Core

Core regroups the general purpose tools of the Truss package.

Nodes

class truss.core.Node(coords=array([ 0., 0.]), label=None, force=array([ 0., 0.]), block=array([False, False], dtype=bool), block_side=1)

Creates a node.

Parameters:
  • coords (length 2 float array) – coordinates of the node.
  • force (length 2 float array) – external force applied on the node.
  • block (length 2 boolean array) – bloked degrees of freedom.
  • label (string) – label of the node.
 
>>> from truss.core import Node
>>> A = Node((1.,5.), label = "A", block = (False, True) )
Node.data()

Returns the data associated with the node as a pandas.Series object.

>>> A.data()
block   bx    True
        by    True
coords  x        0
        y        0
disp    ux       0
        uy       0
force   Fx   -2000
        Fy   -1000
label   o        A
dtype: object

Bars

class truss.core.Bar(n1, n2, section=1.0, modulus=1.0, density=1.0, yield_stress=0.001)

A bar class.

Parameters:
  • n1 (truss.core.Node instance.) – start node of the bar.
  • n2 (truss.core.Node instance.) – end node of the bar.
  • section (float) – cross section of the bar.
  • modulus (float) – Young’s modulus of the bar’s constitutive material.
  • density (float) – density of the bar’s constitutive material.
  • yield_stress (float) – yield_stress of the bar’s constitutive material.
 
>>> from truss.core import Node, Bar, Model
>>> m = Model()
>>> A = m.add_node((0., 1.), label = "A")
>>> B = m.add_node((1., 1.), label = "B")
>>> b = Bar(A, B, section = 1., modulus = 210.e9, density = 7800.)
>>> b
<Bar: (0.0, 1.0) -> (1.0, 1.0), S = 1.0, E = 2.1e+11, rho = 7800.0>
Bar.data()

Returns the data associated with the bar as a pandas.Series.

>>> AB.data()
conn       c1                     A
           c2                     B
direction  dx                     0
           dy                     1
geometry   length                 1
           volume            0.0001
props      density             2700
           mass                0.27
           section           0.0001
state      elongation    4.7619e-05
           strain        4.7619e-05
           stress             1e+07
           tension             1000
dtype: object
Bar.length(deformed=False)

Returns the length of the bar.

Parameters:deformed (Bool) – False for undeformed configuration, True for deformed configuration.
Return type:float
Bar.volume()

Returns the (undeformed) volume of the bar.

Return type:float
Bar.mass()

Returns the mass of the bar.

Return type:float
Bar.direction(deformed=False)

Returns the unit vector corresponding to the direction of the bar from start to end.

Return type:length 2 array
Bar.normal(deformed=False)

Returns the unit vector corresponding to the normal direction of the bar.

Return type:length 2 array
Bar.stiffness()

Returns the stiffness of the bar.

Return type:float
Bar.stiffness_matrix()

Returns stiffness matrix of the bar.

Return type:(4,4) array 
>>> from truss.core import Node, Bar, Model
>>> m = Model()
>>> B = m.add_node((0., 1.), label = "B")
>>> A = m.add_node((0., 0.), label = "A")
>>> b = Bar(A, B)
>>> b.stiffness_matrix()
array([[ 0.,  0.,  0.,  0.],
       [ 0.,  1.,  0., -1.],
       [ 0.,  0.,  0.,  0.],
       [ 0., -1.,  0.,  1.]])

Models

class truss.core.Model

Truss model

Model.data(at='nodes')

Returns the data associated with the bars/nodes a dataframe.

Inputs:

  • at: should be ‘nodes’ or ‘bars’
>>> m.data(at = "nodes")
    block        coords            disp              force       label
    bx     by      x  y           ux           uy    Fx    Fy     o
0   True   True      0  0            0            0 -2000 -1000     A
1   True  False      0  1            0   4.7619e-05  1000     0     B
2  False  False      1  0  9.52381e-05  0.000277544  1000  1000     C
3  False  False      1  1            0  0.000277544     0     0     D

>>> m.data(at = "bars")
    conn    direction           geometry                props                            c1 c2        dx        dy   length       volume density      mass section   
0    A  B         0         1        1       0.0001    2700      0.27  0.0001   
1    A  C         1         0        1       0.0001    2700      0.27  0.0001   
2    B  C  0.707107 -0.707107  1.41421  0.000141421    2700  0.381838  0.0001   
3    C  D         0         1        1       0.0001    2700      0.27  0.0001   
4    B  D         1         0        1       0.0001    2700      0.27  0.0001   
         state                                         
    elongation       strain       stress      tension  
0   4.7619e-05   4.7619e-05        1e+07         1000  
1  9.52381e-05  9.52381e-05        2e+07         2000  
2 -9.52381e-05 -6.73435e-05 -1.41421e+07     -1414.21  
3 -5.42101e-20 -5.42101e-20 -1.13841e-08 -1.13841e-12  
4            0            0            0            0
Model.add_node(node, *args, **kwargs)

Adds a node to the model. If node is an instance of the truss.core.node, it is added. If node an length 2 array containing, a node instance is created and node it is used as coordinates and other arguments can be provided as well.

Parameters:node (array or truss.core.node instance.) – node label or node. 
>>> m = truss.core.Model()
>>> A = m.add_node((1., 3.), label = "A")
<Node A: x = 1.0, y = 3.0>
>>> B = truss.core.Node((4., 5.), label = "B")
>>> m.add_node(B)
<Node B: x = 4.0, y = 5.0>
Model.add_bar(*args, **kwargs)

Add a bar to the model.

>>> from truss.core import Node, Bar, Model
>>> m = Model()
>>> B = m.add_node((0., 1.), label = "B")
>>> A = m.add_node((0., 0.), label = "A")
>>> b = Bar(A, B)
Model.add_node(node, *args, **kwargs)

Adds a node to the model. If node is an instance of the truss.core.node, it is added. If node an length 2 array containing, a node instance is created and node it is used as coordinates and other arguments can be provided as well.

Parameters:node (array or truss.core.node instance.) – node label or node. 
>>> m = truss.core.Model()
>>> A = m.add_node((1., 3.), label = "A")
<Node A: x = 1.0, y = 3.0>
>>> B = truss.core.Node((4., 5.), label = "B")
>>> m.add_node(B)
<Node B: x = 4.0, y = 5.0>
Model.add_force(node, magnitude)

Adds an external force on an existing node.

Parameters:
  • node (truss.core.Node instance.) – node on which the force is added.
  • magnitude (length 2 array.) – force magnitude on both directions
Model.stiffness_matrix()

Returns the full assembled stiffness matrix of the model.

Model.force_vector()

Returns the full force vector applied on the system.

Model.solve()

Solves the system.

Model.active_dof()

Returns the indices of the active (i. e. not blocked) degrees of freedom.

Model.bbox(deformed=True, factor=0.2)

Returns the bounding box of the truss.

Model.draw(ax, deformed=True, field='stress', label=True, forces=True, displacements=False, force_scale=1.0, displacement_scale=1.0)

Draws the truss in matplotlib axes.

Parameters:
  • ax (matplotlib.axes instance) – matplotlib axes.
  • deformed (String) – configuration to be plotted.
  • field – field to be plotted. Options are “tension” or “stress”.
  • label (Bool) – if True, node labels are plotted.
  • forces (Bool) – if True, external forces are plotted.
  • displacements (Bool) – if True, displacements are plotted.
  • force_scale (float) – scale of the external forces vector.
  • displacement_scale (float) – scale of the external displacement vector.