G2 Example 3

G2Example3.py

# ------------------------------------------------------------------------
# The following Python code is implemented 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 warranty of any kind.
# ------------------------------------------------------------------------

from G2AnalysisNonlinearStatic import *
from G2Model import *

#                      |                 |                  |
#                      | P               | P                | P
#                      |                 |                  |
#    2        (3)      V 4      (7)      V 6     (11)       V 8
# ###*-----------------*-----------------*------------------*       A
#    | *               | *               | *                |       |
#    |    *  (4)       |    *  (8)       |    *  (12)       |       |
#    |(2)    *         |(6)    *         |(10)   *          |(13)   | H
#    |          *      |          *      |          *       |       |
#    | 1      (1)   *  | 3      (5)   *  | 5      (9)   *   | 7     |
# ###*-----------------*-----------------*------------------*       V
#
#    <------- L -------><------- L ------><------- L ------->

# Input [N, m, kg, sec]
elementType = 2          # Nonlinear truss element with path-dependent material
materialType = 'BoucWen' # 'Bilinear' / 'Plasticity' / 'BoucWen'
L = 2.0                  # Dimension in figure above
H = 2.0                  # Dimension in figure above
P = 100e3                # Load in figure above
A = 0.04**2              # Section area
E = 200e9                # Young's modulus
fy = 350e6               # Yield stress
alpha = 0.02             # Second-slope stiffness
eta = 2                  # Bouc-Wen sharpness
gamma = 0.5              # Bouc-Wen parameter
beta = 0.5               # Bouc-Wen parameter
Hk = alpha*E/(1-alpha)   # Kinematic hardening parameter
K = 0                    # Linear isotropic hardening parameter
delta = 0                # Saturation isotropic hardening parameter
fy_inf = 100.0           # Asymptotic yield stress for saturation isotropic hardening
dt = 1/20                # Delta-t
nsteps = 25              # Number of pseudo-time steps, each of length dt
KcalcFrequency = 1       # 0=initial stress method, 1=Newton-Raphson, maxIter=Modified NR
maxIter = 100            # Maximum number of equilibrium iterations in the Newton-Raphson algorithm
tol = 1e-5               # Convergence tolerance for the Newton-Raphson algorithm
trackNode = 8            # Node to be plotted
trackDOF = 2             # DOF to be plotted

# Nodal coordinates
NODES = [[0.0, 0.0],
        [0.0,  H],
        [L,    0.0],
        [L,    H],
        [2*L,  0.0],
        [2*L,  H],
        [3*L,  0.0],
        [3*L,  H]]

# Boundary conditions (0=free, 1=fixed, sets #DOFs per node)
CONSTRAINTS = [[1, 1],
               [1, 1],
               [0, 0],
               [0, 0],
               [0, 0],
               [0, 0],
               [0, 0],
               [0, 0]]

# Element connectivity and type
ELEMENTS = [[elementType, 0, 1, 3],
            [elementType, 0, 1, 2],
            [elementType, 0, 2, 4],
            [elementType, 0, 2, 3],
            [elementType, 0, 3, 5],
            [elementType, 0, 3, 4],
            [elementType, 0, 4, 6],
            [elementType, 0, 4, 5],
            [elementType, 0, 5, 7],
            [elementType, 0, 5, 6],
            [elementType, 0, 6, 8],
            [elementType, 0, 6, 7],
            [elementType, 0, 7, 8]]

# Section information (one section per element)
nel = len(ELEMENTS)
SECTIONS = []
for i in range(nel):
    SECTIONS.append(['Truss', A])

# Material information (one material per element)
MATERIALS = []
for i in range(nel):
    if materialType == 'Bilinear':
        MATERIALS.append(['Bilinear', E, fy, alpha])
    elif materialType == 'Plasticity':
        MATERIALS.append(['Plasticity', E, fy, Hk, K, delta, fy_inf])
    elif materialType == 'BoucWen':
        MATERIALS.append(['BoucWen', E, fy, alpha, eta, beta, gamma])
    else:
        print('\n'"Error: Wrong material type")
        import sys
        sys.exit()

# Nodal loads
LOADS = [[0.0, 0.0],
         [0.0, 0.0],
         [0.0, 0.0],
         [0.0, -P],
         [0.0, 0.0],
         [0.0, -P],
         [0.0, 0.0],
         [0.0, -P]]

# Placeholder for mass matrix
MASS = [[0, 0],
        [0, 0],
        [0, 0],
        [0, 0],
        [0, 0],
        [0, 0],
        [0, 0],
        [0, 0]]

# Create the model object
a = [NODES, CONSTRAINTS, ELEMENTS, SECTIONS, MATERIALS, LOADS, MASS]
m = model(a)

# Analyze
loadFactor, u, dudx = nonlinearStaticAnalysis(m, nsteps, dt, maxIter, KcalcFrequency, tol, trackNode, trackDOF, [])