5 Ply Mechanics

The Ply Mechanics chapter contains most, if not all, of the formulas in Chapter Ply Mechanics of the textbook. These are mostly coordinate transformations to handle the various orientations of the laminas in the laminates. Laminates are dealt with in chapter Macromechanics.

If you expand Ply Mechanics (by clicking the \includegraphics[width=14pt]{./Images/expand.png} sign) you get something like this:
\includegraphics[]{./Images/PlyMechanics.png}

As you can see, Ply Mechanics lets you calculate stiffness matrices (Q, and C) and compliance matrices (S) in 2D (plane stress) and 3D. Also, you can do strain and stress transformations from one coordinate system (say lamina c.s., which is 1,2 axes) to laminate c.s. (which is x,y axes).

All of this is quite involved, so you have to read chapter 5 in the textbook to take full advantage of this. Here we show you only the nomenclature, as follows:

S is the plane stress compliance matrix in lamina c.s. This 3x3 matrix contains in-plane values only. The 9 values are taken directly from the 6x6 matrix with the same name, in 3D. This is explained in the textbook.

S* is the intralaminar, also called out-of-plane compliance matrix in lamina c.s. This a 2x2 matrix, which is useful in finite element analysis (FEA) when using Reissner-Mindlin plate elements, also called First Order Shear Deformations (FSDT) elements [3, 4].

Q is the plane stress stiffness matrix in lamina c.s. This 3x3 contains in-plane values only.

Q* is the intralaminar, also called out-of-plane stiffness matrix in lamina c.s. This a 2x2 matrix, which is useful in finite element analysis (FEA) when using Reissner-Mindlin plate elements, also called First Order Shear Deformations (FSDT) elements.

C is the 3D stiffness matrix in lamina c.s. This 6x6 matrix contains in-plane values only.