Get Truss Stiffness 2D

getTrussStiffness2D.py

# ------------------------------------------------------------------------
# The following function is implemented in Python by Professor Terje Haukaas
# at the University of British Columbia in Vancouver, Canada. It is made
# freely available online at terje.civil.ubc.ca together with notes,
# examples, and additional Python code. Please be cautious when using
# this code; it may contain bugs and comes without any form of warranty.
# ------------------------------------------------------------------------

def getTrussStiffness2D(E, A, L, delta_x, delta_y, N):

    # Local stiffness matrix
    Kl = np.array([(E*A/L,  0, -E*A/L, 0),
                   (0,      0,   0,    0),
                   (-E*A/L, 0, E*A/L,  0),
                   (0,      0,   0,    0)])

    # Geometric stiffness matrix
    Kgeometric = np.array([(0,  0,  0,   0),
                          (0,  N/L, 0, -N/L),
                          (0,   0,  0,   0),
                          (0, -N/L, 0, N/L)])

    # Transformation matrix Tlg
    if delta_x == 0:
        if delta_y < 0:
            theta = -np.pi/2.0
        else:
            theta = np.pi/2.0
    else:
        theta = np.arctan(delta_y/delta_x)

    c = np.cos(theta)
    s = np.sin(theta)
    Tlg = np.array([(c,  s, 0,  0),
                    (-s, c, 0,  0),
                    (0,  0, c,  s),
                    (0,  0, -s, c)])

    return [Kl, Kgeometric, Tlg]