sfepy.terms.terms_membrane module

class sfepy.terms.terms_membrane.TLMembraneTerm(*args, **kwargs)

Mooney-Rivlin membrane with plain stress assumption.

The membrane has a uniform initial thickness

System Message: WARNING/2 (h_0)

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and obeys a hyperelastic material law with strain energy by Mooney-Rivlin:

System Message: WARNING/2 (\Psi = a_1 (I_1 - 3) + a_2 (I_2 - 3))

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.

Call signature:

dw_tl_membrane

(material_a1, material_a2, material_h0, virtual, state)

Arguments:

• material_a1 :

  System Message: WARNING/2 (a_1)

  latex exited with error [stdout] This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/TeX Live for SUSE Linux) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2011/06/27> Babel <3.9f> and hyphenation patterns for 78 languages loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2007/10/19 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.131 \endinput ^^M No pages of output. Transcript written on math.log.
• material_a2 :

  System Message: WARNING/2 (a_2)

  latex exited with error [stdout] This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/TeX Live for SUSE Linux) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2011/06/27> Babel <3.9f> and hyphenation patterns for 78 languages loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2007/10/19 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.131 \endinput ^^M No pages of output. Transcript written on math.log.
• material_h0 :

  System Message: WARNING/2 (h_0)

  latex exited with error [stdout] This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/TeX Live for SUSE Linux) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2011/06/27> Babel <3.9f> and hyphenation patterns for 78 languages loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2007/10/19 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.131 \endinput ^^M No pages of output. Transcript written on math.log.
• virtual :

  System Message: WARNING/2 (\ul{v})

  latex exited with error [stdout] This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/TeX Live for SUSE Linux) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2011/06/27> Babel <3.9f> and hyphenation patterns for 78 languages loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2007/10/19 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.131 \endinput ^^M No pages of output. Transcript written on math.log.
• state :

  System Message: WARNING/2 (\ul{u})

  latex exited with error [stdout] This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/TeX Live for SUSE Linux) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2011/06/27> Babel <3.9f> and hyphenation patterns for 78 languages loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2007/10/19 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.131 \endinput ^^M No pages of output. Transcript written on math.log.

arg_shapes = {'material_a2': '1, 1', 'state': 'D', 'material_a1': '1, 1', 'material_h0': '1, 1', 'virtual': ('D', 'state')}

arg_types = ('material_a1', 'material_a2', 'material_h0', 'virtual', 'state')

static eval_function(out, a1, a2, h0, mtx_c, c33, mtx_b, mtx_t, geo, term_mode, fmode)

static function(out, fun, *args)

Notes

fun is either weak_function or eval_function according to evaluation mode.

geometries = ['3_4', '3_8']

get_eval_shape(a1, a2, h0, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)

get_fargs(a1, a2, h0, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)

integration = 'surface'

name = 'dw_tl_membrane'

static weak_function(out, a1, a2, h0, mtx_c, c33, mtx_b, mtx_t, bfg, geo, fmode)

sfepy.terms.terms_membrane.eval_membrane_mooney_rivlin(a1, a2, mtx_c, c33, mode)

Evaluate stress or tangent stiffness of the Mooney-Rivlin membrane.

[1] Baoguo Wu, Xingwen Du and Huifeng Tan: A three-dimensional FE nonlinear analysis of membranes, Computers & Structures 59 (1996), no. 4, 601–605.