Simple triangular truss.

This example is structurally identical to ExampleTruss01 but utilizes the alternative input style for adding Nodes and Elements to the model.

The system is statically determined and allows for easy validation of calculated deformation, reactions and internal forces.

Author: Peter Mackenzie-Helnwein

Setup

import matplotlib.pyplot as plt

from femedu.examples import Example

from femedu.domain import System, Node
from femedu.elements.linear import Truss
from femedu.materials import FiberMaterial


class ExampleTruss03(Example):

    def problem(self):
        # initialize a system model
        B = 6.0 * 12
        H = 3.0 * 12
        params = {'E': 10., 'A': 1., 'nu': 0.0, 'fy': 1.e30}

        model = System()

        # create nodes
        nd0 = Node(0.0, 0.0)
        nd1 = Node(  B, 0.0)
        nd2 = Node(0.5*B, H)

        model += nd0
        model += nd1
        model += nd2

        # create elements
        model += Truss(nd0, nd1, FiberMaterial(params))  # bottom 1
        model += Truss(nd0, nd2, FiberMaterial(params))  # up right diag 1
        model += Truss(nd1, nd2, FiberMaterial(params))  # up left diag 1

        # define support(s)
        nd0.fixDOF('ux')    # horizontal support left end
        #nd0 //= 0
        nd0.fixDOF('uy')    # vertical support left end
        nd1.fixDOF('uy')    # vertical support right end

        # add loads
        # .. load only the upper nodes
        nd2.setLoad((0.0, -1.0), ('ux','uy'))

        # analyze the model
        model.solve()

        # write out report
        model.report()

        # create plots
        model.plot(factor=1., filename="truss03_deformed_a.png")

        # fix horizontal motion of node 1
        nd1.fixDOF('ux')

        # add loads: same load -- nothing to do

        # RE-analyze the model
        model.resetDisp()
        model.solve()

        # skip the report
        model.report()

        # create plots
        model.plot(factor=1., filename="truss03_deformed_b.png")

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

if __name__ == "__main__":
    ex = ExampleTruss03()
    ex.run()

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System Analysis Report
=======================

Nodes:
---------------------
  Node_36:
      x:    [0. 0.]
      fix:  ['ux', 'uy']
      u:    [0. 0.]
  Node_37:
      x:    [72.  0.]
      fix:  ['uy']
      u:    [3.6 0. ]
  Node_38:
      x:    [36. 36.]
      P:    [ 0. -1.]
      u:    [ 1.8        -6.89116882]

Elements:
---------------------
  Truss: Node_36 to Node_37:
      material properties: FiberMaterial(Material)({'E': 10.0, 'A': 1.0, 'nu': 0.0, 'fy': 1e+30})  strain:0.04999999999999999   stress:{'xx': 0.4999999999999999, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: 0.4999999999999999
  Truss: Node_36 to Node_38:
      material properties: FiberMaterial(Material)({'E': 10.0, 'A': 1.0, 'nu': 0.0, 'fy': 1e+30})  strain:-0.07071067811865474   stress:{'xx': -0.7071067811865474, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: -0.7071067811865474
  Truss: Node_37 to Node_38:
      material properties: FiberMaterial(Material)({'E': 10.0, 'A': 1.0, 'nu': 0.0, 'fy': 1e+30})  strain:-0.07071067811865472   stress:{'xx': -0.7071067811865472, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: -0.7071067811865472


System Analysis Report
=======================

Nodes:
---------------------
  Node_36:
      x:    [0. 0.]
      fix:  ['ux', 'uy']
      u:    [0. 0.]
  Node_37:
      x:    [72.  0.]
      fix:  ['uy', 'ux']
      u:    [0. 0.]
  Node_38:
      x:    [36. 36.]
      P:    [ 0. -1.]
      u:    [ 0.         -5.09116882]

Elements:
---------------------
  Truss: Node_36 to Node_37:
      material properties: FiberMaterial(Material)({'E': 10.0, 'A': 1.0, '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_36 to Node_38:
      material properties: FiberMaterial(Material)({'E': 10.0, 'A': 1.0, 'nu': 0.0, 'fy': 1e+30})  strain:-0.07071067811865472   stress:{'xx': -0.7071067811865472, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: -0.7071067811865472
  Truss: Node_37 to Node_38:
      material properties: FiberMaterial(Material)({'E': 10.0, 'A': 1.0, 'nu': 0.0, 'fy': 1e+30})  strain:-0.07071067811865472   stress:{'xx': -0.7071067811865472, 'yy': 0.0, 'zz': 0.0, 'xy': 0.0}
      internal force: -0.7071067811865472