Modelling methods

class anastruct.fem.system.SystemElements(figsize=(12, 8), EA=15000.0, EI=5000.0, load_factor=1, mesh=50)

Modelling any structure starts with an object of this class.

Variables:

• EA – Standard axial stiffness of elements, default=15,000
• EI – Standard bending stiffness of elements, default=5,000
• figsize – (tpl) Matplotlibs standard figure size
• element_map – (dict) Keys are the element ids, values are the element objects
• node_map – (dict) Keys are the node ids, values are the node objects.
• node_element_map – (dict) maps node ids to element objects.
• supports_fixed – (list) All the fixed supports in the system.
• supports_hinged – (list) All the hinged supports in the system.
• supports_roll – (list) All the roll supports in the system.
• supports_spring_x – (list) All the spring supports in x-direction in the system.
• supports_spring_z – (list) All the spring supports in z-direction in the system.
• supports_spring_y – (list) All the spring supports in y-direction in the system.
• supports_roll_direction – (list) The directions of the rolling supports.
• loads_point – (dict) Maps node ids to point loads.
• loads_q – (dict) Maps element ids to q-loads.
• loads_moment – (dict) Maps node ids to moment loads.
• loads_dead_load – (set) Element ids that have a dead load applied.

Add elements

SystemElements.add_truss_element(location, EA=None)

Add an element that only has axial force.

Parameters:

• location –

  (list/ Vertex) The two nodes of the element or the next node of the element.

  Example:

  location=[[x, y], [x, y]]
  location=[Vertex, Vertex]
  location=[x, y]
  location=Vertex
  

• EA – (flt) EA

Returns:

(int) Elements ID.

SystemElements.add_element(location, EA=None, EI=None, g=0, mp=None, spring=None, **kwargs)

Parameters:

• location –

  (list/ Vertex) The two nodes of the element or the next node of the element.

  Example:

  location=[[x, y], [x, y]]
  location=[Vertex, Vertex]
  location=[x, y]
  location=Vertex
  

• EA – (flt) EA
• EI – (flt) EI
• g – (flt) Weight per meter. [kN/m] / [N/m]
• mp –

  (dict) Set a maximum plastic moment capacity. Keys are integers representing the nodes. Values

  are the bending moment capacity.

  Example:

  mp={1: 210e3,
      2: 180e3}
  

• spring –

  (dict) Set a rotational spring or a hinge (k=0) at node 1 or node 2.

  Example:

  spring={1: k
          2: k}
  
  
  # Set a hinged node:
  spring={1: 0}
  

Returns:

(int) Elements ID.

SystemElements.add_multiple_elements(location, n=None, dl=None, EA=None, EI=None, g=0, mp=None, spring=None, **kwargs)

Add multiple elements defined by the first and the last point.

Parameters:

• location – See ‘add_element’ method
• n – (int) Number of elements.
• dl – (flt) Distance between the elements nodes.
• EA – See ‘add_element’ method
• EI – See ‘add_element’ method
• g – See ‘add_element’ method
• mp – See ‘add_element’ method
• spring – See ‘add_element’ method

Keyword Args:

Parameters:

• element_type – (str) See ‘add_element’ method
• first – (dict) Different arguments for the first element
• last –

  (dict) Different arguments for the last element

  Example:

  last={'EA': 1e3, 'mp': 290}
  

Returns:

(list) Element IDs

SystemElements.add_element_grid(x, y, EA=None, EI=None, g=None, mp=None, spring=None, **kwargs)

Add multiple elements defined by two containers with coordinates.

Parameters:

• x – (list/ np.array) x coordinates.
• y – (list/ np.array) y coordinates.
• EA – See ‘add_element’ method
• EI – See ‘add_element’ method
• g – See ‘add_element’ method
• mp – See ‘add_element’ method
• spring – See ‘add_element’ method

Paramg **kwargs**kwargs:  

See ‘add_element’ method

Returns:

None

SystemElements.discretize(n=10)

Takes an already defined SystemElements object and increases the number of elements.

Parameters:n – (int) Divide the elements into n sub-elements.

Apply forces

SystemElements.point_load(node_id, Fx=0, Fy=0, rotation=0)

Apply a point load to a node.

Parameters:

• node_id – (int/ list) Nodes ID.
• Fx – (flt/ list) Force in global x direction.
• Fy – (flt/ list) Force in global x direction.
• rotation – (flt/ list) Rotate the force clockwise. Rotation is in degrees.

SystemElements.q_load(q, element_id, direction='element')

Apply a q-load to an element.

Parameters:

• element_id – (int/ list) representing the element ID
• q – (flt) value of the q-load
• direction – (str) “element”, “x”, “y”

SystemElements.moment_load(node_id, Ty)

Apply a moment on a node.

Parameters:

• node_id – (int/ list) Nodes ID.
• Ty – (flt/ list) Moments acting on the node.

Supporting conditions

SystemElements.add_support_hinged(node_id)

Model a hinged support at a given node.

Parameters:node_id – (int/ list) Represents the nodes ID

SystemElements.add_support_roll(node_id, direction=2)

Adds a rolling support at a given node.

Parameters:

• node_id – (int/ list) Represents the nodes ID
• direction – (int/ list) Represents the direction that is fixed: x = 1, y = 2

SystemElements.add_support_fixed(node_id)

Add a fixed support at a given node.

Parameters:node_id – (int/ list) Represents the nodes ID

SystemElements.add_support_spring(node_id, translation, k, roll=False)

Add a translational support at a given node.

Parameters:

• translation –

  (int/ list) Represents the prevented translation.

  Note

  1 = translation in x

  2 = translation in z

  3 = rotation in y
• node_id – (int/ list) Integer representing the nodes ID.
• k – (flt) Stiffness of the spring
• roll – (bool) If set to True, only the translation of the spring is controlled.

Find a solution

SystemElements.solve(force_linear=False, verbosity=0, max_iter=200, geometrical_non_linear=False, **kwargs)

Compute the results of current model.

Parameters:

• force_linear – (bool) Force a linear calculation. Even when the system has non linear nodes.
• verbosity – (int) 0. Log calculation outputs. 1. silence.
• max_iter – (int) Maximum allowed iterations.
• geometrical_non_linear – (bool) Calculate second order effects and determine the buckling factor.

Returns:

(array) Displacements vector.

Development **kwargs:

param naked:(bool) Whether or not to run the solve function without doing post processing. param discretize_kwargs:  When doing a geometric non linear analysis you can reduce or increase the number of elements created that are used for determining the buckling_factor

Visual feedback

SystemElements.show_structure(verbosity=0, scale=1.0, offset=(0, 0), figsize=None, show=True, supports=True, values_only=False)

Plot the structure.

Parameters:

• verbosity – (int) 0: All information, 1: Suppress information.
• scale – (flt) Scale of the plot.
• offset – (tpl) Offset the plots location on the figure.
• figsize – (tpl) Change the figure size.
• show – (bool) Plot the result or return a figure.
• supports – (bool) Show the supports.
• values_only – (bool) Return the values that would be plotted as tuple containing two arrays: (x, y)

Returns:

(figure)

SystemElements.show_bending_moment(factor=None, verbosity=0, scale=1, offset=(0, 0), figsize=None, show=True, values_only=False)

Plot the bending moment.

Parameters:

• factor – (flt) Influence the plotting scale.
• verbosity – (int) 0: All information, 1: Suppress information.
• scale – (flt) Scale of the plot.
• offset – (tpl) Offset the plots location on the figure.
• figsize – (tpl) Change the figure size.
• show – (bool) Plot the result or return a figure.
• values_only – (bool) Return the values that would be plotted as tuple containing two arrays: (x, y)

Returns:

(figure)

SystemElements.show_axial_force(factor=None, verbosity=0, scale=1, offset=(0, 0), figsize=None, show=True, values_only=False)

Plot the axial force.

Parameters:

• factor – (flt) Influence the plotting scale.
• verbosity – (int) 0: All information, 1: Suppress information.
• scale – (flt) Scale of the plot.
• offset – (tpl) Offset the plots location on the figure.
• figsize – (tpl) Change the figure size.
• show – (bool) Plot the result or return a figure.
• values_only – (bool) Return the values that would be plotted as tuple containing two arrays: (x, y)

Returns:

(figure)

SystemElements.show_shear_force(factor=None, verbosity=0, scale=1, offset=(0, 0), figsize=None, show=True, values_only=False)

Plot the shear force. :param factor: (flt) Influence the plotting scale. :param verbosity: (int) 0: All information, 1: Suppress information. :param scale: (flt) Scale of the plot. :param offset: (tpl) Offset the plots location on the figure. :param figsize: (tpl) Change the figure size. :param show: (bool) Plot the result or return a figure. :param values_only: (bool) Return the values that would be plotted as tuple containing two arrays: (x, y) :return: (figure)

SystemElements.show_reaction_force(verbosity=0, scale=1, offset=(0, 0), figsize=None, show=True)

Plot the reaction force.

Parameters:

• verbosity – (int) 0: All information, 1: Suppress information.
• scale – (flt) Scale of the plot.
• offset – (tpl) Offset the plots location on the figure.
• figsize – (tpl) Change the figure size.
• show – (bool) Plot the result or return a figure.

Returns:

(figure)

SystemElements.show_displacement(factor=None, verbosity=0, scale=1, offset=(0, 0), figsize=None, show=True, linear=False, values_only=False)

Plot the displacement.

Parameters:

• factor – (flt) Influence the plotting scale.
• verbosity – (int) 0: All information, 1: Suppress information.
• scale – (flt) Scale of the plot.
• offset – (tpl) Offset the plots location on the figure.
• figsize – (tpl) Change the figure size.
• show – (bool) Plot the result or return a figure.
• linear – (bool) Don’t evaluate the displacement values in between the elements
• values_only – (bool) Return the values that would be plotted as tuple containing two arrays: (x, y)

Returns:

(figure)

Numerical feedback

SystemElements.get_node_results_system(node_id=0)

These are the node results. These are the opposite of the forces and displacements working on the elements and may seem counter intuitive.

Parameters:node_id – (integer) representing the node’s ID. If integer = 0, the results of all nodes are returned Returns:

if node_id == 0: (list)

Returns a list containing tuples with the results:

[(id, Fx, Fy, Ty, ux, uy, phi_y), (id, Fx, Fy...), () .. ]

if node_id > 0: (dict)

SystemElements.get_node_displacements(node_id=0)

Parameters:node_id – (int) Represents the node’s ID. If integer = 0, the results of all nodes are returned. Returns:

if node_id == 0: (list)

Returns a list containing tuples with the results:

[(id, ux, uy, phi_y), (id, ux, uy, phi_y),  ... (id, ux, uy, phi_y) ]

if node_id > 0: (dict)

SystemElements.get_node_result_range(unit)

Query a list with node results.

param unit:(str) - ‘uy’ - ‘ux’ - ‘phi_y’

Returns:(list)

SystemElements.get_element_results(element_id=0, verbose=False)

Parameters:

• element_id – (int) representing the elements ID. If elementID = 0 the results of all elements are returned.
• verbose – (bool) If set to True the numerical results for the deflection and the bending moments are returned.

Returns:

if node_id == 0: (list)

Returns a list containing tuples with the results:

[(id, length, alpha, u, N_1, N_2), (id, length, alpha, u, N_1, N_2), ... (id, length, alpha, u, N_1, N_2)]

if node_id > 0: (dict)

SystemElements.get_element_result_range(unit)

Useful when added lots of elements. Returns a list of all the queried unit.

Parameters:unit – (str) - ‘shear’ - ‘moment’ - ‘axial’ Returns:(list)

Utility methods for interacting with the elements and nodes

SystemElements.find_node_id(vertex)

Retrieve the ID of a certain location.

Parameters:vertex – (Vertex/ list/ tpl) Vertex_xz, [x, y], (x, y) Returns:(int/ None) id of the node at the location of the vertex

SystemElements.nodes_range(dimension)

Retrieve a list with coordinates x or z (y).

Parameters:dimension – (str) “both”, ‘x’, ‘y’ or ‘z’ Returns:(list)

SystemElements.nearest_node(dimension, val)

Retrieve the nearest node ID.

Parameters:

• dimension – (str) “both”, ‘x’, ‘y’ or ‘z’
• val – (flt) Value of the dimension.

Returns:

(int) ID of the node.