beam_networks package

Contents

beam_networks package#

Submodules#

beam_networks.assembly module#

beam_networks.assembly.assemble_global_system(nodes_positions, edges_indices, dr, beam_prop, sorted_edges=True, vectorize=True, matrix='bsr', verbose=False)#

Assembly of the global stiffness matrix for a Timoshenko beam network (wrapper)

Parameters:

  • nodes_positions (np.ndarray) – Nodal coordinates

  • edges_indices (np.ndarray (of ints)) – Edge connectivity

  • dr (np.ndarray) – Edge vectors

  • beam_prop (dict) – Beam properties (cross section and elastic properties)

  • sorted_edges (bool, optional) – Edge indices are sorted (the default is True)

  • vectorize (bool, optional) – Collect all element stiffness matrices in a large array before assembly. Faster, but may cause memory issues for very large systems (the default is True).

  • matrix (str, optional) – Format of the global stiffness matrix during assembly. Choose from [‘bsr’, ‘lil’, ‘dense’]. ‘bsr’ : Block sparse row matrix (Default) ‘lil’ : List of lists ‘dense’: Only for small matrices

  • verbose (bool, optional) – Verbosity (the default is False which hides the progress bar)

Returns:

The global matrix

Return type:

np.ndarray or scipy.sparse.bsr_array

beam_networks.bc module#

beam_networks.fracture module#

class beam_networks.fracture.FractureProblem(*args, save_trajectory=False, no_output=False, **kwargs)#

Bases: BeamNetwork

failure_criterion(name='vM')#
property removed_edges#

List of inactive edges.

Returns:

Inactive edges indices

Return type:

list

run(mode='cascade', sign=-1, dist=None, fail_crit='vM', no_output=False)#
write()#

Wrapper for different output writers. Currently only calls HDF5 output.

beam_networks.geo module#

beam_networks.geo.get_geometric_props(beam_prop)#

Get geometric properties of the beam cross section.

Parameters:

beam_prop (dict) – Beam properties (cross section and elastic properties)

Returns:

  • float – Second moment of area Iy

  • float – Second moment of area Iz

  • float – Second polar moment of area Ip

  • float – Area

  • float – Shear correction factor

  • float – Maximum distance from beam neutral axis to the surface

beam_networks.geo.get_geometric_props_derivative(beam_prop, derivative)#

Get derivative of geometric properties of the beam cross section with respect to radius

Parameters:

  • beam_prop (dict) – Beam properties (cross section and elastic properties)

  • derivative (bool) – if not None returns the derivative with respect to a shape parameter. The shape parameter is determined by the value of derivative which depends on the shape of your beam.

Returns:

  • float – Derivative of second moment of area Iy

  • float – Derivative of second moment of area Iz

  • float – Derivative of second polar moment of area Ip

  • float – Derivative of area

  • float – Derivative of shear correction factor

  • float – Derivative of maximum distance from beam neutral axis to the surface

beam_networks.io module#

beam_networks.network module#

class beam_networks.network.Network(nodes_positions, edges_indices, periodic=None, boxsize=None, valid=True)#

Bases: object

Base class for network structure.

Contains methods to generate lattice structures and some basic properties of the network.

property Lx#

Boxlength (x)

Return type:

float

property Ly#

Boxlength (y)

Return type:

float

property Lz#

Boxlength (z)

Return type:

float

property bondlengths#
property bounds#

Lower and upper bounds of the nodal coordinates

Returns:

xlo, xhi, ylo, yhi[, zlo, zhi]

Return type:

list

property boxsize#
property coordination#

Mean coordination number.

Return type:

float

property edge_vectors#
property edges#

Exposes only active edges.

Return type:

np.ndarray

classmethod generate_bowtie_lattice(a=1.0, w=0.1, bbox=[1.0, 1.0])#

Generates a bowtie lattice.

Parameters:

  • a (float, optional) – Lattice constant (distance between nearest neighbors)

  • bbox (array-like) – Size of the bounding box, filled with repeated unit cells (the default is [1., 1., 1.])

Returns:

Class instance with nodes and edges given by the prescribed lattice

Return type:

beam_networks.network.Network

classmethod generate_cubic_lattice(a=1.0, pbc=None, bbox=[1.0, 1.0, 1.0], lattice_type='sc')#

Generates a cubic lattice.

Parameters:

  • a (float, optional) – Lattice constant (distance between nearest neighbors)

  • pbc (iterable, optional) – Periodic boundary conditions (the default is None, which means no periodic BCs).

  • bbox (array-like) – Size of the bounding box, filled with repeated unit cells (the default is [1., 1., 1.])

  • lattice_type (str, optional) – Name of the lattice type [‘sc’, ‘bcc’, ‘fcc’] (the default is ‘sc’)

Returns:

Class instance with nodes and edges given by the prescribed lattice

Return type:

beam_networks.network.Network

classmethod generate_square_lattice(a=1.0, bbox=[1.0, 1.0], lattice_type='sc')#

Generates a cubic lattice.

Parameters:

  • a (float, optional) – Lattice constant (distance between nearest neighbors)

  • bbox (array-like) – Size of the bounding box, filled with repeated unit cells (the default is [1., 1., 1.])

  • lattice_type (str, optional) – Name of the lattice type [‘sc’, ‘bcc’, ‘fcc’] (the default is ‘sc’)

Returns:

Class instance with nodes and edges given by the prescribed lattice

Return type:

beam_networks.network.Network

property is_connected#

Check if structure is fully connected

Return type:

bool

property nodes#

Exposes only activated nodes.

Return type:

np.ndarray

property num_edges#

Number of active edges

Return type:

int

property num_nodes#

Number of active nodes

Return type:

int

property pbc_edges#

Mask for edges that cross periodic boundary conditions.

Return type:

np.ndarray

property pbc_nodes#

Nodal positions for edges that cross periodic boundary conditions. Nodes are shifted to the neighboring periodic images for visualization purposes.

Returns:

Nodal coordinates

Return type:

np.ndarray

property volume#

Compute volume of network as convex hull.

Return type:

float

property xhi#
property xlo#
property yhi#
property ylo#
property zhi#
property zlo#

beam_networks.problem module#

class beam_networks.problem.BeamNetwork(nodes, edges, beam_prop={'E': 1.0, 'name': 'circle', 'nu': 0.3, 'radius': 1.0}, periodic=None, boxsize=None, valid=True, options={'matrix': 'bsr', 'vectorize': True, 'verbose': True}, outdir='.', assemble_on_init=True)#

Bases: Network

Beam Network structure. Derives from Network.

Adding a cross section and elastic properties to the edges of a network makes it a beam network. Solves the elastic problem given appropriate boundary conditions.

add_BC(name, type, select, selection, vector, active=True, num_per_point=1)#

Add boundary condition.

Parameters:

  • name (str) – Name/Identifier of the BC

  • type (str) – BC type, either ‘D’ for Dirichlet or ‘N’ for Neumann

  • select (str) – How to select nodes, either ‘box’, ‘node’, or ‘point’

  • selection (array-like) – For box selection: lower and upper limits of bounding box in relative units, i.e. [xlo, xhi, ylo, yhi[, zlo, zhi]]. None entries cooresponds to the min/max limits, e.g. [None, None, 0.5, None, None, None] means upper half of the domain in the y-direction. For node selection: list of nodes.

  • vector (array-like) – Vector of length 3 and 6 for 2D and 3D systems, respectively. None means the corresponding DOF is not affected. In 2D: [ux, uy, tz] (Dircihlet) or [Fx, Fy, Mz] (Neumann) In 3D: [ux, uy, uz, tx, ty, tz] (Dircihlet) or [Fx, Fy, Fz, Mx, My, Mz] (Neumann)

  • num_per_point (int) – For point selection only, maximum number of closest nodes to select. The default is 1.

assemble_BCs()#
compute_equivalent_stress(mode='mean')#

Calculate von Mises stress and store it in self._sVM.

Parameters:

mode (str) – Either ‘max’ or ‘mean’, i.e. calculate maximum or mean stress per beam

Return type:

None

compute_principal_stresses(mode='max')#
compute_ratio()#
delete_BC(name)#

Delete boundary condition.

Parameters:

name (str) – Name of the BC to be removed

property displaced_edge_vectors#
property displaced_nodes#
property displacement#

Nodal displacements

Returns:

Shape (num_nodes, dim)

Return type:

numpy.ndarray

property dof_per_node#
property has_bc#
property has_stiffness#
classmethod load(filename, recompute=True)#

Create a class instance from a tar archive.

Parameters:

filename (str) – Name of the archive

Returns:

A new class instance

Return type:

BeamNetwork

modify_BC(name, vector)#

Modify an existing BC by changing its vector. This does not change the constraint DOFs, i.e. vector needs to have ‘None’ in the same place as before. Useful for stepwise change of a load/displacement

Parameters:

  • name (str) – Name of the BC to be removed

  • vector (array-like) – Vector of length 3 and 6 for 2D and 3D systems, respectively. None means the corresponding DOF is not affected. In 2D: [ux, uy, tz] (Dircihlet) or [Fx, Fy, Mz] (Neumann) In 3D: [ux, uy, uz, tx, ty, tz] (Dircihlet) or [Fx, Fy, Fz, Mx, My, Mz] (Neumann)

property num_dof#
plot(ax, node_ids=False, contour=None, cax=None, aspect=1.0, lim=None, lw=2.0, scale=1.0)#

Generate 2D plot of the deformed network structure.

Parameters:

  • ax (matplotlib.pyplot.axis object) – Axis to plot into

  • node_ids (bool, optional) – Print node numbers nect to undeformed structure (the default is False)

  • contour (numpy.ndarray, optional) – Scalar field to plot as color on edges (the default is None, which means no coloring)

  • cax (matplotlib.pyplot.axis object or None, optional) – Axis to plot colorbar into if contour is not None (the default is None, which takes space from ax)

  • aspect (float, optional) – Aspect ratio (the default is 1.)

  • lim (tuple, optional) – Colorbar limits (the default is None, which takes the limits of contour)

Returns:

The plotted axis

Return type:

matplotlib.pyplot.axis object

property rotation#

Nodal rotations

Returns:

Shape (num_nodes, 3) for 3D; (num_nodes, 1) for 2D

Return type:

numpy.ndarray

save(filename)#

Save the current state of the solver as gzipped tar archive

Parameters:

filename (str) – Name of the archive

scale_BC(type, factor)#

Scale all BCs of a certain type by a given factor

Parameters:

  • type (str) – BC type (either ‘D’ or ‘N’)

  • factor (float) – factor

scale_solution(scale_factor)#
solve(solver=None, stress_mode='mean', preconditioner=None, verbosity=0)#

Solve the linear system.

Stores the solution for all DOFs and computes the reaction forces at constraint DOFs

Parameters:

  • solver (str, optional) – Type of solver to use, currently ‘direct’ and ‘cg’ available (the default is ‘direct’)

  • stress_mode (str) – Either ‘max’ or ‘mean’, i.e. calculate maximum or mean von Mises stress per beam

  • preconditioner (str, optional) – Type of preconditioner, ‘diagonal’ or None (the default is None)

  • verbosity (int, optional) – level of verbosity, if between 25/50 print information about displacements and reaction forces, if between 50/100 print information about stiffness matrix, if greater equal 100 print condition number (default is 0). Only active for sparse matrices.

Raises:

RuntimeError – System can only be solved if boundary conditions are given.

property stiffness#

Global stiffness matrix

Return type:

numpy.ndarray or scipy.sparse.csr_array

to_stl(file, clean=False, tol=1e-06)#
to_vtk(file='foo.vtk')#

Write structure and possibly solution to VTK file

Parameters:

file (str, optional) – Output filename (the default is “foo.vtk”)

beam_networks.solve module#

beam_networks.solve.solve(K, bc_D, d_D, bc_N, F_N, solver='direct', preconditioner=None, verbosity=0)#

Solve the linear system.

Parameters:

  • K (np.ndarry or scipy.sparse.csr_matrix) – Stiffness matrix

  • bc_D (iterable) – List of constraint DOFs (Dirichlet BCs)

  • d_D (iterable) – List of constraint DOF values (Dirichlet BCs)

  • bc_N (iterable) – List of DOFs with nonzero loads (Neumann BCs)

  • F_N (iterable) – List of DOF values with nonzero loads (Neumann BCs)

  • solver (str, optional) – Type of solver, ‘direct’ or ‘cg’ (the default is ‘direct’)

  • preconditioner (str, optional) – Type of preconditioner, ‘diagonal’ or None (the default is None). Only active for sparse matrices.

  • verbosity (int, optional) – level of verbosity, if between 25/50 print information about displacements and reaction forces, if between 50/100 print information about stiffness matrix, if greater equal 100 print condition number (default is 0). Only active for sparse matrices.

Returns:

  • d (np.ndarray) – Global solution vector

  • F (np.ndarray) – Global load vector

  • info (int) – Info about numerical solution, 0 if successful

beam_networks.stiffness module#

beam_networks.stiffness.get_element_stiffness_global(beam_prop, d, derivative=None)#

Single element stiffness matrix in global frame.

Parameters:

  • beam_prop (dict) – Beam properties (cross section and elastic constants)

  • d (np.ndarray) – Vector pointing from one beam endpoint to the other

  • sparse (bool, optional) – Return as sparse matrix if true (the default is True)

  • derivative (None or int) – if not None returns the derivative with respect to a shape parameter. The shape parameter is determined by the value of derivative which depends on the shape of your beam.

Returns:

Element stiffness matrix in global frame

Return type:

np.ndarray or

beam_networks.stiffness.get_element_stiffness_global_vec(beam_prop, d_vec, derivative=None)#

Get all element stiffness matrices in the global frame.

Parameters:

  • beam_prop (dict) – Beam properties (cross section and elastic constants)

  • d (np.ndarray) – Vectors pointing from one beam endpoint to the other

  • derivative (None or int) – if not None returns the derivative with respect to a shape parameter. The shape parameter is determined by the value of derivative which depends on the shape of your beam.

Returns:

Array with shape (num_elements, num_elem_dof, num_elem_dof)

Return type:

np.ndarray

beam_networks.stiffness.get_element_stiffness_local_vec(beam_prop, d, ndim, derivative=None)#

Get all element stiffness matrices in the local frame (w.o. transformation)

Parameters:

  • beam_prop (dict) – Beam properties (cross section and elastic constants)

  • d (np.ndarray) – Edge lengths

  • ndim (int) – Dimension of the problem

  • derivative (None or int) – if not None returns the derivative with respect to a shape parameter. The shape parameter is determined by the value of derivative which depends on the shape of your beam.

Returns:

Array with shape (num_elements, num_elem_dof, num_elem_dof)

Return type:

np.ndarray

beam_networks.stress module#

beam_networks.stress.get_element_mises_stress(coords, adj, d_vec, sol, beam_prop, rot=None, mode='max', return_ratio=False)#

Compute the von Mises stress for all beam elements

Parameters:

  • coords (np.ndarray) – Nodal positions

  • adj (np.ndarray) – Edges indices

  • d_vec (np.ndarray) – Edge vectors

  • sol (np.ndarray) – Global solution vector

  • beam_prop (dict) – Beam properties

  • rot (np.ndarray or None, optional) – If all elements have the same orientation, rot is the transformation matrix from the global to the local frame (the default is None).

  • mode (str, optional) – Either ‘max’ or ‘mean’, i.e. calculate maximum or mean stress per beam (the default is ‘max’).

Returns:

Von Mises stress

Return type:

np.ndarray

beam_networks.stress.get_element_principal_stress(coords, adj, d_vec, sol, beam_prop, rot=None, mode='max')#
Parameters:

  • coords (np.ndarray) – Nodal positions

  • adj (np.ndarray) – Edges indices

  • d_vec (np.ndarray) – Edge vectors

  • sol (np.ndarray) – Global solution vector

  • beam_prop (dict) – Beam properties

  • rot (np.ndarray or None, optional) – If all elements have the same orientation, rot is the transformation matrix from the global to the local frame (the default is None).

  • mode (str, optional) – Either ‘max’ or ‘mean’, i.e. calculate maximum or mean stress per beam (the default is ‘max’).

Return type:

np.ndarray

beam_networks.stress.principal_stress(rhs, beam_prop, mode)#

Compute element-wise principal stress.

Principal stress values are sorted in decreasing order along the second axis.

Parameters:

  • rhs (np.ndarray) – Element-wise right-hand side in local frame

  • beam_prop (dict) – Beam properties

  • mode (str) – Either ‘max’ or ‘mean’, i.e. calculate maximum or mean stress per beam

Returns:

Principal stresses per beam (shape: (n_beams, 3))

Return type:

np.ndarry

beam_networks.stress.stretch_bend_ratio(rhs, beam_prop)#
beam_networks.stress.vmises_stress(rhs, beam_prop, mode)#

Wrapper for von Mises stress calculation

Parameters:

  • rhs (np.ndarray) – Element-wise right-hand side in local frame

  • beam_prop (dict) – Beam properties

  • mode (str) – Either ‘max’ or ‘mean’, i.e. calculate maximum or mean stress per beam

Returns:

Von Mises stress, shape=(num_elements,)

Return type:

np.ndarray

beam_networks.tesselate module#

beam_networks.tesselate.renumber_adjacency(adj, indices_delete)#

Renumber the indices by adjusting the counting for deleted nodes.

Parameters:

  • adj (np.array) – adjacency matrix.

  • indices_delete (np.array) – indices to be deleted.

Returns:

adj – updated adjacency.

Return type:

np.array

beam_networks.tesselate.sanity_checks(coords, adj, cell, overlap=True, overlap_tol=1e-05, connected=True, duplicate_bonds=True)#

Check a given network of nodes for consistency.

Parameters:

  • coords (np.ndarray) – coordinates of shape (n_nodes,ndim).

  • adj (np.ndarray) – adjacency list of shape (n_bonds,2).

  • cell (None or np.ndarray, optional) – cell lengths of shape (ndim). If None infer from coordinates (max-min).

  • overlap (bool, optional) – check for overlapping nodes via cKDTree.

  • overlap_tol (float, optional) – tolerance for detecting overlaps.

  • connected (bool, optional) – check whether all nodes are connected.

  • duplicate_bonds (bool, optional) – check for duplicate bonds.

Raises:

AssertionError – if any discrepancies (overlapping nodes, disconnected network, duplicate bonds) detected.

beam_networks.tesselate.tesselate(coords, adj, rep, cell=None, pbc=False, overlap_tol=1e-08, debug=False)#

Repeat unit cell in each direction. Currently implemented by copying coordinates and adjacency cell repeatedly and then detecting overlapping nodes via a cKDTree. The overlapping nodes are reduced to one node which overtakes all the connections from the overlapping nodes. Then the overlapping nodes are deleted and the adjacency matrix renumbered to account for deleted nodes.

Parameters:

  • coords (np.ndarray) – coordinates of shape (n_nodes,ndim).

  • adj (np.ndarray) – adjacency list of shape (n_bonds,2).

  • rep (list or np.ndarray) – number of repetitions in each direction

  • cell (None or np.ndarray, optional) – cell lengths of shape (ndim). If None infer from coordinates (max-min).

  • pbc (bool or list, optional) – Collect all element stiffness matrices in a large array before assembly. Faster, but may cause memory issues for very large systems (the default is True).

  • overlap_tol (float, optional) – tolerance for detecting overlaps.

  • debug (bool, optional) – print out information for debugging.

Returns:

  • coords (np.ndarray) – coordinates of shape (n_nodes_tesselate,ndim).

  • adj (np.ndarray) – adjacency list of shape (n_bonds_tesselate,2).

  • cell (np.ndarray) – cell lengths of shape (ndim).

beam_networks.utils module#

beam_networks.utils.box_selection(nodes, lim)#

Select nodes which are within a cuboid.

Parameters:

  • nodes (np.ndarray) – Nodal coordinates

  • lim (iterable) – Lower and upper bounds of the cuboid

Returns:

Masking array for nodes

Return type:

np.ndarray

beam_networks.utils.check_input_dict(container, keys, defaults, allowed)#

Sanitize output settings

Parameters:

options (dict) – Output settings

Returns:

Sanitized output settings

Return type:

dict

beam_networks.utils.get_edges_from_disks(file, cutoff=3.0, atol=1e-05)#

Get adjacency matrix from a collextion of hard disks in 2D

The input file has the format:

L n_1, x_1, y_1, r_1 n_2, x_2, y_2, r_2 … n_n, x_n, y_n, r_n

where n_* denotes the disk index (1 based, will be shifted to zero), x_*, y_* are the coordinates, and r_* the radius of the disk

Parameters:

  • file (str) – Filename

  • cutoff (float, optional) – Distance cutoff to check for possible neighbors (the default is 3.)

  • atol (float, optional) – Absoulte tolerance for comparison between distance and composite radius of possibly neighboring disks (the default is 1e-5)

Returns:

  • np.ndarray – Nodes

  • np.ndarray – Edges

  • float – Lx

  • float – Ly

beam_networks.utils.point_selection(nodes, point, num=1)#

Select nodes which are closest to a given point.

Parameters:

  • nodes (np.ndarray) – Nodal coordinates

  • point (array-like) – Coordinates of the point

  • num (int) – Number of points. The default is 1.

Returns:

Masking array for nodes

Return type:

np.ndarray

beam_networks.utils.zero_pad_2d_array(arr)#

beam_networks.viz module#

beam_networks.viz.plot_solution_1D(ax, d, s, length=1.0)#

Plot a 1D solution along a 1D beam (composed of more than one element)

Parameters:

  • ax (matplotlib.pyplot.axis object) – Axis to plot into

  • d (np.ndarray) – Solution (ux[0], uy[0], theta_z[0], …)

  • s (np.ndarray) – Von Mises stress per element

  • length (float, optional) – Length of the beam (the default is 1.)

beam_networks.viz.vtk2img(wdir=None, dpi=300, cbar_global_lim=False, ftype='png')#

Module contents#

Contents