LinAlgError: Singular matrix by `a, r = cfc.solveq(K,f,bc)`

[Martin15135215]

This is my example truss:

This is the code:

import numpy as np
import calfem.core as cfc

# Topology matrix Edof
Edof = np.array([
    [1,2,3,4,5,6], # Element 1
    [1,2,3,7,8,9], # Element 2
    [1,2,3,10,11,12], # Element 3
])

K = np.matrix(np.zeros((12,12)))
f = np.matrix(np.zeros((12,1)))

# Area and E-Modulus
E = 1000 # N/mm²
A = 1000 # mm²
ep = [E,A]

#Element coordinates
ex1 = np.array([0., 0.])  # Element 1
ex2 = np.array([0., -4.]) # Element 2
ex3 = np.array([0., -4.]) # Element 3

ey1 = np.array([0., 0.]) # Element 1
ey2 = np.array([0., 0.]) # Element 2
ey3 = np.array([0., 0.]) # Element 3

ez1 = np.array([3., 0.])  # Element 1
ez2 = np.array([3., 3.])  # Element 2
ez3 = np.array([3., 6.])  # Element 3

# Element stiffness matrices
Ke1 = cfc.bar3e(ex1,ey1,ez1,ep)
Ke2 = cfc.bar3e(ex2,ey2,ez2,ep)
Ke3 = cfc.bar3e(ex3,ey3,ez3,ep)

# Assemble Ke into K
cfc.assem(Edof[0,:],K,Ke1)
cfc.assem(Edof[1,:],K,Ke2)
cfc.assem(Edof[2,:],K,Ke3)

# prescribed displacements in bc
bc = np.array([4,5,6,7,8,9,10,11,12])

f[1] = 100000 # N
f[2] = -100000 # N

a, r = cfc.solveq(K,f,bc)

When I run this, I get this error message:

LinAlgError                               Traceback (most recent call last)
Cell In[14], line 49
     46 f[1] = 100000 # N
     47 f[2] = -100000 # N
---> 49 a, r = cfc.solveq(K,f,bc)

File ~/.local/share/python3.11/site-packages/calfem/core.py:5317, in solveq(K, f, bcPrescr, bcVal)
   5313 bcDofs = bcDofs[bc]
   5315 fsys = f[bcDofs]-K[np.ix_((bcDofs), (bcPrescr-1))] * \
   5316     np.asmatrix(bcVal).reshape(nPdofs, 1)
-> 5317 asys = np.linalg.solve(K[np.ix_((bcDofs), (bcDofs))], fsys)
   5319 a = np.zeros([nDofs, 1])
   5320 a[np.ix_(bcPrescr-1)] = np.asmatrix(bcVal).reshape(nPdofs, 1)

File <__array_function__ internals>:200, in solve(*args, **kwargs)

File ~/.local/share/python3.11/site-packages/numpy/linalg/linalg.py:386, in solve(a, b)
    384 signature = 'DD->D' if isComplexType(t) else 'dd->d'
    385 extobj = get_linalg_error_extobj(_raise_linalgerror_singular)
--> 386 r = gufunc(a, b, signature=signature, extobj=extobj)
    388 return wrap(r.astype(result_t, copy=False))

File ~/.local/share/python3.11/site-packages/numpy/linalg/linalg.py:89, in _raise_linalgerror_singular(err, flag)
     88 def _raise_linalgerror_singular(err, flag):
---> 89     raise LinAlgError("Singular matrix")

LinAlgError: Singular matrix

My example truss is 2-dimensional, but I wanted to test bar3e whether it also works in 3 dimensions, and accordingly set all coordinates to zero on one axis.

[Martin15135215]

I forgot to add a support:

Now, the code is working without error.

import numpy as np
import calfem.core as cfc

# Topology matrix Edof
Edof = np.array([
    [1,2,3,4,5,6], # Element 1
    [1,2,3,7,8,9], # Element 2
    [1,2,3,10,11,12], # Element 3
])

K = np.matrix(np.zeros((12,12)))
f = np.matrix(np.zeros((12,1)))

# Area and E-Modulus
E =  1000000.0 # E-Modulus kN/m²
A = 0.001 # Area m²
ep = [E,A]

#Element coordinates
ex1 = np.array([0., 0.])  # Element 1
ex2 = np.array([0., -4.]) # Element 2
ex3 = np.array([0., -4.]) # Element 3

ey1 = np.array([0., 0.]) # Element 1
ey2 = np.array([0., 0.]) # Element 2
ey3 = np.array([0., 0.]) # Element 3

ez1 = np.array([3., 0.])  # Element 1
ez2 = np.array([3., 3.])  # Element 2
ez3 = np.array([3., 6.])  # Element 3

# Element stiffness matrices
Ke1 = cfc.bar3e(ex1,ey1,ez1,ep)
Ke2 = cfc.bar3e(ex2,ey2,ez2,ep)
Ke3 = cfc.bar3e(ex3,ey3,ez3,ep)

# Assemble Ke into K
cfc.assem(Edof[0,:],K,Ke1)
cfc.assem(Edof[1,:],K,Ke2)
cfc.assem(Edof[2,:],K,Ke3)

# prescribed displacements in bc
bc = np.array([2, # has also a support
    4,5,6,7,8,9,10,11,12])

f[1] = 100 # kN
f[2] = -100 # kN

a, r = cfc.solveq(K,f,bc)