linear_elasticity/its2D_5.py

Description

Diametrically point loaded 2-D disk with postprocessing and probes. See Primer.

Find such that:

where

source code

r"""
Diametrically point loaded 2-D disk with postprocessing and probes. See
:ref:`sec-primer`.

Find :math:`\ul{u}` such that:

.. math::
    \int_{\Omega} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u})
    = 0
    \;, \quad \forall \ul{v} \;,

where

.. math::
    D_{ijkl} = \mu (\delta_{ik} \delta_{jl}+\delta_{il} \delta_{jk}) +
    \lambda \ \delta_{ij} \delta_{kl}
    \;.
"""
from __future__ import absolute_import
from sfepy.examples.linear_elasticity.its2D_1 import *

from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson
from sfepy.postprocess.probes_vtk import Probe

import os
from six.moves import range

def stress_strain(out, pb, state, extend=False):
    """
    Calculate and output strain and stress for given displacements.
    """
    from sfepy.base.base import Struct
    import matplotlib.pyplot as plt
    import matplotlib.font_manager as fm

    ev = pb.evaluate
    strain = ev('ev_cauchy_strain.2.Omega(u)', mode='el_avg')
    stress = ev('ev_cauchy_stress.2.Omega(Asphalt.D, u)', mode='el_avg')

    out['cauchy_strain'] = Struct(name='output_data', mode='cell',
                                  data=strain, dofs=None)
    out['cauchy_stress'] = Struct(name='output_data', mode='cell',
                                  data=stress, dofs=None)

    probe = Probe(out, pb.domain.mesh, probe_view=True)

    ps0 = [[0.0,  0.0, 0.0], [ 0.0,  0.0, 0.0]]
    ps1 = [[75.0, 0.0, 0.0], [ 0.0, 75.0, 0.0]]
    n_point = 10

    labels = ['%s -> %s' % (p0, p1) for p0, p1 in zip(ps0, ps1)]
    probes = []
    for ip in range(len(ps0)):
        p0, p1 = ps0[ip], ps1[ip]
        probes.append('line%d' % ip)
        probe.add_line_probe('line%d' % ip, p0, p1, n_point)

    for ip, label in zip(probes, labels):
        fig = plt.figure()
        plt.clf()
        fig.subplots_adjust(hspace=0.4)
        plt.subplot(311)
        pars, vals = probe(ip, 'u')
        for ic in range(vals.shape[1] - 1):
            plt.plot(pars, vals[:,ic], label=r'$u_{%d}$' % (ic + 1),
                     lw=1, ls='-', marker='+', ms=3)
        plt.ylabel('displacements')
        plt.xlabel('probe %s' % label, fontsize=8)
        plt.legend(loc='best', prop=fm.FontProperties(size=10))

        sym_labels = ['11', '22', '12']

        plt.subplot(312)
        pars, vals = probe(ip, 'cauchy_strain')
        for ii in range(vals.shape[1]):
            plt.plot(pars, vals[:, ii], label=r'$e_{%s}$' % sym_labels[ii],
                     lw=1, ls='-', marker='+', ms=3)
        plt.ylabel('Cauchy strain')
        plt.xlabel('probe %s' % label, fontsize=8)
        plt.legend(loc='best', prop=fm.FontProperties(size=8))

        plt.subplot(313)
        pars, vals = probe(ip, 'cauchy_stress')
        for ii in range(vals.shape[1]):
            plt.plot(pars, vals[:, ii], label=r'$\sigma_{%s}$' % sym_labels[ii],
                     lw=1, ls='-', marker='+', ms=3)
        plt.ylabel('Cauchy stress')
        plt.xlabel('probe %s' % label, fontsize=8)
        plt.legend(loc='best', prop=fm.FontProperties(size=8))

        opts = pb.conf.options
        filename_results = os.path.join(opts.get('output_dir'),
                                        'its2D_probe_%s.png' % ip)

        fig.savefig(filename_results)

    return out

materials['Asphalt'][0].update({'D' : stiffness_from_youngpoisson(2, young, poisson)})

options.update({
    'post_process_hook' : 'stress_strain',
})