(x\) axis where to calculate the displacement field.

gridyint, optional

Number of points along the \(y\) where to calculate the displacement field.

nr_x_gauss, nr_y_gaussint

Number of gauss sampling points along x and y respectively where the displacement field is to be calculated Either one of nr_x_gauss and nr_y_gauss needs to be specified or both Both can be different

eval_panelShell object

Used to evaluate results for a single panel (that is passed) instead of an entire group of panels

Returns:
outtuple

A tuple of np.ndarrays containing (xs, ys, u, v, w, phix, phiy).

Notes

The returned values u`, v, w, phix, phiy are stored as parameters with the same name in the Shell object.

Applications of multidomain#