Post-buckling of a truss column using displacement Control.

This is the same structure as in problem Post-buckling of a truss column using load Control. but using a mix of load control and displacement control.

Author: Peter Mackenzie-Helnwein

Setup

import numpy as np
import matplotlib.pyplot as plt

from femedu.examples import Example

from femedu.domain import System, Node
from femedu.elements.finite import Truss
from femedu.materials import FiberMaterial
from femedu.solver import NewtonRaphsonSolver

Create the example by subclassing the Example

class ExampleTruss08(Example):

    def problem(self):
        # units
        mm = 1.
        m = 1000. * mm
        N  = 1.0
        kN = 1000. * N
        MN = 1000. * kN
        Pa = N / m**2
        MPa = 1.e6 * Pa
        GPa = 1000. * MPa

        # mesh parameters
        H = 5.00 * m
        W = H / 20

        Px = 0.05 * kN

        #Ny = 11
        Ny = 20

        params_vert = dict(
            E = 200 * GPa,
            A = 10 * mm**2
        )

        params_diag = dict(
            E = 200 * GPa,
            A = 50 * mm**2
        )

        params_brace = dict(
            E = 200 * GPa,
            A = 50 * mm**2
        )

        EI = params_vert['E'] * params_vert['A'] * W**2 / 2
        Py = EI * np.pi**2 / (2*H)**2

        # initialize a system model
        model = System()
        model.setSolver(NewtonRaphsonSolver())

        # create floor nodes
        h = 0.0
        nd0 = Node(0.0, h)
        nd1 = Node(  W, h)

        nd_00 = nd0
        nd_01 = nd1

        model.addNode(nd0, nd1)

        for layer in range(Ny):
            h += H / Ny
            nd_10 = Node(0.0, h)
            nd_11 = Node(  W, h)

            model.addNode(nd_10, nd_11)

            # create elements
            model += Truss(nd_00, nd_10, FiberMaterial(params_vert))
            model += Truss(nd_01, nd_11, FiberMaterial(params_vert))
            model += Truss(nd_00, nd_11, FiberMaterial(params_diag))
            model += Truss(nd_10, nd_11, FiberMaterial(params_brace))

            # prep for the next level
            nd_00 = nd_10
            nd_01 = nd_11

        # apply boundary conditions
        nd0.fixDOF(['ux','uy'])
        nd1.fixDOF(['ux','uy'])

        # build reference load
        nd_10.addLoad([-Py/2],['uy'])
        nd_11.addLoad([-Py/2],['uy'])
        nd_10.addLoad([ Px/2],['ux'])
        nd_11.addLoad([ Px/2],['ux'])

        # write out report
        model.report()

        # create plots
        model.setLoadFactor(1.0)    # needed to show the reference load
        model.plot(factor=0., filename="truss08_undeformed.png", show_loads=1, show_bc=1, title="Undeformed System")

        #
        # performing the analysis
        #
        model.resetDisp()
        model.setLoadFactor(0.0)

        # setting target load levels
        levels = np.linspace(0.0, 2.00, 30)

        # set up data collection
        load_list = []
        data_list = []

        # reset the analysis
        model.resetDisp()

        # apply all load steps
        for lam in levels:

            model.setLoadFactor(lam)
            model.solve()

            # collect data
            load_list.append(lam)
            data_list.append(nd_11.getDisp())

            # stop load control once lateral displacement of the top node exceeds 75 mm
            if nd_11.getDisp('ux')[0] > 75 * mm:
                break

        # plot the deformed shape
        model.plot(factor=1.0,
                   title="Deformed Sytem at Transition to Displacement Control",
                   filename="truss08_deformed_end_load_control.png",
                   show_loads=False, show_reactions=False)

        #
        # switching to displacement control
        #

        # remember displacement at which we switched to displacement control
        disp_switch = nd_11.getDisp('ux')[0]

        # let's start the displacement control at the current level to verify
        # functionality.
        target = disp_switch

        while True:

            model.setDisplacementControl(nd_11, 'ux', target)
            model.solve()

            # collect data
            lam = model.loadfactor
            load_list.append(lam)
            data_list.append(nd_11.getDisp())

            # increase the target displacement by 200 mm
            target += 200 * mm

            # stop displacement control once lateral displacement of the top node exceeds 3500 mm
            if nd_11.getDisp('ux')[0] > 3500 * mm:
                break

        model.plot(factor=1.0,
                   title="Deformed Sytem at Transition back to Load Control",
                   filename="truss08_deformed_end_disp_control.png",
                   show_loads=False, show_reactions=False)

        #
        # returning to load control
        #

        # remember displacement at which we switched to displacement control
        lam_switch = model.loadfactor

        # let's start the load control at the current level to verify
        # functionality.
        lam = lam_switch

        while True:

            model.setLoadFactor(lam)
            model.solve()

            # collect data
            load_list.append(lam)
            data_list.append(nd_11.getDisp())

            # increase the target load level by $ \Delta \lambda = 0.10 $
            lam += 0.10

            # stop load control once the load level exceeds 2.0
            if lam > 2.0:
                break

        # plot the deformed shape
        model.plot(factor=1.0,
                   title="Deformed Sytem at $ \\lambda={:.2f} $".format(lam),
                   filename="truss08_deformed_end_load_2_control.png",
                   show_loads=False, show_reactions=False)

        levels = np.array(load_list)
        data   = np.array(data_list)

        plt.figure()
        plt.plot(data, levels, '--o')

        plt.plot([disp_switch, disp_switch], [0.0,1.1],'-r')
        plt.text(2.0*disp_switch, 1.05, "transition to\ndisplacement control", rotation=90.)

        plt.plot([0.5*target,1.1*target], [lam_switch, lam_switch], '-g')
        plt.text(0.5*target, 1.05 * lam_switch, "transition to\nload control" , ha='left')

        plt.grid(True)
        plt.xlabel('displacements $ u_i $')
        plt.ylabel('load factor $ \\lambda $')
        plt.legend(['$ u_x $','$ u_y $'])
        plt.savefig("truss08_deformation_history.png")
        plt.show()

Run the example by creating an instance of the problem and executing it by calling Example.run()

if __name__ == "__main__":
    ex = ExampleTruss08()
    ex.run()
  • Undeformed System
  • Deformed Sytem at Transition to Displacement Control
  • Deformed Sytem at Transition back to Load Control
  • Deformed Sytem at $ \lambda=2.08 $
  • plot truss08
System Analysis Report
=======================

Nodes:
---------------------
  Node_93:
      x:    [0.000 0.000]
      fix:  ['ux', 'uy']
      u:    None
  Node_94:
      x:    [250.000 0.000]
      fix:  ['ux', 'uy']
      u:    None
  Node_95:
      x:    [0.000 250.000]
      u:    None
  Node_96:
      x:    [250.000 250.000]
      u:    None
  Node_97:
      x:    [0.000 500.000]
      u:    None
  Node_98:
      x:    [250.000 500.000]
      u:    None
  Node_99:
      x:    [0.000 750.000]
      u:    None
  Node_100:
      x:    [250.000 750.000]
      u:    None
  Node_101:
      x:    [0.000 1000.000]
      u:    None
  Node_102:
      x:    [250.000 1000.000]
      u:    None
  Node_103:
      x:    [0.000 1250.000]
      u:    None
  Node_104:
      x:    [250.000 1250.000]
      u:    None
  Node_105:
      x:    [0.000 1500.000]
      u:    None
  Node_106:
      x:    [250.000 1500.000]
      u:    None
  Node_107:
      x:    [0.000 1750.000]
      u:    None
  Node_108:
      x:    [250.000 1750.000]
      u:    None
  Node_109:
      x:    [0.000 2000.000]
      u:    None
  Node_110:
      x:    [250.000 2000.000]
      u:    None
  Node_111:
      x:    [0.000 2250.000]
      u:    None
  Node_112:
      x:    [250.000 2250.000]
      u:    None
  Node_113:
      x:    [0.000 2500.000]
      u:    None
  Node_114:
      x:    [250.000 2500.000]
      u:    None
  Node_115:
      x:    [0.000 2750.000]
      u:    None
  Node_116:
      x:    [250.000 2750.000]
      u:    None
  Node_117:
      x:    [0.000 3000.000]
      u:    None
  Node_118:
      x:    [250.000 3000.000]
      u:    None
  Node_119:
      x:    [0.000 3250.000]
      u:    None
  Node_120:
      x:    [250.000 3250.000]
      u:    None
  Node_121:
      x:    [0.000 3500.000]
      u:    None
  Node_122:
      x:    [250.000 3500.000]
      u:    None
  Node_123:
      x:    [0.000 3750.000]
      u:    None
  Node_124:
      x:    [250.000 3750.000]
      u:    None
  Node_125:
      x:    [0.000 4000.000]
      u:    None
  Node_126:
      x:    [250.000 4000.000]
      u:    None
  Node_127:
      x:    [0.000 4250.000]
      u:    None
  Node_128:
      x:    [250.000 4250.000]
      u:    None
  Node_129:
      x:    [0.000 4500.000]
      u:    None
  Node_130:
      x:    [250.000 4500.000]
      u:    None
  Node_131:
      x:    [0.000 4750.000]
      u:    None
  Node_132:
      x:    [250.000 4750.000]
      u:    None
  Node_133:
      x:    [0.000 5000.000]
      P:    [25.000 -3084.251]
      u:    None
  Node_134:
      x:    [250.000 5000.000]
      P:    [25.000 -3084.251]
      u:    None

Elements:
---------------------
  Truss: Node_93 to Node_95:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_94 to Node_96:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_93 to Node_96:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_95 to Node_96:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_95 to Node_97:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_96 to Node_98:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_95 to Node_98:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_97 to Node_98:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_97 to Node_99:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_98 to Node_100:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_97 to Node_100:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_99 to Node_100:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_99 to Node_101:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_100 to Node_102:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_99 to Node_102:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_101 to Node_102:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_101 to Node_103:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_102 to Node_104:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_101 to Node_104:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_103 to Node_104:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_103 to Node_105:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_104 to Node_106:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_103 to Node_106:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_105 to Node_106:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_105 to Node_107:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_106 to Node_108:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_105 to Node_108:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_107 to Node_108:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_107 to Node_109:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_108 to Node_110:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_107 to Node_110:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_109 to Node_110:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_109 to Node_111:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_110 to Node_112:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_109 to Node_112:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_111 to Node_112:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_111 to Node_113:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_112 to Node_114:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_111 to Node_114:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_113 to Node_114:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_113 to Node_115:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_114 to Node_116:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_113 to Node_116:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_115 to Node_116:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_115 to Node_117:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_116 to Node_118:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_115 to Node_118:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_117 to Node_118:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_117 to Node_119:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_118 to Node_120:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_117 to Node_120:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_119 to Node_120:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_119 to Node_121:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_120 to Node_122:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_119 to Node_122:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_121 to Node_122:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_121 to Node_123:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_122 to Node_124:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_121 to Node_124:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_123 to Node_124:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_123 to Node_125:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_124 to Node_126:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_123 to Node_126:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_125 to Node_126:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_125 to Node_127:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_126 to Node_128:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_125 to Node_128:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_127 to Node_128:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_127 to Node_129:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_128 to Node_130:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_127 to Node_130:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_129 to Node_130:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_129 to Node_131:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_130 to Node_132:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_129 to Node_132:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_131 to Node_132:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_131 to Node_133:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_132 to Node_134:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 10.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_131 to Node_134:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0
  Truss: Node_133 to Node_134:
      material properties: FiberMaterial(Material)({'E': 200000.0, 'A': 50.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.0   stress:{'xx': 0.0, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.0

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Total running time of the script: (0 minutes 6.288 seconds)

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