6.5 Laminate Compliance matrix

$\alpha $, $\beta $, $\delta $, h are the membrane, bending-extension, bending, and intralaminar compliance matrices of the laminate. See §6.14 in the textbook. This page is very useful. You can calculate the laminate strains and curvatures for a given load. The laminate strains include 3 midsurface (membrane) strains, 3 curvatures (bending), and 2 intralaminar shear strains (transverse shear). The page is shown below:

\includegraphics[]{./Images/ComplianceEqsEx61Nx.png}
Figure 6.2: Laminate strains for Example 6.1 with a unit membrane traction applied. Click the Back button on your browser to return to your previous page.

Note how a twisting curvature $\kappa _{xy}$=3.423 10$^{-6}$/mm is generated for an in-plane load $N_ x$=1 N/mm for this $[55/-55]$ laminate.
\includegraphics[]{./Images/Fig67c.png}

This behavior is caused by the extension-twisting coupling coefficient $\beta _{16}=3.42\  10^{-6}$ MPa$^{-1}$ mm$^{-2}$. The value is not shown on the page but you can see it in Excel, if you click ToExcel at the bottom of the page. You may have to click Enable Editing for the Excel sheet to update the calculated fields, and/or follow the instructions at the bottom of the Excel sheet:
\includegraphics[]{./Images/ExcelComplianceEx61.png}