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joss-2023

structural_mechanics_softening.py
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			#!/usr/bin/env python
			# coding: utf-8

			""" structural_mechanics_softening.py: Structural mechanics with softening"""

			__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 test there is a beam consisting of three parts, all have the same materials.
			# The left most node is fixed.
			# On the right most node a force is applied in x direction.
			#
			# After a certain time, the material of the middle _element_ is waekened, lower Young's modulus.
			# In each step the modulus is lowered by a coinstant factor.

			import akantu as aka
			import numpy
			import numpy as np
			try:
			import matplotlib.pyplot as plt
			has_matplotlib = True
			except ImportError:
			has_matplotlib = False


			# ### 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(3, aka._bernoulli_beam_2)
			beamAcc.resizeNodes(4)

			# #### Setting the Nodes
			Nodes = beam.getNodes()
			Nodes[0, :] = [0., 0.]
			Nodes[1, :] = [1., 0.]
			Nodes[2, :] = [2., 0.]
			Nodes[3, :] = [3., 0.]


			# Setting the Connections
			Conn = beam.getConnectivity(aka._bernoulli_beam_2)
			Conn[0, :] = [0, 1]
			Conn[1, :] = [1, 2]
			Conn[2, :] = [2, 3]

			# 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.A = 1.
			mat1.GJ = 1.
			mat1ID = model.addMaterial(mat1, 'mat1')

			mat2 = aka.StructuralMaterial()
			mat2.E = 1e9
			mat2.rho = 1.
			mat2.I = 1. # noqa: E741
			mat2.A = 1.
			mat2.GJ = 1.
			mat2ID = model.addMaterial(mat2, 'mat2')

			mat3 = aka.StructuralMaterial()
			mat3.E = mat2.E / 100000
			mat3.rho = 1.
			mat3.I = 1. # noqa: E741
			mat3.A = mat2.A / 100
			mat3.GJ = 1.
			mat3ID = model.addMaterial(mat3, 'mat3')

			# ##### Initializing the Model
			model.initFull(aka.AnalysisMethod._implicit_dynamic)

			# ##### Assigning the Materials
			materials = model.getElementMaterial(aka._bernoulli_beam_2)

			materials[0][0] = mat1ID
			materials[1][0] = mat2ID
			materials[2][0] = mat1ID


			# ##### 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
			boundary[3, :] = False

			# ### Solving the System
			# Set up the system
			deltaT = 1e-9
			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 = 10000 * 60

			disp0 = np.zeros(N)
			disp1 = np.zeros(N)
			disp2 = np.zeros(N)
			disp3 = np.zeros(N)
			times = np.zeros(N)
			switchT = None
			switchEnd = None

			softDuration = 1000
			SoftStart = (N // 2) - softDuration // 2
			SoftEnd = SoftStart + softDuration
			if(softDuration > 0):
			softFactor = (model.getMaterial('mat3').E
			/ model.getMaterial('mat2').E) ** (1.0 / softDuration)

			mat2 = model.getMaterial('mat2')

			for i in range(N):
			times[i] = deltaT * i

			if((SoftStart <= i <= SoftEnd) and (softDuration > 0)):
			if switchT is None:
			switchT = times[i]
			elif(i == SoftEnd):
			switchEnd = times[i]
			#
			mat2.E *= softFactor
			#

			model.solveStep()
			disp = model.getDisplacement()
			disp0[i] = disp[0, 0]
			disp1[i] = disp[1, 0]
			disp2[i] = disp[2, 0]
			disp3[i] = disp[3, 0]

			disps = [disp0, disp1, disp2, disp3]
			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(disp0, times, color='k', label = "left node (fix)")
			plt.plot(disp1, times, color='g', label="middle, left node")
			plt.plot(disp2, times, color='g', linestyle='--',
			label="middle, right node")
			plt.plot(disp3, times, color='b', label="right node")

			if(softDuration > 0):
			plt.plot((maxMin[1], maxMin[0]), (switchT, switchT),)
			plt.plot((maxMin[1], maxMin[0]), (switchEnd, switchEnd), )

			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()

			# If the softening is disabled, then the displacement looks wierd.
			# Because the displacement first increases and then decreases.
			# In this case `softDuration > 0` holds.
			#
			# However if the softening is enabled, it looks rather good. The left middle
			# node will start to vibrate, because it is not pulled in the other direction.

rAKA/examples/python/structural_mechanics/structural_mechanics_softening.py9d1b388c8329features/joss-2023

structural_mechanics_softening.pyView Options

rAKA/examples/python/structural_mechanics/structural_mechanics_softening.py
9d1b388c8329features/joss-2023

structural_mechanics_softening.py
View Options