Linear static analysis

The function solve() solves a linear system of equations, removing the null rows and columns of the stiffness matrix, which typically correspond to constrained degrees of freedom. The values of the solution at these degrees of freedom are zero. The code below is extracted from one of the structsolve unit tests:

def test_solve_with_null_columns():
    """Solve a system where some DOFs are constrained (null rows/cols)"""
    n = 6
    K_dense = np.zeros((n, n))
    # Only DOFs 1,2,3,4 are active
    active = np.array([1, 2, 3, 4])
    for i in active:
        K_dense[i, i] = float(i + 1)
    K = csc_matrix(K_dense)
    f = np.zeros(n)
    f[active] = 1.0
    u = solve(K, f, silent=True)
    # DOFs 0 and 5 should remain zero
    assert u[0] == 0.0
    assert u[5] == 0.0
    for i in active:
        np.testing.assert_allclose(u[i], 1.0 / (i + 1))

Linear static analyses can also be run with static(), or with the class Analysis, which receives callables that calculate the external force vector and the stiffness matrix:

def _make_linear_system(n=10):
    """Create simple linear system callables"""
    K = csc_matrix(np.eye(n) * 3.0)
    f = np.ones(n) * 6.0

    def calc_fext(inc=1., silent=True):
        return f

    def calc_kC(c=None, NLgeom=False, silent=True):
        return K

    return calc_fext, calc_kC, K, f

def test_analysis_linear_static():
    """Test Analysis class for linear static analysis"""
    n = 10
    calc_fext, calc_kC, K, f = _make_linear_system(n)

    an = Analysis(calc_fext=calc_fext, calc_kC=calc_kC)
    increments, cs = an.static(NLgeom=False, silent=True)

    assert len(increments) == 1
    assert increments[0] == 1.0
    assert len(cs) == 1
    np.testing.assert_allclose(cs[0], 2.0 * np.ones(n))
    assert an.last_analysis == 'static'