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Shape Function Generation#

[7]:

import numpy as np

[8]:

from polymesh.cells import H8

pcoords = H8.lcoords()
shpf = H8.shape_function_values
shpmf = H8.shape_function_matrix
dshpf = H8.shape_function_derivatives

[9]:

shpf(pcoords).shape, shpf(pcoords[:2]).shape

[9]:

((8, 8), (2, 8))

[10]:

shpmf(pcoords).shape, shpmf(pcoords[:2]).shape

[10]:

((8, 3, 24), (2, 3, 24))

[11]:

dshpf(pcoords).shape, dshpf(pcoords[:2]).shape

[11]:

((8, 8, 3), (2, 8, 3))

[12]:

pcoords = H8.lcoords()
*_, shpfH8, shpmfH8, dshpfH8 = H8.generate_class_functions()

[13]:

np.all(np.isclose(shpfH8(pcoords), shpf(pcoords)))

[13]:

True

[14]:

np.all(np.isclose(dshpfH8(pcoords), dshpf(pcoords)))

[14]:

True

[15]:

np.all(np.isclose(shpmfH8(pcoords), shpmf(pcoords)))

[15]:

True

[16]:

from polymesh.cells import TET10

pcoords = TET10.lcoords()
shp, dshp, shpf, shpmf, dshpf = TET10.generate_class_functions()

[17]:

shpf(pcoords).shape, shpf(pcoords[:2]).shape

[17]:

((10, 10), (2, 10))

[18]:

shpmf(pcoords).shape, shpmf(pcoords[:2]).shape

[18]:

((10, 3, 30), (2, 3, 30))

[19]:

dshpf(pcoords).shape, dshpf(pcoords[:2]).shape

[19]:

((10, 10, 3), (2, 10, 3))

[20]:

shpf(pcoords).shape

[20]:

(10, 10)