is it possible to solve displacement a linear truss structure?

[AhmdG]

given a 2byn array of vertices coordinates and a 2bym array of elements defining the connectivity between the vertices, an area A, and boundary condition stiffness BCStifnes. Is it possible to build a mesh, basis, and function to perform assembly using asm()?
vertices = np.array([[0, 0], [10, 5], [10, 0], [20, 8], [20, 0],
[30, 9], [30, 0], [40, 8], [40, 0], [50, 5],
[50, 0], [60, 0]])
elements = np.array([[0, 2], [2, 4], [4, 6], [6, 8], [8, 10], [10, 11],
[0, 1], [1, 3], [3, 5], [5, 7], [7, 9], [9, 11],
[1, 2], [3, 4], [5, 6], [7, 8], [9, 10],
[1, 4], [3, 6], [6, 7], [8, 9]])

[kinnala]

No truss assembler in scikit-fem. It should be max. 20 lines of code to implement it from scratch.

[AhmdG]

thank you very much for your response. I just wanted to avoid the loop for building the K matrix and take advantage of the elegant asm() function.

[kinnala]

If you really, really, want to do it, this is how it can be done:

from skfem import *
from skfem.helpers import *
import numpy as np

m = MeshTri(np.array([[0, 0],
                      [10, 5],
                      [10, 0],
                      [20, 8],
                      [20, 0],
                      [30, 9],
                      [30, 0],
                      [40, 8],
                      [40, 0],
                      [50, 5],
                      [50, 0],
                      [60, 0]]).T,
            np.array([[7, 8, 9],
                      [9, 10, 11],
                      [8, 9, 10],
                      [1, 3, 4],
                      [0, 1, 2],
                      [3, 5, 6],
                      [5, 6, 7],
                      [3, 4, 6],
                      [6, 7, 8],
                      [1, 2, 4]]).T)

fbasis = FacetBasis(m, ElementVector(ElementTriP1()))
ifbasis = InteriorFacetBasis(m, ElementVector(ElementTriP1()), side=0)


@BilinearForm
def bilinf(u, v, w):
    t = np.array([-w.n[1], w.n[0]])
    ut = ddot(grad(u), prod(t, t))
    vt = ddot(grad(v), prod(t, t))
    return ut * vt


A = asm(bilinf, [ifbasis, fbasis])
f = ifbasis.zeros()
f[ifbasis.get_dofs(nodes=(30, 0)).all('u^2')] = -1e-2

D1 = ifbasis.get_dofs(nodes=(0, 0)).all()
D2 = ifbasis.get_dofs(nodes=(60, 0)).all()
D = np.concatenate((D1, D2))

x = solve(*condense(A, f, D=D))
m.translated(x[fbasis.nodal_dofs]).draw(node_numbering=True).show()

[AhmdG]

thank you very much
much appreciated.