Example Problem 4 page 313 from Mark. E. Tuttle's "Structural Analysis of Polymeric Composite Materials", first edition.



In [1]:

    
import pyPLY

GraphiteEpoxy = pyPLY.CompositeMaterial()
GraphiteEpoxy.define("GraphiteEpoxy", "metric", E11=170e9, E22=10e9, G12=13e9, niu12=0.3, thk=0.125e-3,
             Sigma_ut0 = 1500e6, Sigma_uc0 = 1200e6, Sigma_ut90 = 50e6, Sigma_uc90 = 100e6, Tau_u = 75e6,
             alpha_11 = -0.9e-6, alpha_22 = 27.0e-6, beta_11 = 150e-6, beta_22 = 4800)

layer1 = pyPLY.Lamina()
layer2 = pyPLY.Lamina()
layer3 = pyPLY.Lamina()

layer1.define("Layer_1", 1, 30)
layer2.define("Layer_2", 1, 0)
layer3.define("Layer_3", 1, 90)

layer1.update()
layer2.update()
layer3.update()

laminate1 = pyPLY.Laminate()
laminate1.add_Lamina(layer1)
laminate1.add_Lamina(layer2)
laminate1.add_Lamina(layer3)

laminate1.update()

Results:

[ABD] matrix:



In [2]:

    
from pyPLYTools import LXMatrix
from IPython.display import Latex

Latex("$ABD = " + LXMatrix(laminate1.ABD, '.3e', ipython=True) + "$")









    Out[2]:





$ABD = \left[\begin{array}{cccccc}
	3.608e+07 & 4.012e+06 & 6.017e+06 & -1.525e+03 & -3.601e+02 & -7.521e+02\\
	4.012e+06 & 2.602e+07 & 2.690e+06 & -3.601e+02 & 2.245e+03 & -3.362e+02\\
	6.017e+06 & 2.690e+06 & 7.756e+06 & -7.521e+02 & -3.362e+02 & -3.601e+02\\
	-1.525e+03 & -3.601e+02 & -7.521e+02 & 2.768e-01 & 6.202e-02 & 1.018e-01\\
	-3.601e+02 & 2.245e+03 & -3.362e+02 & 6.202e-02 & 4.208e-01 & 4.553e-02\\
	-7.521e+02 & -3.362e+02 & -3.601e+02 & 1.018e-01 & 4.553e-02 & 1.059e-01
	\end{array}\right]$

[abd] matrix:



In [3]:

    
Latex("$abd = " + LXMatrix(laminate1.abd, '.3e', ipython=True) + "$")









    Out[3]:





$abd = \left[\begin{array}{cccccc}
	3.757e-08 & -1.964e-09 & -1.038e-08 & 1.440e-04 & 3.905e-06 & 8.513e-05\\
	-1.964e-09 & 1.037e-07 & -4.234e-08 & -1.866e-05 & -6.361e-04 & 4.628e-04\\
	-1.038e-08 & -4.234e-08 & 2.004e-07 & 3.661e-04 & 3.251e-04 & -1.851e-05\\
	1.440e-04 & -1.866e-05 & 3.661e-04 & 7.064e+00 & -3.122e-02 & -4.572e+00\\
	3.905e-06 & -6.361e-04 & 3.251e-04 & -3.122e-02 & 6.429e+00 & -3.620e+00\\
	8.513e-05 & 4.628e-04 & -1.851e-05 & -4.572e+00 & -3.620e+00 & 1.741e+01
	\end{array}\right]$