215 degree arc
Contents
215 degree arc#
The problem provided in this example is a \(215^\circ\) arch with pinned-fixed boundary conditions subjected to a point load at the center of the arch. The arch is modeled with 2D geometrically exact beams (i.e. Simo-Reissner Beams). For more information on beams see here.
1%matplotlib inline
2from dolfin import *
3import numpy as np
4import matplotlib.pyplot as plt
5import os
6from arc_length.force_control_solver import force_control # import force control formulation of arc-length solver
7# Dealing with ufl legacy
8try:
9 from ufl import diag, Jacobian, shape
10except:
11 from ufl_legacy import diag, Jacobian, shape
12
13parameters["form_compiler"]["representation"] = "uflacs"
14parameters["form_compiler"]["optimize"] = True
15parameters["form_compiler"]["cpp_optimize"] = True
16parameters["form_compiler"]["quadrature_degree"] = 1
17parameters['reorder_dofs_serial'] = False
18
19
20ffc_options = {"optimize": True, \
21 "eliminate_zeros": True, \
22 "precompute_basis_const": True, \
23 "precompute_ip_const": True}
Import Mesh and define function spaces#
In the case of 2D beams we also define the rotation matrix about the \(z\) axis and directional derivative with respect to the beam centerline.
1mesh_215 = Mesh()
2with XDMFFile('mesh/215_arch2D.xdmf') as infile:
3 infile.read(mesh_215)
4
5
6Ue = VectorElement("CG", mesh_215.ufl_cell(), 1, dim=2) # displacement
7Te = FiniteElement("CG", mesh_215.ufl_cell(), 1) # rotation
8V = FunctionSpace(mesh_215, MixedElement([Ue, Te]))
9
10v_ = TestFunction(V)
11u_, theta_ = split(v_)
12dv = TrialFunction(V)
13v = Function(V, name="Generalized displacement")
14u, theta = split(v)
15
16VR = TensorFunctionSpace(mesh_215, "DG", 0, shape=(2, 2))
17
18V0 = FunctionSpace(mesh_215, "DG", 0)
19
20
21Vu = V.sub(0).collapse()
22disp = Function(Vu)
23
24Jac = Jacobian(mesh_215)
25gdim = mesh_215.geometry().dim()
26Jac = as_vector([Jac[i, 0] for i in range(gdim)])
27g01 = Jac/sqrt(dot(Jac, Jac))
28g02 = as_vector([-g01[1],g01[0]])
29
30r01 = outer(g01,as_vector([1,0]))
31r02 = outer(g02, as_vector([0,1]))
32
33R0 = r01+r02
34
35#-----------------------Define Functions for beams-----------------------------------#
36def tgrad(u): # directional derivative w.r.t. beam centerline
37 return dot(grad(u), g01)
38
39def rotation_matrix(theta): # 2D rotation matrix -- there is no need to do rotation parametrization for 2D beams
40 return as_tensor([[cos(theta), -sin(theta)],[sin(theta), cos(theta)]])
41Rot = rotation_matrix(theta)
Define Dirichlet Boundary Conditions#
1r = 100
2arch = 215
3
4left_theta =180+(90-(360-arch)/2)
5right_theta = -(90-(360-arch)/2)
6
7def x_coord(r,theta):
8 return r*np.cos(np.deg2rad(theta))
9
10def y_coord(r,theta):
11 return r*np.sin(np.deg2rad(theta))
12
13x_coord_left = x_coord(r,left_theta)
14y_coord_left = y_coord(r,left_theta)
15x_coord_right = x_coord(r,right_theta)
16y_coord_right = y_coord(r,right_theta)
1def pinned_left(x, on_boundary):
2 return near(x[0], x_coord_left, 1e-6)
3
4def fixed_right(x, on_boundary):
5 return near(x[0], x_coord_right, 1e-6)
6
7def load_center(x, on_boundary):
8 return near(x[1], r, 1e-6)
9
10# Mark integration boundary
11facets = MeshFunction("size_t", mesh_215, 0)
12facets.set_all(0)
13AutoSubDomain(load_center).mark(facets,1)
14
15Pinned = DirichletBC(V.sub(0), Constant((0.0, 0.0)), pinned_left, method='pointwise') # Fixed displacement
16Fixed = DirichletBC(V, Constant((0.0, 0.0, 0.0)), fixed_right, method='pointwise') # Fixed displacement and rotation
17bcs = [Pinned, Fixed]
Kinematics and Weak form#
1# 2D beam Kinematics
2defo = dot(R0.T,dot(Rot.T, g01 + tgrad(u)) - g01)
3curv = tgrad(theta)
1# Geometrical properties
2S = 2.29 # cross-sectional area
3I = 1.0 # Area moment
4J = 2.0 # Polar Moment
5E = 1.0e6 # Elastic modulus
6nu = 0 # Poisson's Ratio
7
8G = E/(2*(1+nu)) # Shear Modulus
9kappa = 1.0 # Shear correction
10
11# Stiffness moduli
12ES = E*S
13GS = G*S
14GS_2 = G*S*kappa
15GS_3 = G*S*kappa
16EI = E*I
1# Constitutive Equations
2C_N = diag(as_vector([ES, GS_2]))
3
4# Applied Load:
5F_max = Constant((0.0,-1.0))
6M_max = Constant(0.0)
7load = Expression("t", t=0, degree = 0)
8
9dS = Measure("dS", domain=mesh_215, subdomain_data=facets) # Note its dS not ds -- interior facet
10dx = Measure("dx", domain=mesh_215)
11
12elastic_energy = 0.5 * (dot(defo, dot(C_N, defo)) + (EI*curv**2))*dx
13
14F_int = derivative(elastic_energy, v, v_)
15F_ext = avg(load * (-M_max*theta_ + dot(F_max, u_))) * dS(1) # avg function is used to integrte over disconticuous interior facets
16residual = F_int - F_ext
17tangent_form = derivative(residual, v, dv)
Solver#
To use our solver we first have to define the type of solver (i.e. displacement control or force control) and solver parameters before using the solver. Note that the correct type of solver has to first be imported (see first cell).
Solver parameters#
Here the parameters for both types of solvers:
psi: the scalar arc-length parameter. When psi = 1, the method becomes the spherical arc-length method and when psi = 0 the method becomes the cylindrical arc-length method
abs_tol(optional) : absolute residual tolerance for the linear solver (default value: 1e-10)
rel_tol(optional) : relative residual tolerance for solver; the relative residual is defined as the ration between the current residual and initial residual (default value: DOLFIN_EPS)
lmbda0: the initial load parameter
max_iter: maximum number of iterations for the linear solver
solver(optional): type of linear solver for the FEniCS linear solve function – default FEniCS linear solver is used if no argument is used.
Aside from these solver parameters, the arguments need to solve the FEA problem must also be passed into the solver:
u: the solution function
F_int: First variation of strain energy (internal nodal forces)
F_ext: Externally applied load (external applied force)
J: The Jacobian of the residual with respect to the deformation (tangential stiffness matrix)
load_factor: The incremental load factor
The solver can be called by:
solver = force_control(psi,abs_tol,rel_tol,lmbda0,max_iter,u,F_int,F_ext,bcs,J,load_factor,solver)
Using the solver#
Initialize the solver by calling solver.initialize()
Iteratively call solver.solve() until desired stopping condition
1# Solver Parameters
2psi = 1.0
3abs_tol = 1.0e-6
4lmbda0 = 50.0
5max_iter = 10
6solver = 'mumps' # optional
7
8# Set up force control arc-length solver
9solver = force_control(psi=psi, abs_tol=abs_tol, lmbda0=lmbda0, max_iter=max_iter, u=v,
10 F_int=F_int, F_ext=F_ext, bcs=bcs, J=tangent_form, load_factor=load, solver=solver)
1# Iterative solving
2disp = [v.vector()[:]]
3lmbda = [0]
4
5for ii in range(99):
6 solver.solve()
7 if solver.converged: # We only want to save the solution step if the solver coverges
8 disp.append(v.vector()[:])
9 lmbda.append(load.t)
Initializing solver parameters...
Starting initial Force Control with Newton Method:
Iteration 0: |
Absolute Residual: 5.0000e+01| Relative Residual: 1.0000e+00
Iteration 1: |
Absolute Residual: 8.7164e+02| Relative Residual: 1.7433e+01
Iteration 2: |
Absolute Residual: 7.6766e+00| Relative Residual: 1.5353e-01
Iteration 3: |
Absolute Residual: 1.4991e+00| Relative Residual: 2.9982e-02
Iteration 4: |
Absolute Residual: 4.7541e-05| Relative Residual: 9.5081e-07
Iteration 5: |
Absolute Residual: 3.2137e-09| Relative Residual: 6.4273e-11
Arc-Length Step 1 :
Iteration: 0
|Total Norm: 3.2137e-09 |Residual: 3.2137e-09 |A: -4.5475e-13| Relative Norm : 1.0000e+00
Arc-Length Step 2 :
Iteration: 0
|Total Norm: 2.1210e+03 |Residual: 2.1210e+03 |A: -4.5475e-13| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.9729e+01 |Residual: 1.9726e+01 |A: 3.5863e-01| Relative Norm : 9.3018e-03
Iteration: 2
|Total Norm: 9.3217e+00 |Residual: 9.0868e+00 |A: 2.0795e+00| Relative Norm : 4.3949e-03
Iteration: 3
|Total Norm: 2.0805e-03 |Residual: 2.0373e-03 |A: 4.2200e-04| Relative Norm : 9.8090e-07
Iteration: 4
|Total Norm: 1.0508e-07 |Residual: 1.0277e-07 |A: 2.1919e-08| Relative Norm : 4.9542e-11
Arc-Length Step 3 :
Iteration: 0
|Total Norm: 2.7079e+03 |Residual: 2.7079e+03 |A: 2.1919e-08| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 2.2988e+01 |Residual: 2.2983e+01 |A: 4.6549e-01| Relative Norm : 8.4889e-03
Iteration: 2
|Total Norm: 1.3520e+01 |Residual: 1.3124e+01 |A: 3.2483e+00| Relative Norm : 4.9929e-03
Iteration: 3
|Total Norm: 5.9263e-03 |Residual: 5.8374e-03 |A: 1.0226e-03| Relative Norm : 2.1885e-06
Iteration: 4
|Total Norm: 9.8708e-07 |Residual: 9.6150e-07 |A: 2.2326e-07| Relative Norm : 3.6451e-10
Arc-Length Step 4 :
Iteration: 0
|Total Norm: 3.5206e+03 |Residual: 3.5206e+03 |A: 2.2326e-07| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 2.6965e+01 |Residual: 2.6958e+01 |A: 6.2205e-01| Relative Norm : 7.6592e-03
Iteration: 2
|Total Norm: 1.8936e+01 |Residual: 1.8287e+01 |A: 4.9154e+00| Relative Norm : 5.3786e-03
Iteration: 3
|Total Norm: 1.4918e-02 |Residual: 1.4735e-02 |A: 2.3300e-03| Relative Norm : 4.2375e-06
Iteration: 4
|Total Norm: 7.1139e-06 |Residual: 6.8967e-06 |A: 1.7444e-06| Relative Norm : 2.0207e-09
Iteration: 5
|Total Norm: 3.8333e-09 |Residual: 3.8333e-09 |A: 0.0000e+00| Relative Norm : 1.0888e-12
Arc-Length Step 5 :
Iteration: 0
|Total Norm: 4.6449e+03 |Residual: 4.6449e+03 |A: -3.1832e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 3.2055e+01 |Residual: 3.2044e+01 |A: 8.5831e-01| Relative Norm : 6.9012e-03
Iteration: 2
|Total Norm: 2.5121e+01 |Residual: 2.4108e+01 |A: 7.0620e+00| Relative Norm : 5.4082e-03
Iteration: 3
|Total Norm: 3.2443e-02 |Residual: 3.2087e-02 |A: 4.7918e-03| Relative Norm : 6.9846e-06
Iteration: 4
|Total Norm: 3.7471e-05 |Residual: 3.6119e-05 |A: 9.9773e-06| Relative Norm : 8.0672e-09
Iteration: 5
|Total Norm: 4.6309e-09 |Residual: 4.6309e-09 |A: 0.0000e+00| Relative Norm : 9.9699e-13
Arc-Length Step 6 :
Iteration: 0
|Total Norm: 6.1719e+03 |Residual: 6.1719e+03 |A: -4.5475e-13| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 3.8743e+01 |Residual: 3.8724e+01 |A: 1.2201e+00| Relative Norm : 6.2774e-03
Iteration: 2
|Total Norm: 3.0747e+01 |Residual: 2.9285e+01 |A: 9.3699e+00| Relative Norm : 4.9819e-03
Iteration: 3
|Total Norm: 5.8359e-02 |Residual: 5.7750e-02 |A: 8.4111e-03| Relative Norm : 9.4557e-06
Iteration: 4
|Total Norm: 1.3111e-04 |Residual: 1.2549e-04 |A: 3.7970e-05| Relative Norm : 2.1244e-08
Iteration: 5
|Total Norm: 5.8932e-09 |Residual: 5.8932e-09 |A: 4.5475e-13| Relative Norm : 9.5486e-13
Arc-Length Step 7 :
Iteration: 0
|Total Norm: 8.1579e+03 |Residual: 8.1579e+03 |A: -2.2737e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 4.7240e+01 |Residual: 4.7207e+01 |A: 1.7637e+00| Relative Norm : 5.7907e-03
Iteration: 2
|Total Norm: 3.3683e+01 |Residual: 3.1797e+01 |A: 1.1113e+01| Relative Norm : 4.1289e-03
Iteration: 3
|Total Norm: 8.2232e-02 |Residual: 8.1381e-02 |A: 1.1800e-02| Relative Norm : 1.0080e-05
Iteration: 4
|Total Norm: 2.7098e-04 |Residual: 2.5720e-04 |A: 8.5311e-05| Relative Norm : 3.3217e-08
Iteration: 5
|Total Norm: 5.8905e-09 |Residual: 5.8905e-09 |A: 9.0949e-13| Relative Norm : 7.2207e-13
Arc-Length Step 8 :
Iteration: 0
|Total Norm: 1.0562e+04 |Residual: 1.0562e+04 |A: -1.3642e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 5.6970e+01 |Residual: 5.6914e+01 |A: 2.5276e+00| Relative Norm : 5.3941e-03
Iteration: 2
|Total Norm: 3.2160e+01 |Residual: 3.0062e+01 |A: 1.1424e+01| Relative Norm : 3.0450e-03
Iteration: 3
|Total Norm: 8.6039e-02 |Residual: 8.5136e-02 |A: 1.2437e-02| Relative Norm : 8.1465e-06
Iteration: 4
|Total Norm: 2.9619e-04 |Residual: 2.7851e-04 |A: 1.0081e-04| Relative Norm : 2.8045e-08
Iteration: 5
|Total Norm: 8.1189e-09 |Residual: 8.1189e-09 |A: 9.0949e-13| Relative Norm : 7.6873e-13
Arc-Length Step 9 :
Iteration: 0
|Total Norm: 1.3197e+04 |Residual: 1.3197e+04 |A: 5.0022e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 6.6540e+01 |Residual: 6.6449e+01 |A: 3.4870e+00| Relative Norm : 5.0420e-03
Iteration: 2
|Total Norm: 2.6413e+01 |Residual: 2.4462e+01 |A: 9.9636e+00| Relative Norm : 2.0014e-03
Iteration: 3
|Total Norm: 6.4323e-02 |Residual: 6.3626e-02 |A: 9.4446e-03| Relative Norm : 4.8740e-06
Iteration: 4
|Total Norm: 1.5906e-04 |Residual: 1.4820e-04 |A: 5.7757e-05| Relative Norm : 1.2052e-08
Iteration: 5
|Total Norm: 7.0038e-09 |Residual: 7.0038e-09 |A: 0.0000e+00| Relative Norm : 5.3070e-13
Arc-Length Step 10 :
Iteration: 0
|Total Norm: 1.5770e+04 |Residual: 1.5770e+04 |A: 2.7285e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 7.4474e+01 |Residual: 7.4336e+01 |A: 4.5323e+00| Relative Norm : 4.7226e-03
Iteration: 2
|Total Norm: 1.8754e+01 |Residual: 1.7270e+01 |A: 7.3128e+00| Relative Norm : 1.1893e-03
Iteration: 3
|Total Norm: 3.3902e-02 |Residual: 3.3517e-02 |A: 5.0894e-03| Relative Norm : 2.1498e-06
Iteration: 4
|Total Norm: 4.1234e-05 |Residual: 3.8151e-05 |A: 1.5645e-05| Relative Norm : 2.6147e-09
Iteration: 5
|Total Norm: 1.0335e-08 |Residual: 1.0335e-08 |A: -4.5475e-13| Relative Norm : 6.5540e-13
Arc-Length Step 11 :
Iteration: 0
|Total Norm: 1.7991e+04 |Residual: 1.7991e+04 |A: 0.0000e+00| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 7.9979e+01 |Residual: 7.9789e+01 |A: 5.5075e+00| Relative Norm : 4.4455e-03
Iteration: 2
|Total Norm: 1.1721e+01 |Residual: 1.0819e+01 |A: 4.5099e+00| Relative Norm : 6.5151e-04
Iteration: 3
|Total Norm: 1.2683e-02 |Residual: 1.2534e-02 |A: 1.9408e-03| Relative Norm : 7.0497e-07
Iteration: 4
|Total Norm: 5.3015e-06 |Residual: 4.8904e-06 |A: 2.0469e-06| Relative Norm : 2.9467e-10
Iteration: 5
|Total Norm: 1.1407e-08 |Residual: 1.1407e-08 |A: 0.0000e+00| Relative Norm : 6.3405e-13
Arc-Length Step 12 :
Iteration: 0
|Total Norm: 1.9686e+04 |Residual: 1.9686e+04 |A: 6.3665e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 8.3047e+01 |Residual: 8.2809e+01 |A: 6.2818e+00| Relative Norm : 4.2185e-03
Iteration: 2
|Total Norm: 6.5959e+00 |Residual: 6.1755e+00 |A: 2.3170e+00| Relative Norm : 3.3505e-04
Iteration: 3
|Total Norm: 3.3833e-03 |Residual: 3.3439e-03 |A: 5.1473e-04| Relative Norm : 1.7186e-07
Iteration: 4
|Total Norm: 3.4578e-07 |Residual: 3.1955e-07 |A: 1.3212e-07| Relative Norm : 1.7564e-11
Arc-Length Step 13 :
Iteration: 0
|Total Norm: 2.0817e+04 |Residual: 2.0817e+04 |A: 1.3212e-07| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 8.4144e+01 |Residual: 8.3870e+01 |A: 6.7890e+00| Relative Norm : 4.0420e-03
Iteration: 2
|Total Norm: 3.4450e+00 |Residual: 3.3083e+00 |A: 9.6083e-01| Relative Norm : 1.6549e-04
Iteration: 3
|Total Norm: 6.3383e-04 |Residual: 6.2746e-04 |A: 8.9612e-05| Relative Norm : 3.0447e-08
Iteration: 4
|Total Norm: 1.9593e-08 |Residual: 1.9151e-08 |A: 4.1368e-09| Relative Norm : 9.4118e-13
Arc-Length Step 14 :
Iteration: 0
|Total Norm: 2.1441e+04 |Residual: 2.1441e+04 |A: 4.1409e-09| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 8.3941e+01 |Residual: 8.3646e+01 |A: 7.0243e+00| Relative Norm : 3.9149e-03
Iteration: 2
|Total Norm: 1.8800e+00 |Residual: 1.8536e+00 |A: 3.1365e-01| Relative Norm : 8.7680e-05
Iteration: 3
|Total Norm: 9.4345e-05 |Residual: 9.3795e-05 |A: 1.0171e-05| Relative Norm : 4.4001e-09
Iteration: 4
|Total Norm: 1.7603e-08 |Residual: 1.7602e-08 |A: 7.5488e-11| Relative Norm : 8.2096e-13
Arc-Length Step 15 :
Iteration: 0
|Total Norm: 2.1663e+04 |Residual: 2.1663e+04 |A: 7.3669e-11| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 8.3227e+01 |Residual: 8.2931e+01 |A: 7.0215e+00| Relative Norm : 3.8419e-03
Iteration: 2
|Total Norm: 1.6610e+00 |Residual: 1.6556e+00 |A: 1.3327e-01| Relative Norm : 7.6673e-05
Iteration: 3
|Total Norm: 3.5555e-05 |Residual: 3.5488e-05 |A: 2.1883e-06| Relative Norm : 1.6413e-09
Iteration: 4
|Total Norm: 1.6057e-08 |Residual: 1.6057e-08 |A: 5.4570e-12| Relative Norm : 7.4121e-13
Arc-Length Step 16 :
Iteration: 0
|Total Norm: 2.1608e+04 |Residual: 2.1608e+04 |A: 3.6380e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 8.2916e+01 |Residual: 8.2634e+01 |A: 6.8358e+00| Relative Norm : 3.8373e-03
Iteration: 2
|Total Norm: 2.3598e+00 |Residual: 2.3518e+00 |A: 1.9446e-01| Relative Norm : 1.0921e-04
Iteration: 3
|Total Norm: 4.3756e-05 |Residual: 4.3552e-05 |A: 4.2206e-06| Relative Norm : 2.0250e-09
Iteration: 4
|Total Norm: 2.0744e-08 |Residual: 2.0744e-08 |A: 3.6380e-12| Relative Norm : 9.6003e-13
Arc-Length Step 17 :
Iteration: 0
|Total Norm: 2.1417e+04 |Residual: 2.1417e+04 |A: 3.6380e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 8.4100e+01 |Residual: 8.3846e+01 |A: 6.5348e+00| Relative Norm : 3.9268e-03
Iteration: 2
|Total Norm: 3.5850e+00 |Residual: 3.5693e+00 |A: 3.3457e-01| Relative Norm : 1.6739e-04
Iteration: 3
|Total Norm: 1.3634e-04 |Residual: 1.3573e-04 |A: 1.2979e-05| Relative Norm : 6.3663e-09
Iteration: 4
|Total Norm: 2.0530e-08 |Residual: 2.0530e-08 |A: 1.1823e-11| Relative Norm : 9.5861e-13
Arc-Length Step 18 :
Iteration: 0
|Total Norm: 2.1260e+04 |Residual: 2.1260e+04 |A: 1.2733e-11| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 8.8182e+01 |Residual: 8.7964e+01 |A: 6.1981e+00| Relative Norm : 4.1479e-03
Iteration: 2
|Total Norm: 5.5198e+00 |Residual: 5.4991e+00 |A: 4.7726e-01| Relative Norm : 2.5964e-04
Iteration: 3
|Total Norm: 6.1423e-04 |Residual: 6.1328e-04 |A: 3.4152e-05| Relative Norm : 2.8892e-08
Iteration: 4
|Total Norm: 2.5951e-08 |Residual: 2.5949e-08 |A: 3.0104e-10| Relative Norm : 1.2207e-12
Arc-Length Step 19 :
Iteration: 0
|Total Norm: 2.1369e+04 |Residual: 2.1369e+04 |A: 3.0013e-10| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 9.7222e+01 |Residual: 9.7041e+01 |A: 5.9266e+00| Relative Norm : 4.5496e-03
Iteration: 2
|Total Norm: 9.3950e+00 |Residual: 9.3686e+00 |A: 7.0463e-01| Relative Norm : 4.3965e-04
Iteration: 3
|Total Norm: 2.2011e-03 |Residual: 2.1975e-03 |A: 1.2598e-04| Relative Norm : 1.0300e-07
Iteration: 4
|Total Norm: 9.7523e-08 |Residual: 9.7233e-08 |A: 7.5079e-09| Relative Norm : 4.5636e-12
Arc-Length Step 20 :
Iteration: 0
|Total Norm: 2.2127e+04 |Residual: 2.2127e+04 |A: 7.5156e-09| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.1496e+02 |Residual: 1.1481e+02 |A: 5.8745e+00| Relative Norm : 5.1953e-03
Iteration: 2
|Total Norm: 2.0923e+01 |Residual: 2.0865e+01 |A: 1.5517e+00| Relative Norm : 9.4559e-04
Iteration: 3
|Total Norm: 4.9522e-03 |Residual: 4.8623e-03 |A: 9.3936e-04| Relative Norm : 2.2381e-07
Iteration: 4
|Total Norm: 1.4739e-07 |Residual: 1.4527e-07 |A: 2.4924e-08| Relative Norm : 6.6611e-12
Arc-Length Step 21 :
Iteration: 0
|Total Norm: 2.4293e+04 |Residual: 2.4293e+04 |A: 2.4936e-08| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.4996e+02 |Residual: 1.4982e+02 |A: 6.3548e+00| Relative Norm : 6.1727e-03
Iteration: 2
|Total Norm: 6.5457e+01 |Residual: 6.5244e+01 |A: 5.2829e+00| Relative Norm : 2.6944e-03
Iteration: 3
|Total Norm: 8.6427e-02 |Residual: 8.5672e-02 |A: 1.1394e-02| Relative Norm : 3.5576e-06
Iteration: 4
|Total Norm: 1.1813e-03 |Residual: 1.1699e-03 |A: 1.6399e-04| Relative Norm : 4.8626e-08
Iteration: 5
|Total Norm: 2.3537e-08 |Residual: 2.3537e-08 |A: 3.6380e-12| Relative Norm : 9.6888e-13
Arc-Length Step 22 :
Iteration: 0
|Total Norm: 2.9795e+04 |Residual: 2.9795e+04 |A: 2.2737e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 2.2701e+02 |Residual: 2.2686e+02 |A: 8.2212e+00| Relative Norm : 7.6192e-03
Iteration: 2
|Total Norm: 2.6332e+02 |Residual: 2.6239e+02 |A: 2.2123e+01| Relative Norm : 8.8377e-03
Iteration: 3
|Total Norm: 1.1136e+00 |Residual: 1.1035e+00 |A: 1.4948e-01| Relative Norm : 3.7374e-05
Iteration: 4
|Total Norm: 4.0326e-01 |Residual: 3.9988e-01 |A: 5.2053e-02| Relative Norm : 1.3535e-05
Iteration: 5
|Total Norm: 1.3964e-06 |Residual: 1.3427e-06 |A: 3.8359e-07| Relative Norm : 4.6868e-11
Iteration: 6
|Total Norm: 3.0193e-08 |Residual: 3.0193e-08 |A: 4.5475e-13| Relative Norm : 1.0134e-12
Arc-Length Step 23 :
Iteration: 0
|Total Norm: 4.5147e+04 |Residual: 4.5147e+04 |A: 7.2760e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 4.4606e+02 |Residual: 4.4581e+02 |A: 1.4993e+01| Relative Norm : 9.8803e-03
Iteration: 2
|Total Norm: 1.2914e+03 |Residual: 1.2873e+03 |A: 1.0369e+02| Relative Norm : 2.8606e-02
Iteration: 3
|Total Norm: 7.6766e+00 |Residual: 7.0354e+00 |A: 3.0713e+00| Relative Norm : 1.7004e-04
Iteration: 4
|Total Norm: 2.9492e+01 |Residual: 2.9160e+01 |A: 4.4086e+00| Relative Norm : 6.5324e-04
Iteration: 5
|Total Norm: 3.5891e-02 |Residual: 3.5817e-02 |A: 2.3050e-03| Relative Norm : 7.9499e-07
Iteration: 6
|Total Norm: 7.0098e-04 |Residual: 6.9036e-04 |A: 1.2159e-04| Relative Norm : 1.5527e-08
Iteration: 7
|Total Norm: 3.0097e-08 |Residual: 3.0097e-08 |A: 1.8190e-12| Relative Norm : 6.6665e-13
Arc-Length Step 24 :
Iteration: 0
|Total Norm: 1.0137e+05 |Residual: 1.0137e+05 |A: 1.8190e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.5449e+03 |Residual: 1.5438e+03 |A: 5.7229e+01| Relative Norm : 1.5241e-02
Iteration: 2
|Total Norm: 5.4545e+03 |Residual: 5.4352e+03 |A: 4.5858e+02| Relative Norm : 5.3810e-02
Iteration: 3
|Total Norm: 2.3817e+02 |Residual: 8.5509e+01 |A: 2.2229e+02| Relative Norm : 2.3496e-03
Iteration: 4
|Total Norm: 4.5485e+01 |Residual: 4.2302e+01 |A: 1.6716e+01| Relative Norm : 4.4872e-04
Iteration: 5
|Total Norm: 4.7627e-01 |Residual: 4.7539e-01 |A: 2.8807e-02| Relative Norm : 4.6984e-06
Iteration: 6
|Total Norm: 5.8756e-03 |Residual: 2.9036e-03 |A: 5.1081e-03| Relative Norm : 5.7964e-08
Iteration: 7
|Total Norm: 5.6187e-08 |Residual: 5.5831e-08 |A: 6.3105e-09| Relative Norm : 5.5429e-13
Arc-Length Step 25 :
Iteration: 0
|Total Norm: 2.4140e+05 |Residual: 2.4140e+05 |A: 6.3114e-09| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 7.4635e+03 |Residual: 5.3955e+03 |A: 5.1568e+03| Relative Norm : 3.0918e-02
Iteration: 2
|Total Norm: 4.6509e+03 |Residual: 4.3447e+03 |A: 1.6595e+03| Relative Norm : 1.9267e-02
Iteration: 3
|Total Norm: 7.9982e+02 |Residual: 3.4366e+02 |A: 7.2222e+02| Relative Norm : 3.3133e-03
Iteration: 4
|Total Norm: 4.1375e+03 |Residual: 3.6461e+03 |A: 1.9558e+03| Relative Norm : 1.7140e-02
Iteration: 5
|Total Norm: 4.0463e+02 |Residual: 9.7616e+01 |A: 3.9268e+02| Relative Norm : 1.6762e-03
Iteration: 6
|Total Norm: 7.1484e+02 |Residual: 7.1375e+02 |A: 3.9419e+01| Relative Norm : 2.9613e-03
Iteration: 7
|Total Norm: 2.8292e+00 |Residual: 2.8045e+00 |A: 3.7334e-01| Relative Norm : 1.1720e-05
Iteration: 8
|Total Norm: 3.3809e+00 |Residual: 3.3450e+00 |A: 4.9193e-01| Relative Norm : 1.4006e-05
Iteration: 9
|Total Norm: 7.2058e-04 |Residual: 7.2021e-04 |A: 2.3090e-05| Relative Norm : 2.9850e-09
Arc-Length Step 25 :
Iteration: 0
|Total Norm: 6.6015e+04 |Residual: 6.6015e+04 |A: 1.5792e-09| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.0401e+03 |Residual: 6.4031e+02 |A: 8.1960e+02| Relative Norm : 1.5755e-02
Iteration: 2
|Total Norm: 2.4155e+02 |Residual: 1.4331e+02 |A: 1.9444e+02| Relative Norm : 3.6590e-03
Iteration: 3
|Total Norm: 6.0630e+02 |Residual: 6.0480e+02 |A: 4.2645e+01| Relative Norm : 9.1843e-03
Iteration: 4
|Total Norm: 1.8339e+01 |Residual: 1.8325e+01 |A: 7.1047e-01| Relative Norm : 2.7780e-04
Iteration: 5
|Total Norm: 2.8268e+02 |Residual: 2.8054e+02 |A: 3.4757e+01| Relative Norm : 4.2821e-03
Iteration: 6
|Total Norm: 1.2370e+01 |Residual: 1.0946e+01 |A: 5.7618e+00| Relative Norm : 1.8738e-04
Iteration: 7
|Total Norm: 2.9246e+01 |Residual: 2.8251e+01 |A: 7.5626e+00| Relative Norm : 4.4302e-04
Iteration: 8
|Total Norm: 1.5302e-01 |Residual: 1.4958e-01 |A: 3.2237e-02| Relative Norm : 2.3179e-06
Iteration: 9
|Total Norm: 5.1552e-03 |Residual: 5.0232e-03 |A: 1.1590e-03| Relative Norm : 7.8091e-08
Arc-Length Step 25 :
Iteration: 0
|Total Norm: 8.9483e+03 |Residual: 8.9483e+03 |A: 9.8439e-11| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 9.1139e+02 |Residual: 2.2628e+02 |A: 8.8285e+02| Relative Norm : 1.0185e-01
Iteration: 2
|Total Norm: 5.0036e+04 |Residual: 4.9990e+04 |A: 2.1447e+03| Relative Norm : 5.5917e+00
Iteration: 3
|Total Norm: 1.3839e+04 |Residual: 1.3803e+03 |A: 1.3770e+04| Relative Norm : 1.5465e+00
Iteration: 4
|Total Norm: 8.1557e+05 |Residual: 8.1522e+05 |A: 2.3741e+04| Relative Norm : 9.1143e+01
Iteration: 5
|Total Norm: 8.4064e+06 |Residual: 7.5080e+04 |A: 8.4061e+06| Relative Norm : 9.3945e+02
Iteration: 6
|Total Norm: 4.0253e+06 |Residual: 3.4274e+06 |A: 2.1108e+06| Relative Norm : 4.4984e+02
Iteration: 7
|Total Norm: 1.4000e+06 |Residual: 1.2952e+06 |A: 5.3146e+05| Relative Norm : 1.5645e+02
Iteration: 8
|Total Norm: 1.3729e+05 |Residual: 2.8146e+04 |A: 1.3438e+05| Relative Norm : 1.5343e+01
Iteration: 9
|Total Norm: 2.1361e+05 |Residual: 2.1073e+05 |A: 3.4969e+04| Relative Norm : 2.3872e+01
Arc-Length Step 25 :
Iteration: 0
|Total Norm: 1.8689e+03 |Residual: 1.8689e+03 |A: 6.1937e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 5.0828e+00 |Residual: 5.0641e+00 |A: 4.3660e-01| Relative Norm : 2.7198e-03
Iteration: 2
|Total Norm: 5.9475e+00 |Residual: 5.2997e+00 |A: 2.6993e+00| Relative Norm : 3.1824e-03
Iteration: 3
|Total Norm: 5.3195e+00 |Residual: 5.3080e+00 |A: 3.4895e-01| Relative Norm : 2.8464e-03
Iteration: 4
|Total Norm: 9.7896e-02 |Residual: 9.7079e-02 |A: 1.2624e-02| Relative Norm : 5.2383e-05
Iteration: 5
|Total Norm: 9.5520e-05 |Residual: 4.6914e-05 |A: 8.3205e-05| Relative Norm : 5.1111e-08
Iteration: 6
|Total Norm: 2.7345e-08 |Residual: 2.7337e-08 |A: 6.7900e-10| Relative Norm : 1.4632e-11
Arc-Length Step 26 :
Iteration: 0
|Total Norm: 7.3364e+01 |Residual: 7.3364e+01 |A: 6.7899e-10| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 8.9900e-02 |Residual: 8.9828e-02 |A: 3.6144e-03| Relative Norm : 1.2254e-03
Iteration: 2
|Total Norm: 2.2797e-03 |Residual: 2.1179e-03 |A: 8.4350e-04| Relative Norm : 3.1074e-05
Iteration: 3
|Total Norm: 9.7878e-07 |Residual: 9.7632e-07 |A: 6.9389e-08| Relative Norm : 1.3341e-08
Arc-Length Step 27 :
Iteration: 0
|Total Norm: 2.1918e+02 |Residual: 2.1918e+02 |A: 2.7755e-07| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 5.7245e-01 |Residual: 5.7235e-01 |A: 1.0634e-02| Relative Norm : 2.6118e-03
Iteration: 2
|Total Norm: 9.6389e-02 |Residual: 8.9499e-02 |A: 3.5789e-02| Relative Norm : 4.3977e-04
Iteration: 3
|Total Norm: 4.2264e-04 |Residual: 4.2149e-04 |A: 3.1154e-05| Relative Norm : 1.9283e-06
Iteration: 4
|Total Norm: 2.9989e-08 |Residual: 2.9989e-08 |A: 8.5290e-11| Relative Norm : 1.3682e-10
Arc-Length Step 28 :
Iteration: 0
|Total Norm: 8.8742e+02 |Residual: 8.8742e+02 |A: 3.4169e-10| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.4129e+00 |Residual: 1.4129e+00 |A: 8.0080e-03| Relative Norm : 1.5921e-03
Iteration: 2
|Total Norm: 3.4231e-01 |Residual: 3.2625e-01 |A: 1.0363e-01| Relative Norm : 3.8574e-04
Iteration: 3
|Total Norm: 8.4127e-04 |Residual: 8.3872e-04 |A: 6.5473e-05| Relative Norm : 9.4799e-07
Iteration: 4
|Total Norm: 3.1576e-08 |Residual: 3.1532e-08 |A: 1.6775e-09| Relative Norm : 3.5582e-11
Arc-Length Step 29 :
Iteration: 0
|Total Norm: 3.7624e+03 |Residual: 3.7624e+03 |A: 6.7135e-09| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.1319e+01 |Residual: 1.1318e+01 |A: 1.6537e-01| Relative Norm : 3.0086e-03
Iteration: 2
|Total Norm: 4.0048e+00 |Residual: 3.8898e+00 |A: 9.5270e-01| Relative Norm : 1.0644e-03
Iteration: 3
|Total Norm: 1.5971e-02 |Residual: 1.5910e-02 |A: 1.3936e-03| Relative Norm : 4.2450e-06
Iteration: 4
|Total Norm: 2.0736e-05 |Residual: 2.0358e-05 |A: 3.9436e-06| Relative Norm : 5.5115e-09
Iteration: 5
|Total Norm: 2.9611e-08 |Residual: 2.9611e-08 |A: 1.1369e-13| Relative Norm : 7.8703e-12
Arc-Length Step 30 :
Iteration: 0
|Total Norm: 1.7552e+04 |Residual: 1.7552e+04 |A: 4.0927e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 8.4898e+01 |Residual: 8.4857e+01 |A: 2.6416e+00| Relative Norm : 4.8370e-03
Iteration: 2
|Total Norm: 4.9698e+01 |Residual: 4.9038e+01 |A: 8.0723e+00| Relative Norm : 2.8315e-03
Iteration: 3
|Total Norm: 4.1715e-01 |Residual: 4.1642e-01 |A: 2.4563e-02| Relative Norm : 2.3767e-05
Iteration: 4
|Total Norm: 7.1417e-02 |Residual: 7.0936e-02 |A: 8.2750e-03| Relative Norm : 4.0690e-06
Iteration: 5
|Total Norm: 1.6288e-06 |Residual: 1.6272e-06 |A: 7.2038e-08| Relative Norm : 9.2799e-11
Iteration: 6
|Total Norm: 2.7921e-08 |Residual: 2.7921e-08 |A: 2.2737e-13| Relative Norm : 1.5908e-12
Arc-Length Step 31 :
Iteration: 0
|Total Norm: 8.7084e+04 |Residual: 8.7084e+04 |A: 9.0949e-13| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 8.6011e+02 |Residual: 8.5958e+02 |A: 3.0113e+01| Relative Norm : 9.8768e-03
Iteration: 2
|Total Norm: 5.0802e+02 |Residual: 5.0552e+02 |A: 5.0335e+01| Relative Norm : 5.8337e-03
Iteration: 3
|Total Norm: 3.4628e+00 |Residual: 3.4515e+00 |A: 2.7905e-01| Relative Norm : 3.9764e-05
Iteration: 4
|Total Norm: 7.1546e+00 |Residual: 7.1352e+00 |A: 5.2597e-01| Relative Norm : 8.2157e-05
Iteration: 5
|Total Norm: 1.7574e-03 |Residual: 1.7572e-03 |A: 3.0303e-05| Relative Norm : 2.0181e-08
Iteration: 6
|Total Norm: 2.1456e-06 |Residual: 2.1395e-06 |A: 1.6172e-07| Relative Norm : 2.4639e-11
Iteration: 7
|Total Norm: 2.8879e-08 |Residual: 2.8879e-08 |A: 4.5475e-13| Relative Norm : 3.3163e-13
Arc-Length Step 32 :
Iteration: 0
|Total Norm: 9.1066e+04 |Residual: 9.1066e+04 |A: -8.6402e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 8.5337e+02 |Residual: 8.5297e+02 |A: 2.6175e+01| Relative Norm : 9.3709e-03
Iteration: 2
|Total Norm: 3.1832e+02 |Residual: 3.1742e+02 |A: 2.4018e+01| Relative Norm : 3.4955e-03
Iteration: 3
|Total Norm: 1.9095e+00 |Residual: 1.9086e+00 |A: 5.6558e-02| Relative Norm : 2.0968e-05
Iteration: 4
|Total Norm: 2.4840e+00 |Residual: 2.4800e+00 |A: 1.4105e-01| Relative Norm : 2.7276e-05
Iteration: 5
|Total Norm: 1.6501e-04 |Residual: 1.6499e-04 |A: 2.3621e-06| Relative Norm : 1.8120e-09
Iteration: 6
|Total Norm: 3.7251e-08 |Residual: 3.7231e-08 |A: 1.2128e-09| Relative Norm : 4.0905e-13
Arc-Length Step 33 :
Iteration: 0
|Total Norm: 6.3846e+04 |Residual: 6.3846e+04 |A: 1.2078e-09| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 4.3912e+02 |Residual: 4.3891e+02 |A: 1.3335e+01| Relative Norm : 6.8777e-03
Iteration: 2
|Total Norm: 1.0589e+02 |Residual: 1.0564e+02 |A: 7.2923e+00| Relative Norm : 1.6585e-03
Iteration: 3
|Total Norm: 4.1402e+00 |Residual: 4.1375e+00 |A: 1.5107e-01| Relative Norm : 6.4847e-05
Iteration: 4
|Total Norm: 5.1976e+00 |Residual: 5.1915e+00 |A: 2.5175e-01| Relative Norm : 8.1408e-05
Iteration: 5
|Total Norm: 7.9734e-03 |Residual: 7.9679e-03 |A: 2.9442e-04| Relative Norm : 1.2488e-07
Iteration: 6
|Total Norm: 1.6263e-05 |Residual: 1.6243e-05 |A: 7.9908e-07| Relative Norm : 2.5472e-10
Iteration: 7
|Total Norm: 2.7721e-08 |Residual: 2.7721e-08 |A: 0.0000e+00| Relative Norm : 4.3419e-13
Arc-Length Step 34 :
Iteration: 0
|Total Norm: 5.0661e+04 |Residual: 5.0661e+04 |A: 4.5475e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 2.8349e+02 |Residual: 2.8336e+02 |A: 8.5173e+00| Relative Norm : 5.5959e-03
Iteration: 2
|Total Norm: 4.2359e+01 |Residual: 4.2258e+01 |A: 2.9283e+00| Relative Norm : 8.3613e-04
Iteration: 3
|Total Norm: 1.5828e-01 |Residual: 1.5819e-01 |A: 5.3238e-03| Relative Norm : 3.1242e-06
Iteration: 4
|Total Norm: 1.6725e-02 |Residual: 1.6709e-02 |A: 7.2229e-04| Relative Norm : 3.3013e-07
Iteration: 5
|Total Norm: 3.4713e-08 |Residual: 3.4710e-08 |A: 4.6430e-10| Relative Norm : 6.8521e-13
Arc-Length Step 35 :
Iteration: 0
|Total Norm: 4.3295e+04 |Residual: 4.3295e+04 |A: 4.7612e-10| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 2.0932e+02 |Residual: 2.0923e+02 |A: 6.2241e+00| Relative Norm : 4.8348e-03
Iteration: 2
|Total Norm: 1.8360e+01 |Residual: 1.8308e+01 |A: 1.3724e+00| Relative Norm : 4.2406e-04
Iteration: 3
|Total Norm: 1.9069e-02 |Residual: 1.9058e-02 |A: 6.2711e-04| Relative Norm : 4.4044e-07
Iteration: 4
|Total Norm: 2.8499e-04 |Residual: 2.8477e-04 |A: 1.1181e-05| Relative Norm : 6.5825e-09
Iteration: 5
|Total Norm: 2.9618e-08 |Residual: 2.9618e-08 |A: 0.0000e+00| Relative Norm : 6.8410e-13
Arc-Length Step 36 :
Iteration: 0
|Total Norm: 3.8870e+04 |Residual: 3.8870e+04 |A: -3.1832e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.6883e+02 |Residual: 1.6875e+02 |A: 4.9767e+00| Relative Norm : 4.3433e-03
Iteration: 2
|Total Norm: 8.3354e+00 |Residual: 8.3047e+00 |A: 7.1527e-01| Relative Norm : 2.1444e-04
Iteration: 3
|Total Norm: 2.7970e-03 |Residual: 2.7947e-03 |A: 1.1491e-04| Relative Norm : 7.1958e-08
Iteration: 4
|Total Norm: 6.2644e-06 |Residual: 6.2603e-06 |A: 2.2669e-07| Relative Norm : 1.6116e-10
Iteration: 5
|Total Norm: 3.5001e-08 |Residual: 3.5001e-08 |A: 4.5475e-13| Relative Norm : 9.0044e-13
Arc-Length Step 37 :
Iteration: 0
|Total Norm: 3.6170e+04 |Residual: 3.6170e+04 |A: 1.5461e-11| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.4516e+02 |Residual: 1.4509e+02 |A: 4.2495e+00| Relative Norm : 4.0132e-03
Iteration: 2
|Total Norm: 4.2778e+00 |Residual: 4.2578e+00 |A: 4.1334e-01| Relative Norm : 1.1827e-04
Iteration: 3
|Total Norm: 1.7208e-04 |Residual: 1.7076e-04 |A: 2.1304e-05| Relative Norm : 4.7576e-09
Iteration: 4
|Total Norm: 3.3716e-08 |Residual: 3.3714e-08 |A: 3.5425e-10| Relative Norm : 9.3216e-13
Arc-Length Step 38 :
Iteration: 0
|Total Norm: 3.4612e+04 |Residual: 3.4612e+04 |A: 3.6425e-10| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.3126e+02 |Residual: 1.3120e+02 |A: 3.8197e+00| Relative Norm : 3.7923e-03
Iteration: 2
|Total Norm: 2.8353e+00 |Residual: 2.8218e+00 |A: 2.7614e-01| Relative Norm : 8.1918e-05
Iteration: 3
|Total Norm: 2.3900e-04 |Residual: 2.3882e-04 |A: 9.3840e-06| Relative Norm : 6.9053e-09
Iteration: 4
|Total Norm: 4.1854e-08 |Residual: 4.1852e-08 |A: 4.7294e-10| Relative Norm : 1.2093e-12
Arc-Length Step 39 :
Iteration: 0
|Total Norm: 3.3903e+04 |Residual: 3.3903e+04 |A: 4.7430e-10| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.2390e+02 |Residual: 1.2385e+02 |A: 3.5824e+00| Relative Norm : 3.6546e-03
Iteration: 2
|Total Norm: 2.5774e+00 |Residual: 2.5672e+00 |A: 2.2836e-01| Relative Norm : 7.6022e-05
Iteration: 3
|Total Norm: 7.5988e-04 |Residual: 7.5959e-04 |A: 2.0927e-05| Relative Norm : 2.2414e-08
Iteration: 4
|Total Norm: 6.8315e-08 |Residual: 6.8292e-08 |A: 1.7480e-09| Relative Norm : 2.0150e-12
Arc-Length Step 40 :
Iteration: 0
|Total Norm: 3.3901e+04 |Residual: 3.3901e+04 |A: 1.7503e-09| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.2163e+02 |Residual: 1.2158e+02 |A: 3.4864e+00| Relative Norm : 3.5879e-03
Iteration: 2
|Total Norm: 3.9943e+00 |Residual: 3.9871e+00 |A: 2.3999e-01| Relative Norm : 1.1782e-04
Iteration: 3
|Total Norm: 2.1299e-03 |Residual: 2.1294e-03 |A: 4.7324e-05| Relative Norm : 6.2829e-08
Iteration: 4
|Total Norm: 1.4254e-06 |Residual: 1.4248e-06 |A: 4.1704e-08| Relative Norm : 4.2046e-11
Iteration: 5
|Total Norm: 3.4827e-08 |Residual: 3.4827e-08 |A: 4.5475e-13| Relative Norm : 1.0273e-12
Arc-Length Step 41 :
Iteration: 0
|Total Norm: 3.4559e+04 |Residual: 3.4559e+04 |A: -1.3642e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.2403e+02 |Residual: 1.2398e+02 |A: 3.5097e+00| Relative Norm : 3.5890e-03
Iteration: 2
|Total Norm: 7.5214e+00 |Residual: 7.5152e+00 |A: 3.0324e-01| Relative Norm : 2.1764e-04
Iteration: 3
|Total Norm: 5.4359e-03 |Residual: 5.4350e-03 |A: 9.8985e-05| Relative Norm : 1.5729e-07
Iteration: 4
|Total Norm: 1.9945e-05 |Residual: 1.9937e-05 |A: 5.5771e-07| Relative Norm : 5.7713e-10
Iteration: 5
|Total Norm: 3.8125e-08 |Residual: 3.8125e-08 |A: 0.0000e+00| Relative Norm : 1.1032e-12
Arc-Length Step 42 :
Iteration: 0
|Total Norm: 3.5907e+04 |Residual: 3.5907e+04 |A: 6.8212e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.3148e+02 |Residual: 1.3142e+02 |A: 3.6499e+00| Relative Norm : 3.6615e-03
Iteration: 2
|Total Norm: 1.3557e+01 |Residual: 1.3550e+01 |A: 4.2612e-01| Relative Norm : 3.7756e-04
Iteration: 3
|Total Norm: 1.4047e-02 |Residual: 1.4045e-02 |A: 2.1937e-04| Relative Norm : 3.9120e-07
Iteration: 4
|Total Norm: 2.0526e-04 |Residual: 2.0519e-04 |A: 5.5082e-06| Relative Norm : 5.7164e-09
Iteration: 5
|Total Norm: 3.6514e-08 |Residual: 3.6514e-08 |A: 4.5475e-13| Relative Norm : 1.0169e-12
Arc-Length Step 43 :
Iteration: 0
|Total Norm: 3.8055e+04 |Residual: 3.8055e+04 |A: -1.8190e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.4523e+02 |Residual: 1.4518e+02 |A: 3.9222e+00| Relative Norm : 3.8163e-03
Iteration: 2
|Total Norm: 2.3428e+01 |Residual: 2.3419e+01 |A: 6.3523e-01| Relative Norm : 6.1563e-04
Iteration: 3
|Total Norm: 4.1184e-02 |Residual: 4.1180e-02 |A: 6.0889e-04| Relative Norm : 1.0822e-06
Iteration: 4
|Total Norm: 2.2378e-03 |Residual: 2.2371e-03 |A: 5.7917e-05| Relative Norm : 5.8805e-08
Iteration: 5
|Total Norm: 3.3246e-08 |Residual: 3.3246e-08 |A: 7.2760e-12| Relative Norm : 8.7363e-13
Arc-Length Step 44 :
Iteration: 0
|Total Norm: 4.1219e+04 |Residual: 4.1219e+04 |A: 5.4570e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.6791e+02 |Residual: 1.6785e+02 |A: 4.3651e+00| Relative Norm : 4.0735e-03
Iteration: 2
|Total Norm: 4.0042e+01 |Residual: 4.0029e+01 |A: 9.8946e-01| Relative Norm : 9.7143e-04
Iteration: 3
|Total Norm: 1.9178e-01 |Residual: 1.9175e-01 |A: 3.2877e-03| Relative Norm : 4.6527e-06
Iteration: 4
|Total Norm: 4.4537e-02 |Residual: 4.4523e-02 |A: 1.1172e-03| Relative Norm : 1.0805e-06
Iteration: 5
|Total Norm: 2.8635e-07 |Residual: 2.8630e-07 |A: 5.0431e-09| Relative Norm : 6.9469e-12
Arc-Length Step 45 :
Iteration: 0
|Total Norm: 4.5787e+04 |Residual: 4.5787e+04 |A: 5.0445e-09| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 2.0459e+02 |Residual: 2.0453e+02 |A: 5.0546e+00| Relative Norm : 4.4683e-03
Iteration: 2
|Total Norm: 6.9716e+01 |Residual: 6.9698e+01 |A: 1.6177e+00| Relative Norm : 1.5226e-03
Iteration: 3
|Total Norm: 1.2046e+01 |Residual: 1.2042e+01 |A: 2.9798e-01| Relative Norm : 2.6309e-04
Iteration: 4
|Total Norm: 2.1253e+01 |Residual: 2.1246e+01 |A: 5.2226e-01| Relative Norm : 4.6416e-04
Iteration: 5
|Total Norm: 1.9226e+00 |Residual: 1.9220e+00 |A: 4.7250e-02| Relative Norm : 4.1990e-05
Iteration: 6
|Total Norm: 2.4866e-01 |Residual: 2.4859e-01 |A: 6.0416e-03| Relative Norm : 5.4308e-06
Iteration: 7
|Total Norm: 2.4744e-04 |Residual: 2.4736e-04 |A: 6.0863e-06| Relative Norm : 5.4041e-09
Iteration: 8
|Total Norm: 3.6833e-08 |Residual: 3.6833e-08 |A: 9.9590e-11| Relative Norm : 8.0444e-13
Arc-Length Step 46 :
Iteration: 0
|Total Norm: 5.2458e+04 |Residual: 5.2458e+04 |A: 9.7771e-11| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 2.6553e+02 |Residual: 2.6546e+02 |A: 6.1396e+00| Relative Norm : 5.0618e-03
Iteration: 2
|Total Norm: 1.2735e+02 |Residual: 1.2732e+02 |A: 2.8240e+00| Relative Norm : 2.4277e-03
Iteration: 3
|Total Norm: 4.2392e-01 |Residual: 4.2388e-01 |A: 5.5484e-03| Relative Norm : 8.0810e-06
Iteration: 4
|Total Norm: 6.6654e-01 |Residual: 6.6635e-01 |A: 1.6049e-02| Relative Norm : 1.2706e-05
Iteration: 5
|Total Norm: 1.1600e-05 |Residual: 1.1599e-05 |A: 1.5377e-07| Relative Norm : 2.2113e-10
Iteration: 6
|Total Norm: 3.6889e-08 |Residual: 3.6889e-08 |A: 1.2733e-11| Relative Norm : 7.0320e-13
Arc-Length Step 47 :
Iteration: 0
|Total Norm: 6.2560e+04 |Residual: 6.2560e+04 |A: 1.2733e-11| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 3.7329e+02 |Residual: 3.7321e+02 |A: 7.9313e+00| Relative Norm : 5.9670e-03
Iteration: 2
|Total Norm: 2.5260e+02 |Residual: 2.5254e+02 |A: 5.4171e+00| Relative Norm : 4.0377e-03
Iteration: 3
|Total Norm: 4.6659e-01 |Residual: 4.6655e-01 |A: 6.1962e-03| Relative Norm : 7.4583e-06
Iteration: 4
|Total Norm: 1.0908e+00 |Residual: 1.0905e+00 |A: 2.6176e-02| Relative Norm : 1.7436e-05
Iteration: 5
|Total Norm: 6.8784e-06 |Residual: 6.8774e-06 |A: 1.1779e-07| Relative Norm : 1.0995e-10
Iteration: 6
|Total Norm: 3.7628e-08 |Residual: 3.7628e-08 |A: 5.9117e-12| Relative Norm : 6.0147e-13
Arc-Length Step 48 :
Iteration: 0
|Total Norm: 7.8839e+04 |Residual: 7.8839e+04 |A: 5.4570e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 5.8416e+02 |Residual: 5.8406e+02 |A: 1.1155e+01| Relative Norm : 7.4095e-03
Iteration: 2
|Total Norm: 5.6834e+02 |Residual: 5.6821e+02 |A: 1.1914e+01| Relative Norm : 7.2088e-03
Iteration: 3
|Total Norm: 8.3688e-01 |Residual: 8.3660e-01 |A: 2.1368e-02| Relative Norm : 1.0615e-05
Iteration: 4
|Total Norm: 3.6126e+00 |Residual: 3.6116e+00 |A: 8.8821e-02| Relative Norm : 4.5823e-05
Iteration: 5
|Total Norm: 1.7746e-05 |Residual: 1.7717e-05 |A: 1.0224e-06| Relative Norm : 2.2510e-10
Iteration: 6
|Total Norm: 4.5654e-08 |Residual: 4.5654e-08 |A: 1.7280e-11| Relative Norm : 5.7908e-13
Arc-Length Step 49 :
Iteration: 0
|Total Norm: 1.0768e+05 |Residual: 1.0768e+05 |A: 1.7280e-11| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.0652e+03 |Residual: 1.0650e+03 |A: 1.7783e+01| Relative Norm : 9.8919e-03
Iteration: 2
|Total Norm: 1.5166e+03 |Residual: 1.5163e+03 |A: 3.1470e+01| Relative Norm : 1.4084e-02
Iteration: 3
|Total Norm: 2.7538e+00 |Residual: 2.7500e+00 |A: 1.4542e-01| Relative Norm : 2.5574e-05
Iteration: 4
|Total Norm: 1.6473e+01 |Residual: 1.6467e+01 |A: 4.4538e-01| Relative Norm : 1.5298e-04
Iteration: 5
|Total Norm: 1.1577e-03 |Residual: 1.1572e-03 |A: 3.5636e-05| Relative Norm : 1.0752e-08
Iteration: 6
|Total Norm: 1.2794e-05 |Residual: 1.2790e-05 |A: 3.3276e-07| Relative Norm : 1.1881e-10
Iteration: 7
|Total Norm: 3.6893e-08 |Residual: 3.6893e-08 |A: -4.5475e-13| Relative Norm : 3.4262e-13
Arc-Length Step 50 :
Iteration: 0
|Total Norm: 1.6624e+05 |Residual: 1.6624e+05 |A: 0.0000e+00| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 2.4416e+03 |Residual: 2.4413e+03 |A: 3.4386e+01| Relative Norm : 1.4687e-02
Iteration: 2
|Total Norm: 4.2653e+03 |Residual: 4.2644e+03 |A: 8.9682e+01| Relative Norm : 2.5658e-02
Iteration: 3
|Total Norm: 1.4715e+01 |Residual: 1.4645e+01 |A: 1.4368e+00| Relative Norm : 8.8517e-05
Iteration: 4
|Total Norm: 2.5703e+01 |Residual: 2.5685e+01 |A: 9.8622e-01| Relative Norm : 1.5462e-04
Iteration: 5
|Total Norm: 4.9367e-01 |Residual: 4.9336e-01 |A: 1.7398e-02| Relative Norm : 2.9696e-06
Iteration: 6
|Total Norm: 3.4496e-01 |Residual: 3.4478e-01 |A: 1.1114e-02| Relative Norm : 2.0751e-06
Iteration: 7
|Total Norm: 7.6191e-05 |Residual: 7.6145e-05 |A: 2.6436e-06| Relative Norm : 4.5832e-10
Iteration: 8
|Total Norm: 4.2089e-08 |Residual: 4.2088e-08 |A: 2.8786e-10| Relative Norm : 2.5319e-13
Arc-Length Step 51 :
Iteration: 0
|Total Norm: 3.0628e+05 |Residual: 3.0628e+05 |A: 2.8695e-10| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 7.7680e+03 |Residual: 7.7675e+03 |A: 8.8126e+01| Relative Norm : 2.5362e-02
Iteration: 2
|Total Norm: 3.7142e+03 |Residual: 3.7130e+03 |A: 9.4799e+01| Relative Norm : 1.2127e-02
Iteration: 3
|Total Norm: 2.1182e+01 |Residual: 2.1093e+01 |A: 1.9449e+00| Relative Norm : 6.9158e-05
Iteration: 4
|Total Norm: 1.8003e+03 |Residual: 1.7986e+03 |A: 7.6687e+01| Relative Norm : 5.8777e-03
Iteration: 5
|Total Norm: 6.3164e+00 |Residual: 5.6812e+00 |A: 2.7605e+00| Relative Norm : 2.0623e-05
Iteration: 6
|Total Norm: 6.6435e+01 |Residual: 6.6207e+01 |A: 5.4920e+00| Relative Norm : 2.1691e-04
Iteration: 7
|Total Norm: 3.6919e-01 |Residual: 3.6516e-01 |A: 5.4386e-02| Relative Norm : 1.2054e-06
Iteration: 8
|Total Norm: 6.8926e-01 |Residual: 6.8751e-01 |A: 4.9045e-02| Relative Norm : 2.2504e-06
Iteration: 9
|Total Norm: 8.5337e-06 |Residual: 8.3513e-06 |A: 1.7546e-06| Relative Norm : 2.7862e-11
Arc-Length Step 51 :
Iteration: 0
|Total Norm: 8.7121e+04 |Residual: 8.7121e+04 |A: 7.1623e-11| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 7.2391e+02 |Residual: 7.2382e+02 |A: 1.1591e+01| Relative Norm : 8.3093e-03
Iteration: 2
|Total Norm: 2.0955e+03 |Residual: 2.0948e+03 |A: 5.6108e+01| Relative Norm : 2.4053e-02
Iteration: 3
|Total Norm: 9.5433e+00 |Residual: 8.4833e+00 |A: 4.3713e+00| Relative Norm : 1.0954e-04
Iteration: 4
|Total Norm: 1.5261e+02 |Residual: 1.5219e+02 |A: 1.1214e+01| Relative Norm : 1.7517e-03
Iteration: 5
|Total Norm: 5.8578e-01 |Residual: 5.4816e-01 |A: 2.0653e-01| Relative Norm : 6.7238e-06
Iteration: 6
|Total Norm: 2.6581e+00 |Residual: 2.6545e+00 |A: 1.3892e-01| Relative Norm : 3.0511e-05
Iteration: 7
|Total Norm: 2.7636e-04 |Residual: 2.7621e-04 |A: 9.0212e-06| Relative Norm : 3.1721e-09
Iteration: 8
|Total Norm: 7.3010e-07 |Residual: 7.2913e-07 |A: 3.7649e-08| Relative Norm : 8.3803e-12
Arc-Length Step 52 :
Iteration: 0
|Total Norm: 8.1948e+04 |Residual: 8.1948e+04 |A: 3.7649e-08| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 6.7766e+02 |Residual: 6.7756e+02 |A: 1.1824e+01| Relative Norm : 8.2694e-03
Iteration: 2
|Total Norm: 1.4455e+03 |Residual: 1.4443e+03 |A: 5.8366e+01| Relative Norm : 1.7639e-02
Iteration: 3
|Total Norm: 1.7223e+01 |Residual: 1.0583e+01 |A: 1.3588e+01| Relative Norm : 2.1017e-04
Iteration: 4
|Total Norm: 1.0651e+02 |Residual: 1.0199e+02 |A: 3.0683e+01| Relative Norm : 1.2997e-03
Iteration: 5
|Total Norm: 2.2719e+01 |Residual: 2.1108e+01 |A: 8.4042e+00| Relative Norm : 2.7724e-04
Iteration: 6
|Total Norm: 1.1619e+02 |Residual: 1.1482e+02 |A: 1.7823e+01| Relative Norm : 1.4179e-03
Iteration: 7
|Total Norm: 2.0681e+00 |Residual: 2.0567e+00 |A: 2.1631e-01| Relative Norm : 2.5236e-05
Iteration: 8
|Total Norm: 1.2045e+01 |Residual: 1.1995e+01 |A: 1.0980e+00| Relative Norm : 1.4698e-04
Iteration: 9
|Total Norm: 1.5071e-01 |Residual: 1.5058e-01 |A: 6.2524e-03| Relative Norm : 1.8391e-06
Arc-Length Step 52 :
Iteration: 0
|Total Norm: 2.4861e+04 |Residual: 2.4861e+04 |A: 9.4123e-09| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 8.5868e+01 |Residual: 8.5858e+01 |A: 1.3060e+00| Relative Norm : 3.4539e-03
Iteration: 2
|Total Norm: 1.1722e+02 |Residual: 1.1712e+02 |A: 4.7950e+00| Relative Norm : 4.7150e-03
Iteration: 3
|Total Norm: 2.4839e+00 |Residual: 2.3896e+00 |A: 6.7812e-01| Relative Norm : 9.9914e-05
Iteration: 4
|Total Norm: 1.0372e+01 |Residual: 1.0314e+01 |A: 1.0940e+00| Relative Norm : 4.1720e-04
Iteration: 5
|Total Norm: 4.9935e-02 |Residual: 4.9884e-02 |A: 2.2635e-03| Relative Norm : 2.0086e-06
Iteration: 6
|Total Norm: 2.5356e-03 |Residual: 2.5263e-03 |A: 2.1714e-04| Relative Norm : 1.0199e-07
Iteration: 7
|Total Norm: 4.4650e-08 |Residual: 4.4648e-08 |A: 3.5681e-10| Relative Norm : 1.7960e-12
Arc-Length Step 53 :
Iteration: 0
|Total Norm: 1.8627e+04 |Residual: 1.8627e+04 |A: 3.5703e-10| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 6.0131e+01 |Residual: 6.0126e+01 |A: 7.8925e-01| Relative Norm : 3.2281e-03
Iteration: 2
|Total Norm: 4.0217e+01 |Residual: 4.0147e+01 |A: 2.3715e+00| Relative Norm : 2.1590e-03
Iteration: 3
|Total Norm: 7.0874e+00 |Residual: 7.0624e+00 |A: 5.9487e-01| Relative Norm : 3.8049e-04
Iteration: 4
|Total Norm: 4.5474e+00 |Residual: 4.5112e+00 |A: 5.7256e-01| Relative Norm : 2.4413e-04
Iteration: 5
|Total Norm: 2.0718e-01 |Residual: 2.0676e-01 |A: 1.3226e-02| Relative Norm : 1.1123e-05
Iteration: 6
|Total Norm: 1.0536e-03 |Residual: 1.0381e-03 |A: 1.8038e-04| Relative Norm : 5.6564e-08
Iteration: 7
|Total Norm: 5.2885e-08 |Residual: 5.2847e-08 |A: 1.9986e-09| Relative Norm : 2.8391e-12
Arc-Length Step 54 :
Iteration: 0
|Total Norm: 8.0779e+04 |Residual: 8.0779e+04 |A: 7.9958e-09| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 6.8287e+02 |Residual: 6.8273e+02 |A: 1.3488e+01| Relative Norm : 8.4535e-03
Iteration: 2
|Total Norm: 4.0510e+02 |Residual: 4.0376e+02 |A: 3.3017e+01| Relative Norm : 5.0150e-03
Iteration: 3
|Total Norm: 1.2444e+02 |Residual: 4.5640e+01 |A: 1.1577e+02| Relative Norm : 1.5405e-03
Iteration: 4
|Total Norm: 1.2117e+02 |Residual: 5.3626e+01 |A: 1.0866e+02| Relative Norm : 1.5000e-03
Iteration: 5
|Total Norm: 5.2567e+02 |Residual: 5.1915e+02 |A: 8.2504e+01| Relative Norm : 6.5075e-03
Iteration: 6
|Total Norm: 1.2415e+01 |Residual: 5.8974e+00 |A: 1.0925e+01| Relative Norm : 1.5369e-04
Iteration: 7
|Total Norm: 6.5989e+01 |Residual: 6.4346e+01 |A: 1.4636e+01| Relative Norm : 8.1691e-04
Iteration: 8
|Total Norm: 2.7609e+01 |Residual: 2.7149e+01 |A: 5.0202e+00| Relative Norm : 3.4179e-04
Iteration: 9
|Total Norm: 3.1282e+01 |Residual: 2.9869e+01 |A: 9.2942e+00| Relative Norm : 3.8725e-04
Arc-Length Step 54 :
Iteration: 0
|Total Norm: 2.1077e+04 |Residual: 2.1077e+04 |A: 1.9989e-09| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 7.4365e+01 |Residual: 7.4358e+01 |A: 1.0559e+00| Relative Norm : 3.5282e-03
Iteration: 2
|Total Norm: 2.8742e+01 |Residual: 2.8650e+01 |A: 2.2925e+00| Relative Norm : 1.3636e-03
Iteration: 3
|Total Norm: 1.5243e+00 |Residual: 1.5204e+00 |A: 1.0950e-01| Relative Norm : 7.2320e-05
Iteration: 4
|Total Norm: 1.4559e-01 |Residual: 1.3903e-01 |A: 4.3203e-02| Relative Norm : 6.9074e-06
Iteration: 5
|Total Norm: 3.7782e-04 |Residual: 3.7743e-04 |A: 1.7084e-05| Relative Norm : 1.7925e-08
Iteration: 6
|Total Norm: 4.0833e-08 |Residual: 4.0832e-08 |A: 2.9326e-10| Relative Norm : 1.9373e-12
Arc-Length Step 55 :
Iteration: 0
|Total Norm: 2.3072e+04 |Residual: 2.3072e+04 |A: 2.9337e-10| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 8.8257e+01 |Residual: 8.8244e+01 |A: 1.4936e+00| Relative Norm : 3.8253e-03
Iteration: 2
|Total Norm: 1.6513e+01 |Residual: 1.6427e+01 |A: 1.6769e+00| Relative Norm : 7.1571e-04
Iteration: 3
|Total Norm: 4.1620e-01 |Residual: 4.1535e-01 |A: 2.6628e-02| Relative Norm : 1.8040e-05
Iteration: 4
|Total Norm: 3.4984e-03 |Residual: 2.2081e-03 |A: 2.7135e-03| Relative Norm : 1.5163e-07
Iteration: 5
|Total Norm: 8.6104e-07 |Residual: 8.6065e-07 |A: 2.6016e-08| Relative Norm : 3.7320e-11
Arc-Length Step 56 :
Iteration: 0
|Total Norm: 9.4500e+04 |Residual: 9.4500e+04 |A: 1.0406e-07| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 9.4959e+02 |Residual: 9.4833e+02 |A: 4.8883e+01| Relative Norm : 1.0049e-02
Iteration: 2
|Total Norm: 1.3711e+02 |Residual: 1.3593e+02 |A: 1.7969e+01| Relative Norm : 1.4509e-03
Iteration: 3
|Total Norm: 5.0153e+00 |Residual: 4.1021e+00 |A: 2.8856e+00| Relative Norm : 5.3072e-05
Iteration: 4
|Total Norm: 7.1572e-01 |Residual: 2.5487e-01 |A: 6.6880e-01| Relative Norm : 7.5737e-06
Iteration: 5
|Total Norm: 1.0148e-02 |Residual: 1.0145e-02 |A: 2.1638e-04| Relative Norm : 1.0738e-07
Iteration: 6
|Total Norm: 4.2100e-08 |Residual: 3.6183e-08 |A: 2.1522e-08| Relative Norm : 4.4550e-13
Arc-Length Step 57 :
Iteration: 0
|Total Norm: 6.1891e+05 |Residual: 6.1891e+05 |A: 8.6084e-08| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 3.1053e+04 |Residual: 3.1052e+04 |A: 3.0993e+02| Relative Norm : 5.0174e-02
Iteration: 2
|Total Norm: 8.0954e+02 |Residual: 8.0399e+02 |A: 9.4645e+01| Relative Norm : 1.3080e-03
Iteration: 3
|Total Norm: 4.8261e+02 |Residual: 3.8121e+02 |A: 2.9596e+02| Relative Norm : 7.7977e-04
Iteration: 4
|Total Norm: 5.5165e+01 |Residual: 1.6988e+01 |A: 5.2484e+01| Relative Norm : 8.9133e-05
Iteration: 5
|Total Norm: 5.2239e+00 |Residual: 5.1197e+00 |A: 1.0382e+00| Relative Norm : 8.4405e-06
Iteration: 6
|Total Norm: 1.4603e-02 |Residual: 1.4577e-02 |A: 8.7547e-04| Relative Norm : 2.3595e-08
Iteration: 7
|Total Norm: 2.4205e-05 |Residual: 2.1924e-05 |A: 1.0256e-05| Relative Norm : 3.9109e-11
Iteration: 8
|Total Norm: 3.4177e-08 |Residual: 3.4177e-08 |A: 4.5475e-13| Relative Norm : 5.5222e-14
Arc-Length Step 58 :
Iteration: 0
|Total Norm: 9.0231e+05 |Residual: 9.0231e+05 |A: -1.3642e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 6.2019e+04 |Residual: 6.2017e+04 |A: 5.2680e+02| Relative Norm : 6.8734e-02
Iteration: 2
|Total Norm: 9.7332e+02 |Residual: 9.7016e+02 |A: 7.8428e+01| Relative Norm : 1.0787e-03
Iteration: 3
|Total Norm: 8.6251e+02 |Residual: 8.4800e+02 |A: 1.5756e+02| Relative Norm : 9.5589e-04
Iteration: 4
|Total Norm: 5.5740e+01 |Residual: 5.4127e+01 |A: 1.3315e+01| Relative Norm : 6.1775e-05
Iteration: 5
|Total Norm: 2.0340e+01 |Residual: 2.0118e+01 |A: 2.9934e+00| Relative Norm : 2.2542e-05
Iteration: 6
|Total Norm: 2.5687e-02 |Residual: 1.7272e-02 |A: 1.9012e-02| Relative Norm : 2.8468e-08
Iteration: 7
|Total Norm: 2.6885e-04 |Residual: 2.5989e-04 |A: 6.8843e-05| Relative Norm : 2.9796e-10
Iteration: 8
|Total Norm: 4.2364e-08 |Residual: 4.2364e-08 |A: 9.0949e-13| Relative Norm : 4.6950e-14
Arc-Length Step 59 :
Iteration: 0
|Total Norm: 8.5922e+05 |Residual: 8.5922e+05 |A: 1.8190e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 5.6600e+04 |Residual: 5.6598e+04 |A: 4.9412e+02| Relative Norm : 6.5874e-02
Iteration: 2
|Total Norm: 9.8059e+02 |Residual: 9.7822e+02 |A: 6.8157e+01| Relative Norm : 1.1413e-03
Iteration: 3
|Total Norm: 8.8227e+02 |Residual: 8.7249e+02 |A: 1.3099e+02| Relative Norm : 1.0268e-03
Iteration: 4
|Total Norm: 5.4731e+01 |Residual: 5.3653e+01 |A: 1.0809e+01| Relative Norm : 6.3698e-05
Iteration: 5
|Total Norm: 5.9486e+01 |Residual: 5.9019e+01 |A: 7.4394e+00| Relative Norm : 6.9232e-05
Iteration: 6
|Total Norm: 1.3192e-01 |Residual: 8.9010e-02 |A: 9.7371e-02| Relative Norm : 1.5354e-07
Iteration: 7
|Total Norm: 7.8714e-03 |Residual: 7.6407e-03 |A: 1.8919e-03| Relative Norm : 9.1611e-09
Iteration: 8
|Total Norm: 3.9823e-08 |Residual: 3.9819e-08 |A: 5.7707e-10| Relative Norm : 4.6348e-14
Arc-Length Step 60 :
Iteration: 0
|Total Norm: 8.5411e+05 |Residual: 8.5411e+05 |A: 5.7480e-10| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 5.5930e+04 |Residual: 5.5928e+04 |A: 4.9485e+02| Relative Norm : 6.5484e-02
Iteration: 2
|Total Norm: 9.9961e+02 |Residual: 9.9759e+02 |A: 6.3499e+01| Relative Norm : 1.1704e-03
Iteration: 3
|Total Norm: 9.9072e+02 |Residual: 9.7817e+02 |A: 1.5721e+02| Relative Norm : 1.1600e-03
Iteration: 4
|Total Norm: 5.6676e+01 |Residual: 5.4778e+01 |A: 1.4545e+01| Relative Norm : 6.6357e-05
Iteration: 5
|Total Norm: 6.9986e+01 |Residual: 6.9317e+01 |A: 9.6554e+00| Relative Norm : 8.1940e-05
Iteration: 6
|Total Norm: 1.3862e-01 |Residual: 5.2942e-02 |A: 1.2811e-01| Relative Norm : 1.6230e-07
Iteration: 7
|Total Norm: 1.0224e-03 |Residual: 9.4861e-04 |A: 3.8139e-04| Relative Norm : 1.1970e-09
Iteration: 8
|Total Norm: 4.2937e-08 |Residual: 4.2937e-08 |A: 1.9554e-11| Relative Norm : 5.0272e-14
Arc-Length Step 61 :
Iteration: 0
|Total Norm: 8.6023e+05 |Residual: 8.6023e+05 |A: 1.9554e-11| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 5.6640e+04 |Residual: 5.6637e+04 |A: 5.0708e+02| Relative Norm : 6.5843e-02
Iteration: 2
|Total Norm: 1.0220e+03 |Residual: 1.0198e+03 |A: 6.7017e+01| Relative Norm : 1.1880e-03
Iteration: 3
|Total Norm: 1.1690e+03 |Residual: 1.1425e+03 |A: 2.4758e+02| Relative Norm : 1.3590e-03
Iteration: 4
|Total Norm: 6.2350e+01 |Residual: 5.5197e+01 |A: 2.8997e+01| Relative Norm : 7.2481e-05
Iteration: 5
|Total Norm: 4.2679e+01 |Residual: 4.1917e+01 |A: 8.0286e+00| Relative Norm : 4.9613e-05
Iteration: 6
|Total Norm: 7.0869e-02 |Residual: 2.4236e-02 |A: 6.6596e-02| Relative Norm : 8.2385e-08
Iteration: 7
|Total Norm: 2.9535e-04 |Residual: 2.9345e-04 |A: 3.3471e-05| Relative Norm : 3.4334e-10
Iteration: 8
|Total Norm: 4.0397e-08 |Residual: 4.0397e-08 |A: 0.0000e+00| Relative Norm : 4.6961e-14
Arc-Length Step 62 :
Iteration: 0
|Total Norm: 8.5449e+05 |Residual: 8.5449e+05 |A: 1.3642e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 5.5895e+04 |Residual: 5.5893e+04 |A: 5.1076e+02| Relative Norm : 6.5413e-02
Iteration: 2
|Total Norm: 1.0518e+03 |Residual: 1.0487e+03 |A: 8.0482e+01| Relative Norm : 1.2309e-03
Iteration: 3
|Total Norm: 1.4030e+03 |Residual: 1.3337e+03 |A: 4.3556e+02| Relative Norm : 1.6419e-03
Iteration: 4
|Total Norm: 8.1466e+01 |Residual: 5.3513e+01 |A: 6.1426e+01| Relative Norm : 9.5339e-05
Iteration: 5
|Total Norm: 4.9188e+00 |Residual: 3.8982e+00 |A: 2.9997e+00| Relative Norm : 5.7564e-06
Iteration: 6
|Total Norm: 1.4635e-02 |Residual: 1.4486e-02 |A: 2.0817e-03| Relative Norm : 1.7127e-08
Iteration: 7
|Total Norm: 6.6353e-06 |Residual: 6.5731e-06 |A: 9.0662e-07| Relative Norm : 7.7652e-12
Iteration: 8
|Total Norm: 4.0610e-08 |Residual: 4.0610e-08 |A: 0.0000e+00| Relative Norm : 4.7525e-14
Arc-Length Step 63 :
Iteration: 0
|Total Norm: 8.0848e+05 |Residual: 8.0848e+05 |A: -1.8190e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 5.0350e+04 |Residual: 5.0348e+04 |A: 4.7732e+02| Relative Norm : 6.2277e-02
Iteration: 2
|Total Norm: 1.1380e+03 |Residual: 1.1343e+03 |A: 9.1250e+01| Relative Norm : 1.4075e-03
Iteration: 3
|Total Norm: 1.4110e+03 |Residual: 1.3230e+03 |A: 4.9065e+02| Relative Norm : 1.7453e-03
Iteration: 4
|Total Norm: 7.2692e+01 |Residual: 5.2896e+01 |A: 4.9861e+01| Relative Norm : 8.9911e-05
Iteration: 5
|Total Norm: 1.1608e+02 |Residual: 1.1580e+02 |A: 8.0102e+00| Relative Norm : 1.4357e-04
Iteration: 6
|Total Norm: 1.7146e+00 |Residual: 1.7142e+00 |A: 3.6602e-02| Relative Norm : 2.1208e-06
Iteration: 7
|Total Norm: 4.3388e+00 |Residual: 4.3269e+00 |A: 3.2076e-01| Relative Norm : 5.3666e-06
Iteration: 8
|Total Norm: 3.7616e-03 |Residual: 3.7603e-03 |A: 9.8326e-05| Relative Norm : 4.6527e-09
Iteration: 9
|Total Norm: 1.5372e-05 |Residual: 1.5334e-05 |A: 1.0876e-06| Relative Norm : 1.9013e-11
Arc-Length Step 63 :
Iteration: 0
|Total Norm: 2.3088e+05 |Residual: 2.3088e+05 |A: -4.5475e-13| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 4.6285e+03 |Residual: 4.6281e+03 |A: 6.4518e+01| Relative Norm : 2.0047e-02
Iteration: 2
|Total Norm: 4.1800e+02 |Residual: 4.1296e+02 |A: 6.4703e+01| Relative Norm : 1.8105e-03
Iteration: 3
|Total Norm: 1.3069e+01 |Residual: 1.2143e+01 |A: 4.8306e+00| Relative Norm : 5.6604e-05
Iteration: 4
|Total Norm: 3.0706e+00 |Residual: 3.0613e+00 |A: 2.3861e-01| Relative Norm : 1.3300e-05
Iteration: 5
|Total Norm: 3.6282e-03 |Residual: 3.6271e-03 |A: 9.1710e-05| Relative Norm : 1.5715e-08
Iteration: 6
|Total Norm: 6.4177e-06 |Residual: 6.3905e-06 |A: 5.9033e-07| Relative Norm : 2.7797e-11
Iteration: 7
|Total Norm: 3.4448e-08 |Residual: 3.4448e-08 |A: 2.2737e-13| Relative Norm : 1.4920e-13
Arc-Length Step 64 :
Iteration: 0
|Total Norm: 1.1048e+05 |Residual: 1.1048e+05 |A: 2.2737e-13| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.2733e+03 |Residual: 1.2731e+03 |A: 2.1341e+01| Relative Norm : 1.1526e-02
Iteration: 2
|Total Norm: 2.1410e+02 |Residual: 2.1147e+02 |A: 3.3408e+01| Relative Norm : 1.9379e-03
Iteration: 3
|Total Norm: 3.1203e+00 |Residual: 3.0417e+00 |A: 6.9592e-01| Relative Norm : 2.8244e-05
Iteration: 4
|Total Norm: 4.8529e+00 |Residual: 4.8445e+00 |A: 2.8565e-01| Relative Norm : 4.3927e-05
Iteration: 5
|Total Norm: 1.4709e-02 |Residual: 1.4703e-02 |A: 4.2347e-04| Relative Norm : 1.3314e-07
Iteration: 6
|Total Norm: 1.0508e-04 |Residual: 1.0491e-04 |A: 5.9981e-06| Relative Norm : 9.5112e-10
Iteration: 7
|Total Norm: 4.3476e-08 |Residual: 4.3476e-08 |A: 2.2737e-13| Relative Norm : 3.9353e-13
Arc-Length Step 65 :
Iteration: 0
|Total Norm: 3.7930e+05 |Residual: 3.7930e+05 |A: 9.0949e-13| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.2550e+04 |Residual: 1.2549e+04 |A: 1.5941e+02| Relative Norm : 3.3088e-02
Iteration: 2
|Total Norm: 7.9190e+03 |Residual: 7.8978e+03 |A: 5.7887e+02| Relative Norm : 2.0878e-02
Iteration: 3
|Total Norm: 1.4159e+02 |Residual: 1.3570e+02 |A: 4.0413e+01| Relative Norm : 3.7329e-04
Iteration: 4
|Total Norm: 3.7551e+02 |Residual: 3.7534e+02 |A: 1.1246e+01| Relative Norm : 9.9001e-04
Iteration: 5
|Total Norm: 1.4096e+00 |Residual: 1.4090e+00 |A: 3.9525e-02| Relative Norm : 3.7162e-06
Iteration: 6
|Total Norm: 1.0154e+01 |Residual: 1.0150e+01 |A: 3.0835e-01| Relative Norm : 2.6771e-05
Iteration: 7
|Total Norm: 2.5806e-04 |Residual: 2.5739e-04 |A: 1.8523e-05| Relative Norm : 6.8036e-10
Iteration: 8
|Total Norm: 3.6010e-07 |Residual: 3.5993e-07 |A: 1.1097e-08| Relative Norm : 9.4939e-13
Arc-Length Step 66 :
Iteration: 0
|Total Norm: 2.9910e+05 |Residual: 2.9910e+05 |A: 1.1096e-08| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 7.9225e+03 |Residual: 7.9220e+03 |A: 8.8854e+01| Relative Norm : 2.6487e-02
Iteration: 2
|Total Norm: 6.2948e+03 |Residual: 6.2889e+03 |A: 2.7207e+02| Relative Norm : 2.1045e-02
Iteration: 3
|Total Norm: 5.6634e+01 |Residual: 5.5926e+01 |A: 8.9312e+00| Relative Norm : 1.8935e-04
Iteration: 4
|Total Norm: 3.8017e+02 |Residual: 3.8006e+02 |A: 9.4669e+00| Relative Norm : 1.2710e-03
Iteration: 5
|Total Norm: 5.7765e-01 |Residual: 5.7758e-01 |A: 8.8240e-03| Relative Norm : 1.9313e-06
Iteration: 6
|Total Norm: 1.4057e+00 |Residual: 1.4054e+00 |A: 2.9831e-02| Relative Norm : 4.6996e-06
Iteration: 7
|Total Norm: 1.7816e-05 |Residual: 1.7815e-05 |A: 9.4030e-08| Relative Norm : 5.9563e-11
Iteration: 8
|Total Norm: 4.0042e-08 |Residual: 4.0042e-08 |A: 2.9104e-11| Relative Norm : 1.3387e-13
Arc-Length Step 67 :
Iteration: 0
|Total Norm: 7.5493e+04 |Residual: 7.5493e+04 |A: 3.1378e-11| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 6.7729e+02 |Residual: 6.7726e+02 |A: 6.6669e+00| Relative Norm : 8.9716e-03
Iteration: 2
|Total Norm: 2.5015e+03 |Residual: 2.5008e+03 |A: 6.0997e+01| Relative Norm : 3.3136e-02
Iteration: 3
|Total Norm: 8.4217e+00 |Residual: 8.4137e+00 |A: 3.6846e-01| Relative Norm : 1.1156e-04
Iteration: 4
|Total Norm: 1.3422e+02 |Residual: 1.3419e+02 |A: 2.5981e+00| Relative Norm : 1.7779e-03
Iteration: 5
|Total Norm: 4.2581e-02 |Residual: 4.2576e-02 |A: 6.6343e-04| Relative Norm : 5.6404e-07
Iteration: 6
|Total Norm: 4.4814e-03 |Residual: 4.4806e-03 |A: 8.5729e-05| Relative Norm : 5.9362e-08
Iteration: 7
|Total Norm: 4.0643e-08 |Residual: 4.0643e-08 |A: 9.0949e-13| Relative Norm : 5.3837e-13
Arc-Length Step 68 :
Iteration: 0
|Total Norm: 2.0410e+04 |Residual: 2.0410e+04 |A: 1.3642e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 6.2303e+01 |Residual: 6.2299e+01 |A: 7.1306e-01| Relative Norm : 3.0525e-03
Iteration: 2
|Total Norm: 9.4260e+02 |Residual: 9.4241e+02 |A: 1.8716e+01| Relative Norm : 4.6183e-02
Iteration: 3
|Total Norm: 1.0234e+00 |Residual: 1.0228e+00 |A: 3.4461e-02| Relative Norm : 5.0142e-05
Iteration: 4
|Total Norm: 9.8124e-01 |Residual: 9.8107e-01 |A: 1.8406e-02| Relative Norm : 4.8076e-05
Iteration: 5
|Total Norm: 7.0776e-06 |Residual: 7.0774e-06 |A: 4.0513e-08| Relative Norm : 3.4676e-10
Iteration: 6
|Total Norm: 4.0691e-08 |Residual: 4.0691e-08 |A: 2.2737e-12| Relative Norm : 1.9936e-12
Arc-Length Step 69 :
Iteration: 0
|Total Norm: 7.7202e+03 |Residual: 7.7202e+03 |A: 1.8190e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.6202e+01 |Residual: 1.6200e+01 |A: 2.3477e-01| Relative Norm : 2.0987e-03
Iteration: 2
|Total Norm: 2.9089e+02 |Residual: 2.9084e+02 |A: 5.5595e+00| Relative Norm : 3.7680e-02
Iteration: 3
|Total Norm: 9.3849e-02 |Residual: 9.3800e-02 |A: 3.0418e-03| Relative Norm : 1.2156e-05
Iteration: 4
|Total Norm: 4.5324e-03 |Residual: 4.5316e-03 |A: 8.4909e-05| Relative Norm : 5.8709e-07
Iteration: 5
|Total Norm: 3.8833e-08 |Residual: 3.8833e-08 |A: 1.3642e-12| Relative Norm : 5.0301e-12
Arc-Length Step 70 :
Iteration: 0
|Total Norm: 3.9168e+03 |Residual: 3.9168e+03 |A: 7.7307e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.5227e+01 |Residual: 1.5226e+01 |A: 1.5500e-01| Relative Norm : 3.8876e-03
Iteration: 2
|Total Norm: 9.8422e+01 |Residual: 9.8404e+01 |A: 1.8745e+00| Relative Norm : 2.5128e-02
Iteration: 3
|Total Norm: 1.6948e-02 |Residual: 1.6945e-02 |A: 3.4635e-04| Relative Norm : 4.3271e-06
Iteration: 4
|Total Norm: 2.0945e-04 |Residual: 2.0942e-04 |A: 3.9046e-06| Relative Norm : 5.3475e-08
Iteration: 5
|Total Norm: 5.0738e-08 |Residual: 5.0738e-08 |A: 0.0000e+00| Relative Norm : 1.2954e-11
Arc-Length Step 71 :
Iteration: 0
|Total Norm: 2.5291e+03 |Residual: 2.5291e+03 |A: -9.0949e-13| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.2881e+01 |Residual: 1.2880e+01 |A: 1.3299e-01| Relative Norm : 5.0930e-03
Iteration: 2
|Total Norm: 3.6698e+01 |Residual: 3.6691e+01 |A: 7.1627e-01| Relative Norm : 1.4510e-02
Iteration: 3
|Total Norm: 5.4801e-03 |Residual: 5.4799e-03 |A: 5.3928e-05| Relative Norm : 2.1668e-06
Iteration: 4
|Total Norm: 2.1363e-05 |Residual: 2.1359e-05 |A: 3.9646e-07| Relative Norm : 8.4469e-09
Iteration: 5
|Total Norm: 3.4864e-08 |Residual: 3.4864e-08 |A: 0.0000e+00| Relative Norm : 1.3785e-11
Arc-Length Step 72 :
Iteration: 0
|Total Norm: 1.9442e+03 |Residual: 1.9442e+03 |A: 3.1832e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.1170e+01 |Residual: 1.1169e+01 |A: 1.2453e-01| Relative Norm : 5.7451e-03
Iteration: 2
|Total Norm: 1.4595e+01 |Residual: 1.4592e+01 |A: 3.0666e-01| Relative Norm : 7.5067e-03
Iteration: 3
|Total Norm: 1.5890e-03 |Residual: 1.5890e-03 |A: 1.1669e-05| Relative Norm : 8.1730e-07
Iteration: 4
|Total Norm: 1.4469e-06 |Residual: 1.4466e-06 |A: 2.6736e-08| Relative Norm : 7.4419e-10
Iteration: 5
|Total Norm: 5.0148e-08 |Residual: 5.0148e-08 |A: -4.5475e-13| Relative Norm : 2.5793e-11
Arc-Length Step 73 :
Iteration: 0
|Total Norm: 1.6542e+03 |Residual: 1.6542e+03 |A: -4.5475e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 1.0028e+01 |Residual: 1.0028e+01 |A: 1.1979e-01| Relative Norm : 6.0623e-03
Iteration: 2
|Total Norm: 6.0672e+00 |Residual: 6.0653e+00 |A: 1.4920e-01| Relative Norm : 3.6677e-03
Iteration: 3
|Total Norm: 4.0404e-04 |Residual: 4.0402e-04 |A: 3.1613e-06| Relative Norm : 2.4425e-07
Iteration: 4
|Total Norm: 8.8695e-08 |Residual: 8.8685e-08 |A: 1.3733e-09| Relative Norm : 5.3617e-11
Arc-Length Step 74 :
Iteration: 0
|Total Norm: 1.4816e+03 |Residual: 1.4816e+03 |A: 1.3774e-09| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 9.1790e+00 |Residual: 9.1782e+00 |A: 1.1578e-01| Relative Norm : 6.1954e-03
Iteration: 2
|Total Norm: 2.6271e+00 |Residual: 2.6257e+00 |A: 8.4358e-02| Relative Norm : 1.7732e-03
Iteration: 3
|Total Norm: 9.5782e-05 |Residual: 9.5777e-05 |A: 9.9583e-07| Relative Norm : 6.4648e-08
Iteration: 4
|Total Norm: 3.6310e-08 |Residual: 3.6310e-08 |A: 6.1391e-11| Relative Norm : 2.4508e-11
Arc-Length Step 75 :
Iteration: 0
|Total Norm: 1.3609e+03 |Residual: 1.3609e+03 |A: 5.3660e-11| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 8.4773e+00 |Residual: 8.4765e+00 |A: 1.1160e-01| Relative Norm : 6.2292e-03
Iteration: 2
|Total Norm: 1.1960e+00 |Residual: 1.1948e+00 |A: 5.5226e-02| Relative Norm : 8.7886e-04
Iteration: 3
|Total Norm: 2.2242e-05 |Residual: 2.2239e-05 |A: 3.7746e-07| Relative Norm : 1.6344e-08
Iteration: 4
|Total Norm: 3.4466e-08 |Residual: 3.4466e-08 |A: 2.7285e-12| Relative Norm : 2.5326e-11
Arc-Length Step 76 :
Iteration: 0
|Total Norm: 1.2663e+03 |Residual: 1.2663e+03 |A: 4.0927e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 7.8616e+00 |Residual: 7.8609e+00 |A: 1.0716e-01| Relative Norm : 6.2082e-03
Iteration: 2
|Total Norm: 5.8339e-01 |Residual: 5.8199e-01 |A: 4.0332e-02| Relative Norm : 4.6069e-04
Iteration: 3
|Total Norm: 5.3268e-06 |Residual: 5.3238e-06 |A: 1.7969e-07| Relative Norm : 4.2065e-09
Iteration: 4
|Total Norm: 4.3810e-08 |Residual: 4.3810e-08 |A: 0.0000e+00| Relative Norm : 3.4596e-11
Arc-Length Step 77 :
Iteration: 0
|Total Norm: 1.1868e+03 |Residual: 1.1868e+03 |A: -5.9117e-12| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 7.3037e+00 |Residual: 7.3030e+00 |A: 1.0256e-01| Relative Norm : 6.1542e-03
Iteration: 2
|Total Norm: 3.1281e-01 |Residual: 3.1123e-01 |A: 3.1399e-02| Relative Norm : 2.6358e-04
Iteration: 3
|Total Norm: 1.4389e-06 |Residual: 1.4352e-06 |A: 1.0291e-07| Relative Norm : 1.2124e-09
Iteration: 4
|Total Norm: 3.9626e-08 |Residual: 3.9626e-08 |A: -4.5475e-13| Relative Norm : 3.3389e-11
Arc-Length Step 78 :
Iteration: 0
|Total Norm: 1.1170e+03 |Residual: 1.1170e+03 |A: -9.0949e-13| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 6.7883e+00 |Residual: 6.7876e+00 |A: 9.7884e-02| Relative Norm : 6.0771e-03
Iteration: 2
|Total Norm: 1.8867e-01 |Residual: 1.8698e-01 |A: 2.5208e-02| Relative Norm : 1.6890e-04
Iteration: 3
|Total Norm: 5.3094e-07 |Residual: 5.2693e-07 |A: 6.5138e-08| Relative Norm : 4.7531e-10
Arc-Length Step 79 :
Iteration: 0
|Total Norm: 1.0544e+03 |Residual: 1.0544e+03 |A: 6.5134e-08| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 6.3063e+00 |Residual: 6.3056e+00 |A: 9.3171e-02| Relative Norm : 5.9810e-03
Iteration: 2
|Total Norm: 1.2803e-01 |Residual: 1.2638e-01 |A: 2.0481e-02| Relative Norm : 1.2143e-04
Iteration: 3
|Total Norm: 2.8955e-07 |Residual: 2.8636e-07 |A: 4.2912e-08| Relative Norm : 2.7462e-10
Arc-Length Step 80 :
Iteration: 0
|Total Norm: 9.9731e+02 |Residual: 9.9731e+02 |A: 4.2911e-08| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 5.8524e+00 |Residual: 5.8517e+00 |A: 8.8446e-02| Relative Norm : 5.8681e-03
Iteration: 2
|Total Norm: 9.5071e-02 |Residual: 9.3595e-02 |A: 1.6685e-02| Relative Norm : 9.5327e-05
Iteration: 3
|Total Norm: 1.9985e-07 |Residual: 1.9779e-07 |A: 2.8576e-08| Relative Norm : 2.0039e-10
Arc-Length Step 81 :
Iteration: 0
|Total Norm: 9.4486e+02 |Residual: 9.4486e+02 |A: 2.8579e-08| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 5.4235e+00 |Residual: 5.4229e+00 |A: 8.3726e-02| Relative Norm : 5.7400e-03
Iteration: 2
|Total Norm: 7.4556e-02 |Residual: 7.3310e-02 |A: 1.3573e-02| Relative Norm : 7.8907e-05
Iteration: 3
|Total Norm: 1.3627e-07 |Residual: 1.3494e-07 |A: 1.9005e-08| Relative Norm : 1.4422e-10
Arc-Length Step 82 :
Iteration: 0
|Total Norm: 8.9640e+02 |Residual: 8.9640e+02 |A: 1.8995e-08| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 5.0183e+00 |Residual: 5.0176e+00 |A: 7.9035e-02| Relative Norm : 5.5983e-03
Iteration: 2
|Total Norm: 6.0152e-02 |Residual: 5.9136e-02 |A: 1.1008e-02| Relative Norm : 6.7104e-05
Iteration: 3
|Total Norm: 9.7790e-08 |Residual: 9.6979e-08 |A: 1.2568e-08| Relative Norm : 1.0909e-10
Arc-Length Step 83 :
Iteration: 0
|Total Norm: 8.5145e+02 |Residual: 8.5145e+02 |A: 1.2565e-08| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 4.6360e+00 |Residual: 4.6354e+00 |A: 7.4398e-02| Relative Norm : 5.4448e-03
Iteration: 2
|Total Norm: 4.9190e-02 |Residual: 4.8379e-02 |A: 8.8959e-03| Relative Norm : 5.7772e-05
Iteration: 3
|Total Norm: 7.2435e-08 |Residual: 7.1963e-08 |A: 8.2550e-09| Relative Norm : 8.5072e-11
Arc-Length Step 84 :
Iteration: 0
|Total Norm: 8.0966e+02 |Residual: 8.0966e+02 |A: 8.2582e-09| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 4.2763e+00 |Residual: 4.2757e+00 |A: 6.9844e-02| Relative Norm : 5.2816e-03
Iteration: 2
|Total Norm: 4.0462e-02 |Residual: 3.9822e-02 |A: 7.1654e-03| Relative Norm : 4.9974e-05
Iteration: 3
|Total Norm: 6.0051e-08 |Residual: 5.9809e-08 |A: 5.3874e-09| Relative Norm : 7.4168e-11
Arc-Length Step 85 :
Iteration: 0
|Total Norm: 7.7072e+02 |Residual: 7.7072e+02 |A: 5.3938e-09| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 3.9391e+00 |Residual: 3.9385e+00 |A: 6.5403e-02| Relative Norm : 5.1109e-03
Iteration: 2
|Total Norm: 3.3355e-02 |Residual: 3.2855e-02 |A: 5.7546e-03| Relative Norm : 4.3277e-05
Iteration: 3
|Total Norm: 5.2465e-08 |Residual: 5.2349e-08 |A: 3.4952e-09| Relative Norm : 6.8073e-11
Arc-Length Step 86 :
Iteration: 0
|Total Norm: 7.3438e+02 |Residual: 7.3438e+02 |A: 3.4952e-09| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 3.6239e+00 |Residual: 3.6234e+00 |A: 6.1099e-02| Relative Norm : 4.9347e-03
Iteration: 2
|Total Norm: 2.7509e-02 |Residual: 2.7120e-02 |A: 4.6104e-03| Relative Norm : 3.7459e-05
Iteration: 3
|Total Norm: 5.1118e-08 |Residual: 5.1068e-08 |A: 2.2560e-09| Relative Norm : 6.9606e-11
Arc-Length Step 87 :
Iteration: 0
|Total Norm: 7.0042e+02 |Residual: 7.0042e+02 |A: 2.2419e-09| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 3.3304e+00 |Residual: 3.3300e+00 |A: 5.6955e-02| Relative Norm : 4.7549e-03
Iteration: 2
|Total Norm: 2.2683e-02 |Residual: 2.2382e-02 |A: 3.6866e-03| Relative Norm : 3.2385e-05
Iteration: 3
|Total Norm: 4.1461e-08 |Residual: 4.1436e-08 |A: 1.4511e-09| Relative Norm : 5.9195e-11
Arc-Length Step 88 :
Iteration: 0
|Total Norm: 6.6865e+02 |Residual: 6.6865e+02 |A: 1.4611e-09| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 3.0581e+00 |Residual: 3.0576e+00 |A: 5.2989e-02| Relative Norm : 4.5735e-03
Iteration: 2
|Total Norm: 1.8697e-02 |Residual: 1.8463e-02 |A: 2.9438e-03| Relative Norm : 2.7962e-05
Iteration: 3
|Total Norm: 5.0771e-08 |Residual: 5.0763e-08 |A: 9.3132e-10| Relative Norm : 7.5932e-11
Arc-Length Step 89 :
Iteration: 0
|Total Norm: 6.3888e+02 |Residual: 6.3888e+02 |A: 9.2859e-10| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 2.8060e+00 |Residual: 2.8055e+00 |A: 4.9215e-02| Relative Norm : 4.3920e-03
Iteration: 2
|Total Norm: 1.5406e-02 |Residual: 1.5226e-02 |A: 2.3486e-03| Relative Norm : 2.4114e-05
Iteration: 3
|Total Norm: 4.9217e-08 |Residual: 4.9213e-08 |A: 5.9617e-10| Relative Norm : 7.7036e-11
Arc-Length Step 90 :
Iteration: 0
|Total Norm: 6.1096e+02 |Residual: 6.1096e+02 |A: 5.9663e-10| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 2.5733e+00 |Residual: 2.5729e+00 |A: 4.5640e-02| Relative Norm : 4.2120e-03
Iteration: 2
|Total Norm: 1.2692e-02 |Residual: 1.2553e-02 |A: 1.8728e-03| Relative Norm : 2.0774e-05
Iteration: 3
|Total Norm: 4.2273e-08 |Residual: 4.2271e-08 |A: 3.8108e-10| Relative Norm : 6.9191e-11
Arc-Length Step 91 :
Iteration: 0
|Total Norm: 5.8475e+02 |Residual: 5.8475e+02 |A: 3.6925e-10| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 2.3592e+00 |Residual: 2.3588e+00 |A: 4.2271e-02| Relative Norm : 4.0345e-03
Iteration: 2
|Total Norm: 1.0458e-02 |Residual: 1.0351e-02 |A: 1.4934e-03| Relative Norm : 1.7885e-05
Iteration: 3
|Total Norm: 4.3676e-08 |Residual: 4.3676e-08 |A: 2.4374e-10| Relative Norm : 7.4692e-11
Arc-Length Step 92 :
Iteration: 0
|Total Norm: 5.6012e+02 |Residual: 5.6012e+02 |A: 2.3056e-10| Relative Norm : 1.0000e+00
Iteration: 1
|Total Norm: 2.1624e+00 |Residual: 2.1620e+00 |A: 3.9107e-02| Relative Norm : 3.8606e-03
Iteration: 2
|Total Norm: 8.6215e-03 |Residual: 8.5388e-03 |A: 1.1912e-03| Relative Norm : 1.5392e-05
Iteration: 3
|Total Norm: 5.0374e-08 |Residual: 5.0374e-08 |A: 1.5643e-10| Relative Norm : 8.9935e-11
Post Processing#
Here we plot the final deformed shape and the equilibrium path. To verify or solution, we also compare our solutions to ones found in literature.
Solutions are obtained from the paper: A simple extrapolated predictor for overcoming the starting and tracking issues in the arc-length method for nonlinear structural mechanics
1# Get dof coordinates:
2x_dofs = V.sub(0).sub(0).dofmap().dofs()
3y_dofs = V.sub(0).sub(1).dofmap().dofs()
4theta_dofs = V.sub(1).dofmap().dofs()
5dofs = V.tabulate_dof_coordinates()
6dof_coords = dofs.reshape((-1, 2))
7
8eps = 1e-5
9dof = []
10# Identify y-dof at the center of the arch for force application
11for ii in y_dofs:
12 if abs(dof_coords[ii,0]) <= eps:
13 force_dof = ii
1# Get nodal values
2x_nodal_coord = dof_coords[x_dofs][:,0]
3y_nodal_coord = dof_coords[y_dofs][:,1]
4
5# Plot displacement field
6disp_x = x_nodal_coord + disp[-1][x_dofs]
7disp_y = y_nodal_coord + disp[-1][y_dofs]
8
9plt.scatter(x_nodal_coord,y_nodal_coord)
10plt.scatter(disp_x, disp_y)
11
12plt.xlabel('x-coordinates')
13plt.ylabel('y-coordinates')
14plt.axis('equal')
15plt.show()
16
17print(x_nodal_coord.shape)
(61,)
1# Get displacment at force application
2force_disp = []
3for ii in range(len(disp)):
4 force_disp.append(disp[ii][force_dof])
5# Normalize values
6displacement_normalized = -np.array(force_disp)/r
7
8
9lamda_normalized = (np.array(lmbda)*r**2)/EI
10
11plt.figure(figsize=(7,7))
12plt.plot(displacement_normalized, lamda_normalized, c = 'k', marker = 'o')
13plt.title('Equilibrium Path')
14plt.ylabel('Normalized Load')
15plt.xlabel('Normalized Displacement')
Text(0.5, 0, 'Normalized Displacement')
1# get paper solution
2import scipy.io
3paper_soln = scipy.io.loadmat('lit_soln/solution_215.mat')
1plt.figure(figsize=(7,7))
2plt.scatter(paper_soln['soln'][:,0],paper_soln['soln'][:,1], label = 'Paper implementation', facecolors = 'None', edgecolors = 'r', marker = 's')
3plt.scatter(disp_x, disp_y, marker = '.', label = 'Our implementation')
4plt.plot(x_nodal_coord,y_nodal_coord,label = 'Undeformed', color = 'k')
5
6plt.xlabel('x-coordinates')
7plt.ylabel('y-coordinates')
8plt.title('Beam Deformation')
9plt.axis('equal')
10plt.legend()
11plt.show()
1# get paper equilibrium path
2paper_eq = np.loadtxt('lit_soln/path_215.dat')
1plt.figure(figsize=(7,7))
2plt.scatter(-paper_eq[:,2]/r, paper_eq[:,0]*r**2/EI, label = 'Paper implementation', facecolors = 'None', edgecolors = 'r', marker = 's')
3
4plt.scatter(displacement_normalized, lamda_normalized, marker = '.', label = 'Our Implementation')
5plt.title('Equilibrium Path (215 degree arch 2D)')
6plt.ylabel('Normalized Load')
7plt.xlabel('Normalized Y-Displacement')
8plt.legend()
9
10idx = np.where(displacement_normalized<1.5)
11
12print('buckling load:',np.max(lamda_normalized[idx]))
13print('Error:',(np.max(lamda_normalized[idx]) - 8.97)/8.97)
buckling load: 8.96304746977223
Error: -0.0007750869819142799
Optional: Creating an animation from solution snapshots#
1from matplotlib import animation, rc
2
3plt.rcParams["animation.html"] = "jshtml"
4
5fig = plt.figure(figsize=(7,7))
6ax = fig.add_subplot(111)
7
8ax.set_xlim([-150,150])
9ax.set_ylim([-150,150])
10
11deformed, = ax.plot([], [], lw = 7, c = 'r', label = 'Deformed Configuration')
12init, = ax.plot(x_nodal_coord, y_nodal_coord, c='k', lw = 5, ls = ':', label = 'Initial Configuration')
13ax.legend(loc = 'lower right')
14
15def drawframe(n):
16 disp_x = x_nodal_coord + disp[n][x_dofs]
17 disp_y = y_nodal_coord + disp[n][y_dofs]
18
19 deformed.set_data(disp_x,disp_y)
20 return deformed,
21
22plt.close()
23# Note: blit=True re-draws only the parts that have changed.
24anim = animation.FuncAnimation(fig, drawframe, frames=len(lmbda), interval=40, blit=True)
25
26anim