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structural_mechanics.py
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structural_mechanics.py
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#!/usr/bin/env python
# coding: utf-8
""" structural_mechanics.py: Simple structural mechanics example"""
__author__ = "Nicolas Richart"
__credits__ = [
"Nicolas Richart <nicolas.richart@epfl.ch>",
]
__copyright__ = "Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale" \
" de Lausanne) Laboratory (LSMS - Laboratoire de Simulation" \
" en Mécanique des Solides)"
__license__ = "LGPLv3"
# # Test of Structural Mechanics
# In this example a beam, consisting of two elements, three nodes, is created.
# The left most node is fixed and a force is applied at the right most node.
import numpy as np
try:
import matplotlib.pyplot as plt
has_matplotlib = True
except ImportError:
has_matplotlib = False
import akantu as aka
# ### Creating the Mesh
# Create a mesh for the two dimensional case
beam = aka.Mesh(2)
# We now create the connectivity array for the beam.
beam.addConnectivityType(aka._bernoulli_beam_2)
# We need a `MeshAccessor` in order to change the size of the mesh entities.
beamAcc = aka.MeshAccessor(beam)
# Now we create the array to store the nodes and the connectivities and give
# them their size.
beamAcc.resizeConnectivity(2, aka._bernoulli_beam_2)
beamAcc.resizeNodes(3)
Nodes = beam.getNodes()
Nodes[0, :] = [0., 0.]
Nodes[1, :] = [1., 0.]
Nodes[2, :] = [2., 0.]
# #### Setting the Connections
Conn = beam.getConnectivity(aka._bernoulli_beam_2)
Conn[0, :] = [0, 1]
Conn[1, :] = [1, 2]
# #### Ready
# We have to make the mesh ready.
beamAcc.makeReady()
# ### Creating the Model
model = aka.StructuralMechanicsModel(beam)
# #### Setting up the Modell
# ##### Creating and Inserting the Materials
mat1 = aka.StructuralMaterial()
mat1.E = 1e9
mat1.rho = 1.
mat1.I = 1. # noqa: E741
mat1.Iz = 1.
mat1.Iy = 1.
mat1.A = 1.
mat1.GJ = 1.
model.addMaterial(mat1)
mat2 = aka.StructuralMaterial()
mat2.E = 1e9
mat2.rho = 1.
mat2.I = 1. # noqa: E741
mat2.Iz = 1.
mat2.Iy = 1.
mat2.A = 1.
mat2.GJ = 1.
model.addMaterial(mat2)
# ##### Initializing the Model
model.initFull(aka._implicit_dynamic)
# ##### Assigning the Materials
materials = model.getElementMaterial(aka._bernoulli_beam_2)
materials[0][0] = 0
materials[1][0] = 1
# ##### Setting Boundaries
# Neumann
# Apply a force of `10` at the last (right most) node.
forces = model.getExternalForce()
forces[:] = 0
forces[2, 0] = 100.
# Dirichlets
# Block all dofs of the first node, since it is fixed.
# All other nodes have no restrictions
boundary = model.getBlockedDOFs()
boundary[0, :] = True
boundary[1, :] = False
boundary[2, :] = False
# ### Solving the System
# Set up the system
deltaT = 1e-10
model.setTimeStep(deltaT)
solver = model.getNonLinearSolver()
solver.set("max_iterations", 100)
solver.set("threshold", 1e-8)
solver.set("convergence_type", aka.SolveConvergenceCriteria.solution)
# Perform N time steps.
# At each step records the displacement of all three nodes in x direction.
N = 1000000
disp1 = np.zeros(N)
disp2 = np.zeros(N)
disp0 = np.zeros(N)
times = np.zeros(N)
for i in range(N):
model.solveStep()
disp = model.getDisplacement()
disp0[i] = disp[0, 0]
disp1[i] = disp[1, 0]
disp2[i] = disp[2, 0]
times[i] = deltaT * i
disps = [disp0, disp1, disp2]
maxMin = [-1.0, 1.0]
for d in disps:
maxMin[0] = max(np.max(d), maxMin[0])
maxMin[1] = min(np.min(d), maxMin[1])
if has_matplotlib:
plt.plot(disp1, times, color='g', label="middle node")
plt.plot(disp2, times, color='b', label="right node")
plt.title("Displacement in $x$ of the nodes")
plt.ylabel("Time [S]")
plt.xlabel("displacement [m]")
plt.xlim((maxMin[1] * 1.3, maxMin[0] * 1.1))
plt.legend()
plt.show()

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