Matrix Operations

This example shows how to do some matrix operations, including basic mathematical operations (power, add and multiply by a constant, add field containers and invert) and separating and assembling fields and fields containers.

Import the ansys.dpf.core module, included examples file, and the operators.math module.

from ansys.dpf import core as dpf
from ansys.dpf.core import examples
import ansys.dpf.core.operators.math as maths

Open an example and print the Model object The Model class helps to organize access methods for the result by keeping track of the operators and data sources used by the result file.

Printing the model displays this metadata:

• Analysis type

• Available results

• Size of the mesh

• Number of results

my_model = dpf.Model(examples.find_complex_rst())
my_mesh = my_model.metadata.meshed_region
print(my_model)

DPF Model
------------------------------
Harmonic analysis
Unit system: MKS: m, kg, N, s, V, A, degC
Physics Type: Mechanical
Available results:
     -  displacement: Nodal Displacement
     -  reaction_force: Nodal Force
     -  stress: ElementalNodal Stress
     -  elemental_volume: Elemental Volume
     -  stiffness_matrix_energy: Elemental Energy-stiffness matrix
     -  artificial_hourglass_energy: Elemental Hourglass Energy
     -  thermal_dissipation_energy: Elemental thermal dissipation energy
     -  kinetic_energy: Elemental Kinetic Energy
     -  co_energy: Elemental co-energy
     -  incremental_energy: Elemental incremental energy
     -  elastic_strain: ElementalNodal Strain
     -  nmisc: Elemental Elemental Non Summable Miscellaneous Data
     -  elemental_heat_generation: Elemental Elemental Heat Generation
     -  structural_temperature: ElementalNodal Structural temperature
     -  electric_potential: Nodal Electric Potential
     -  electric_flux_density: ElementalNodal Electric flux density
     -  electric_field: ElementalNodal Electric field
------------------------------
DPF  Meshed Region:
  4802 nodes
  657 elements
  Unit: m
  With solid (3D) elements
------------------------------
DPF  Time/Freq Support:
  Number of sets: 1
  With complex values

Cumulative     Frequency (Hz) LoadStep       Substep        RPM
1              343478.200000  1              1              0.000000

Get the stress tensor and define its scoping. Only three nodes will be taken into account to facilitate the visualization.

my_nodes_scoping = dpf.Scoping(ids=[38, 37, 36], location=dpf.locations.elemental)
my_stress = my_model.results.stress(mesh_scoping=my_nodes_scoping).eval()

# We need to average the result from 'elemental_nodal' to an 'elemental' location to plot it.
my_avg_stress = dpf.operators.averaging.to_elemental_fc(
    fields_container=my_stress, mesh=my_mesh
).eval()
print(my_avg_stress)
print(my_avg_stress[0])

DPF stress(s)Fields Container
  with 2 field(s)
  defined on labels: complex time

  with:
  - field 0 {complex:  0, time:  1} with Elemental location, 6 components and 3 entities.
  - field 1 {complex:  1, time:  1} with Elemental location, 6 components and 3 entities.

DPF stress_343478.2Hz_real Field
  Location: Elemental
  Unit: Pa
  3 entities
  Data: 6 components and 3 elementary data

  Elemental
  IDs                   data(Pa)
  ------------          ----------
  38                    -1.708495e+04  -1.180122e+05  -1.239892e+03  -1.071840e+04  6.860520e+01   -5.747203e+02

  37                    -1.969171e+04  -1.162967e+05  -1.240906e+03  -1.771855e+04  1.132344e+02   -5.604889e+02

  36                    -2.358518e+04  -1.136281e+05  -1.239959e+03  -2.447057e+04  1.554545e+02   -5.414763e+02

Separating tensor by component

# If operations need to be done separately in each tensor component, use
# :func:'select_component()<ansys.dpf.core.fields_container.FieldsContainer.select_component>'.
# Here, the stress tensor has 6 components per elementary data (symmetrical tensor XX,YY,ZZ,XY,YZ,XZ).

# Separating the results in different fields containers for each stress tensor component
stress_1 = my_avg_stress.select_component(0)
stress_2 = my_avg_stress.select_component(1)
stress_3 = my_avg_stress.select_component(2)
stress_4 = my_avg_stress.select_component(3)
stress_5 = my_avg_stress.select_component(4)
stress_6 = my_avg_stress.select_component(5)

Mathematical operation on each field

# Here we will do some basic mathematical operations on each stress field

# Power
# Raise each value of the field to power 2
stress_1 = maths.pow_fc(fields_container=stress_1, factor=2.0).eval()

# Add a constant
# Add 2 to each value in the field
stress_2 = maths.add_constant_fc(fields_container=stress_2, weights=2.0).eval()

# Multiply by a constant
# Multiply each value in the field by 3
stress_3 = maths.scale_fc(fields_container=stress_3, weights=3.0).eval()

# Add fields containers
# Each value of each field is added by the correspondent component of the others fields
stress_4 = maths.add_fc(fields_container1=stress_4, fields_container2=stress_5).eval()
stress_5 = maths.add_fc(fields_container1=stress_5, fields_container2=stress_6).eval()

# Invert
# Compute the invert of each element of each field (1./X)
stress_6 = maths.invert_fc(fields_container=stress_6).eval()

Reassembling the stress tensor

# There are different methods to re-assemble the components, here we use the
# operator :class:'assemble_scalars_to_matrices_fc <ansys.dpf.core.operators.utility.assemble_scalars_to_matrices_fc.assemble_scalars_to_matrices_fc>'

re_assemble = dpf.operators.utility.assemble_scalars_to_matrices_fc(
    xx=stress_1, yy=stress_2, zz=stress_3, xy=stress_4, yz=stress_5, xz=stress_6, symmetrical=True
).eval()

print(re_assemble)
print(re_assemble[0])

DPF  Fields Container
  with 2 field(s)
  defined on labels: complex time

  with:
  - field 0 {complex:  0, time:  1} with Elemental location, 6 components and 3 entities.
  - field 1 {complex:  1, time:  1} with Elemental location, 6 components and 3 entities.

DPF stress_343478.2Hz_real5 Field
  Location: Elemental
  Unit: Pa^-1
  3 entities
  Data: 6 components and 3 elementary data

  Elemental
  IDs                   data(Pa^-1)
  ------------          ----------
  38                    2.918956e+08   -1.180102e+05  -3.719676e+03  -1.064980e+04  -5.061151e+02  -1.739977e-03

  37                    3.877632e+08   -1.162947e+05  -3.722718e+03  -1.760532e+04  -4.472545e+02  -1.784157e-03

  36                    5.562606e+08   -1.136261e+05  -3.719876e+03  -2.431511e+04  -3.860217e+02  -1.846803e-03