def solve(self, problem:Problem):
problem.reassign_dofs()
M = problem.M(True)
K = problem.K(True)
ndofs = 3 * len(problem.nodes)
free_dofs = problem.free_dofs()
full_eigenvectors = np.zeros((len(free_dofs), ndofs))
# Unsymmetric reduction
A = np.linalg.solve(M, K)
# Symmetry preserving reduction
#L = np.linalg.cholesky(M)
#A = np.linalg.inv(L) @ K @ np.linalg.inv(L.T)
eigenvalues, eigenvectors = np.linalg.eig(A)
eigenvectors = eigenvectors.T # Row-major
eigenvectors = eigenvectors[eigenvalues.argsort()]
eigenvalues.sort()
full_eigenvectors[:,free_dofs] = eigenvectors
return results.ResultsModal(problem, eigenvalues, full_eigenvectors)
def solve(self, problem:Problem) -> results.ResultsStaticNonlinear:
steps = 500
arclength = 45
A = 0
max_it = 35
t0 = time.time()
problem.reassign_dofs()
problem.remove_dofs()
free_dofs = problem.free_dofs()
max_A = np.linalg.norm(problem.loads[free_dofs])
q = problem.loads[free_dofs] / max_A
displacements = np.zeros(len(problem.nodes) * 3)
loads = np.zeros_like(displacements)
#displ_storage = np.zeros((steps, 3 * len(problem.nodes)))
displ_storage = []
force_storage = []
i = 0
while i < steps and A < max_A:
print("Predictor step {}".format(i))
K = problem.K(True)
wq0 = np.linalg.solve(K, q)
f = np.sqrt(1 + wq0 @ wq0)
sign = np.sign(wq0 @ v0 if i > 1 else 1)
dA = arclength / f * sign
v0 = dA*wq0
A += dA
displacements[free_dofs] = displacements[free_dofs] + v0
for node in problem.nodes:
node.displacements = displacements[node.dofs]
# Corrector
k = 0
residual = self.get_internal_forces(problem)[free_dofs] - q*A
while np.linalg.norm(residual) > 1e-3 and k < max_it:
K = problem.K(True)
wq = np.linalg.solve(K, q)
wr = np.linalg.solve(K, -residual)
dA_ = -wq @ wr / (1 + wq @ wq)
A += dA_
displacements[free_dofs] = displacements[free_dofs] + (wr + dA_*wq)
for node in problem.nodes:
node.displacements = displacements[node.dofs]
k += 1
residual = self.get_internal_forces(problem)[free_dofs] - q*A
#displ_storage[i] = displacements
displ_storage.append(np.array(displacements))
loads[free_dofs] = q*A
force_storage.append(A)
i += 1
#print(f"Finished in {k} corrector steps (stepped {dA}, arclength {arclength})")
if k < 4:
arclength *= 1.05
elif k > 8:
arclength *= 0.6
else:
arclength *= 0.85
t1 = time.time()
dt = t1 - t0
print(np.asarray(displ_storage))
print(f"Ended at A = {A} in {dt} seconds")
return results.ResultsStaticNonlinear(problem, np.asarray(displ_storage),
np.asarray(force_storage))
