pyNastran
0.5.0
pyNastran BDF Reader/Writer, OP2 Parser, and GUI
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Public Member Functions | |
def | __init__ |
def | S |
" Calculates the compliance matrix for a lamina
\[ \large [Q] = [S]^{-1} \] | |
def | ABDH |
tranforms load to strain/bending curvature taken at \( z=0 \)
\[ \large \left[ \begin{array}{c} Nx \\ Ny \\ Nz \\ Mx \\ My \\ Mz \\ \end{array} \right] = \left[ \begin{array}{cc} A & B \\ B & D \\ \end{array} \right] \left[ \begin{array}{c} \epsilon_{xx} \\ \epsilon_{yy} \\ \gamma_{xy} \\ \kappa_{xx} \\ \kappa_{yy} \\ \kappa_{xy} \\ \end{array} \right] \] | |
def | Qall |
Caculates the laminate tranformation stiffness \( [Q]_{all} \)
\[ \large [Q]_{all} = [T]^{-1} [Q] [R][T][R]^{-1} \] \[ \large [Q]_{all} = [T]^{-1} [Q] [T]^{-T} \] | |
def | Q |
" Calculates the stiffness matrix \( [Q] \) for a lamina | |
def | T |
calculates the Transformation matricies $ [T] $ and \( [T]^{-1} \) | |
Static Public Attributes | |
string | type = 'ShellProperty' |
def pyNastran.bdf.cards.properties.shell.ShellProperty.__init__ | ( | self, | |
card = None , |
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data = None |
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) |
Reimplemented from pyNastran.bdf.cards.baseCard.Property.
Reimplemented in pyNastran.bdf.cards.properties.shell.PSHELL, and pyNastran.bdf.cards.properties.shell.PCOMP.
Definition at line 40 of file shell.py.
References pyNastran.bdf.cards.properties.shell.ShellProperty.S().
Referenced by pyNastran.bdf.cards.properties.shell.ShellProperty.T().
" Calculates the compliance matrix for a lamina
\[ \large [Q] = [S]^{-1} \]
Definition at line 49 of file shell.py.
References pyNastran.bdf.cards.properties.shell.ShellProperty.ABDH().
Referenced by pyNastran.bdf.cards.properties.shell.ShellProperty.__init__().
tranforms load to strain/bending curvature taken at \( z=0 \)
\[ \large \left[ \begin{array}{c} Nx \\ Ny \\ Nz \\ Mx \\ My \\ Mz \\ \end{array} \right] = \left[ \begin{array}{cc} A & B \\ B & D \\ \end{array} \right] \left[ \begin{array}{c} \epsilon_{xx} \\ \epsilon_{yy} \\ \gamma_{xy} \\ \kappa_{xx} \\ \kappa_{yy} \\ \kappa_{xy} \\ \end{array} \right] \]
[Nx] = [ ] [ e_xx0 ] [Ny] = [ [A] [B] ] [ e_yy0 ] [Nz] = [ ] [ gamma_xy0] [Mx] = [ ] [ k_xx0 ] [My] = [ [B] [D] ] [ k_yy0 ] [Mz] = [ ] [ k_xy0 ]
\[ \large A_{ij} = \Sigma_{k=1}^N (\overline{Q_{ij}})_k \left( z_k -z_{k-1} \right) = \Sigma_{k=1}^N (Q_{ij})_k t_k \]
\[ \large B_{ij} = \Sigma_{k=1}^N (\overline{Q_{ij}})_k \left( z_k^2-z_{k-1}^2 \right) = \Sigma_{k=1}^N (Q_{ij})_k \left( \overline{z} t_k \right) \]
\[ \large D_{ij} = \Sigma_{k=1}^N (\overline{Q_{ij}})_k \left( z_k^3-z_{k-1}^3 \right) = \Sigma_{k=1}^N (Q_{ij})_k \left( \overline{z}^2 t_k + \frac{t_k^3}{12} \right) \]
\[ \large H_{ij} = \Sigma_{k=1}^N (Q_{ij})_k \left( t_k -\frac{4}{t^2} \left( \overline{z}^2 t_k + \frac{t_k^3}{12} \right) \right) \]
p. 138 of "Introduction to Composite Material Design"
Definition at line 98 of file shell.py.
References pyNastran.bdf.cards.properties.shell.ShellProperty.Qall().
Referenced by pyNastran.bdf.cards.properties.shell.ShellProperty.S().
def pyNastran.bdf.cards.properties.shell.ShellProperty.Qall | ( | self, | |
thetad | |||
) |
Caculates the laminate tranformation stiffness \( [Q]_{all} \)
\[ \large [Q]_{all} = [T]^{-1} [Q] [R][T][R]^{-1} \]
\[ \large [Q]_{all} = [T]^{-1} [Q] [T]^{-T} \]
.
p. 123 of "Introduction to Composite Material Design"
Definition at line 131 of file shell.py.
References pyNastran.bdf.cards.properties.bars.PBAR.E1, pyNastran.bdf.cards.properties.bars.PBAR.E2, pyNastran.bdf.cards.materials.MAT8.nu12, and pyNastran.bdf.cards.properties.shell.ShellProperty.Q().
Referenced by pyNastran.bdf.cards.properties.shell.ShellProperty.ABDH().
" Calculates the stiffness matrix \( [Q] \) for a lamina
114 "Introduction to Composite Material Design"
Definition at line 163 of file shell.py.
References pyNastran.bdf.cards.properties.shell.ShellProperty.T().
Referenced by pyNastran.bdf.cards.properties.shell.ShellProperty.Qall().
def pyNastran.bdf.cards.properties.shell.ShellProperty.T | ( | self, | |
theta | |||
) |
calculates the Transformation matricies $ [T] $ and \( [T]^{-1} \)
self | the object pointer |
theta | in radians... |
Tinv | the inverse transformation matrix |
TinvTranspose | the transposed inverse transformation matrix |
tranformation matrix \( [T] \)
\[ \large [T] = \left[ \begin{array}{ccc} m^2 & n^2 & 2mn \\ n^2 & m^2 & -2mn \\ -mn & mn & m^2-n^2 \end{array} \right] \]
[ m^2 n^2 2mn] [T] = [ n^2 m^2 -2mn] # transformation matrix [ -mn mn m^2-n^2]
inverse transformation matrix \( [T]^{-1} \)
\[ \large [T]^{-1} = \left[ \begin{array}{ccc} m^2 & n^2 & -2mn \\ n^2 & m^2 & 2mn \\ mn & -mn & m^2-n^2 \end{array} \right] \]
[ m^2 n^2 -2mn] [T]^-1 = [ n^2 m^2 2mn] # inverse transform [ mn -mn m^2-n^2]
\[ \large \left[ \begin{array}{c} \sigma_{xx} \\ \sigma_{yy} \\ \sigma_{xy} \end{array} \right] = [T]^{-1} [Q] [R][T] \left[ \begin{array}{c} \epsilon_{xx} \\ \epsilon_{yy} \\ \frac{1}{2} \gamma_{xy} \end{array} \right] \]
p.119 "Introduction to Composite Material Design"
Definition at line 231 of file shell.py.
References pyNastran.bdf.cards.properties.shell.ShellProperty.__init__().
Referenced by pyNastran.bdf.cards.properties.shell.PCOMP.MassPerArea(), and pyNastran.bdf.cards.properties.shell.ShellProperty.Q().
string pyNastran::bdf::cards::properties::shell.ShellProperty::type = 'ShellProperty' [static] |
Reimplemented from pyNastran.bdf.cards.baseCard.BaseCard.
Reimplemented in pyNastran.bdf.cards.properties.shell.PSHELL, pyNastran.bdf.cards.properties.shell.PSHEAR, and pyNastran.bdf.cards.properties.shell.PCOMP.
Definition at line 39 of file shell.py.
Referenced by pyNastran.bdf.cards.nodes.Node::__init__(), pyNastran.bdf.cards.sets.ABQSet1::__init__(), pyNastran.bdf.cards.baseCard.Property::__init__(), pyNastran.bdf.cards.baseCard.Element::__init__(), pyNastran.bdf.cards.sets.CSET1::__init__(), pyNastran.bdf.cards.dmig.NastranMatrix::__repr__(), pyNastran.bdf.cards.dmig.NastranMatrix::getDType(), pyNastran.bdf.cards.elements.solid.SolidElement::isSameCard(), pyNastran.bdf.cards.elements.springs.SpringElement::K(), pyNastran.bdf.cards.properties.shell.PCOMP::nPlies(), pyNastran.bdf.cards.elements.solid.SolidElement::rawFields(), and pyNastran.bdf.cards.elements.elements.CrackElement::rawFields().