132. fe.fe_tools — Utility functions for finite elements applications

This module contains some functions, data and classes for assist finite element modelling. You need to import this module in your scripts to have access to its contents.

132.1. Classes defined in module fe.fe_tools

class fe.fe_tools.IsotropicElasticity(E=None, G=None, nu=None, K=None, lmbda=None, mu=None, D=None)[source]

Material constants for an isotropic linear elastic material.

Exactly 2 out of the following need to be specified:

E, G, nu, K, lmbda, mu, D

class fe.fe_tools.UniaxialStrain(data, type)[source]

Uniaxial finite deformation strain measures.

This class provides a way to store finite deformation strain measures and to convert between different strain measure definitions.

Parameters:

  • data: array_like float (n,): strain values

  • type: one of ‘stretch’, ‘log’, ‘nominal’, ‘green’, ‘almansi’. Defines the type of strain measure:

    • ‘stretch’: stretch (ratio) or extension ratio,

    • ‘nominal’: nominal or engineering strain,

    • ‘log’: logarithmic or true strain,

    • ‘green’: Green strain (values should be >= -0.5),

    • ‘almansi’: Almansi strain (values should be <= 0.5).

    The default is to interprete the data as nominal strains.

Internally, the data are stored as stretch values.

stretch()[source]

Return the strain data as stretch ratios

log()[source]

Return the strain data as logarithmic (true) strains

nominal()[source]

Return the strain data as nominal (engineering) strains

green()[source]

Return the strain data as Green strains

almansi()[source]

Return the strain data as Almansi strains

class fe.fe_tools.UniaxialStress(data, type, strain, straintype=None)[source]

Uniaxial finite deformation stress measures.

This class provides a way to store finite deformation stress measures and to convert between different stress measure definitions.

Parameters:

  • data: array_like float (n,): stress values

  • type: one of ‘cauchy’, ‘nominal’, ‘pk2’. Defines the type of stress measure:

    • ‘cauchy’: Cauchy or true stress,

    • ‘nominal’: nominal, engineering or first Piola-Kirchhoff stress,

    • ‘pk2’: second Piola-Kirchhoff stress.

    The default is to interprete the data as nominal stresses.

  • strain: a UniaxialStrain instance of matching size (n,), or array_like float (n,) with the strain values. In the latter case also straintype should be specified.

  • straintype: if strain is specified as a UniaxialStrain instance, this argument is not used. Else it specifies the strain type (see UniaxialStrain).

Internally, the data are stored as Cauchy stress.

132.2. Functions defined in module fe.fe_tools

fe.fe_tools.smoothAmp(a, n=50)[source]

Compute a single abaqus smooth amplitude.

Parameters:
  • a (array_like (2,2)) – Initial and final (amplitude,time) pairs

  • n (int) – Number of intervals for the time variable

fe.fe_tools.ampSequence(a, n=100, f=<function smoothAmp>)[source]

Compute a final amplitude from a sequence of amplitudes.

Parameters:
  • a (array_like (namp,2)) – Every row is a pair of subsequent (amplitude,time) values

  • n (int) – Number of of intervals for the time variable

  • f (callable) – Amplitude function

fe.fe_tools.transverseShear(E, nu, c, type='generalized')[source]

Compute the shear stiffness for beam and shell element theory

For homogeneous beams/shells made of a linear, orthotropic elastic material.

Parameters:
  • E (float (1 or 2)) – Elastic modulus in the one or two directions. If only one given, the values in each directions are taken the same.

  • nu (float) – Poisson modulus

  • c (float) – Characteristic dimension. For beam elements it is the cross- sectional area, for shell elements the thickness of the element.

  • type (str) – Either ‘shell’ or one of the allowed beam cross section names as defined in abaqus.

Returns:

  • list – A list of 3 values for the transverse shear. For type == ‘shell’:

    • shear stiffness in the 1st direction,

    • shear stiffness in the 2nd direction,

    • coupling term, assumed to be 0.

    In all other cases (beam sections):

    • shear stiffness,

    • shear stiffness,

    • slenderness compensation factor

  • See abaqus documentation for meanings and usage.