Implement Tangent Stiffness Matrix as function of elemental cross-section areas

[adtzlr]

Follow-Up of #10 .

[adtzlr]

Okay, here is a tutorial how to achieve this with the current code of TrussPy (please update TrussPy via pip first):

Create a Model

In a first step we have to create the Model and set the maximum allowed increments to 1 (0 is not possible in TrussPy). We call this function create_model.

import trusspy as tp

def create_model():
    '''Create a TrussPy-Model and return the Model instance.'''
    M = tp.Model(log=0)
    
    with M.Nodes as MN:
        MN.add_node( 1, coord=( 0, 0, 0))
        MN.add_node( 2, coord=( 1, 0, 1))
        MN.add_node( 3, coord=( 2, 0, 0))
    
    with M.Elements as ME:
        ME.add_element( 1, conn=(1,2), gprop=[1] )
        ME.add_element( 2 ,conn=(2,3), gprop=[1] )
        ME.assign_material( 'all', [1])
    
    with M.Boundaries as MB:
        MB.add_bound_U( 1, (0,0,0) )
        MB.add_bound_U( 2, (0,0,1) )
        MB.add_bound_U( 3, (0,0,0) )
    
    with M.ExtForces as MF:
        MF.add_force( 2, ( 0, 0,-1) )
        
    M.Settings.incs = 1
    return M

Function for stiffness evaluation

In a second step we create a function which uses a list of elemental areas as its argument, runs the model and returns the stiffness matrix for the initial increment of zero deformation (may be adapted to your needs). Finally a reduced stiffness matrix for all active degree of freedoms (Kred) is returned. This may also be changed to the whole system stiffness matrix (K) or the one which is used by TrussPy (Kmod). See the documentation for further informations about Kmod.

def stiffness(list_of_areas):
    '''Calculate the stiffness matrix as a function of elemental
    cross-section areas (passed as list).'''
    
    M = create_model()
    M.Elements.assign_geometries('all', list_of_areas)
    
    M.build()
    M.run()
    
    R0 = M.Results.R[0]
    # return K (full system), Kred (only active DOF) 
    # or Kmod (see Documentation)
    return R0.Kred

Now we have a function which evaluates the stiffness matrix based on a list of elemental areas.

Code snippet inside a script

list_of_areas = [2,3]
K = stiffness(list_of_areas)

Have fun!

[adtzlr]

@Giannis1993 please have a look - hope that helps!