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Homework:
- Verify the result given in Equation (3.74).
- Using the invariance property of strain energy density function, show that
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- Obtain the individual terms of transformed stiffness and compliance matrices using Equation (3.73) and Equation (3.80), respectively and verify it with Equation (3.76) and Equation (3.82), respectively.
- Obtain the strain transformation matrix
 using tensorial shear strains. Further, using this transformation matrix obtain the transformed stiffness and compliance matrix in the form similar to Equation (3.75) and Equation (3.81). Compare the new matrices and comment on the observations with justifications.
- Calculate the stiffness and compliance coefficients for following transversely isotropic materials given in Table 3.1.
Table 3.1: Properties for unidirectional transversely isotropic lamina
Property\Material |
T300/BSL914C Epoxy |
E-glass/LY556/ HT907/DY063 Epoxy |
S-glass/MY750/ HY917/DY063 Epoxy |
E1 (GPa) |
138 |
53.48 |
45.6 |
E2=E3(GPa) |
11 |
17.7 |
16.2 |
G12 = G13(GPa) |
5.5 |
5.83 |
5.83 |
ν12= ν13 |
0.28 |
0.278 |
0.278 |
ν23 |
0.4 |
0.4 |
0.4 |
α1 (×10-6/°C) |
-1 |
8.6 |
8.6 |
α2 = α3 (×10-6/°C) |
26 |
26.4 |
26.4 |
- The stiffness matrix for an orthotropic material is given as
Find:
- The compliance matrix
- The engineering constants
 .
- Why are the thermal effects important in composite materials? Explain in detail.
- Plot variation of
 between  for T300/BSL914C Epoxy and E-glass/LY556/ HT907/DY063 Epoxy. See Table 3.1 for the required thermal properties.
- Why are the hygral effects important in composite materials? Explain.
- Search literature to get the coefficients of moisture absorption for at least two composite materials and plot its variation between
- Write a computer code to read the properties of a transversely isotropic material and calculate all the terms of stiffness and compliance matrix. Verify your results with the results given in Example 1. Then use this code to get the stiffness and compliance matrices of T300/BSL914C Epoxy and S-glass/MY750/ HY917/DY063 Epoxy.
- Add another module to the code written for above problem to calculate the transformed stiffness and compliance matrices. Plot all the coefficients between . Compare the corresponding terms of these materials and comment.
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