II.1.1 Conventions

Figure II.1.1 represents some of the conventions used for the definition of laminate in FeResPost. The laminate coordinate system is defined in such a way that the $z$ axis is perpendicular to laminate surface and points from bottom to top surface. $x$ and $y$ vectors are parallel to the laminate plies. Plies are numbered from the bottom to the top surface. If $k$ is the index of a ply, one considers that it is limited by $z$ coordinates $z_{k-1}$ and $z_k$. The origin of the coordinate system is located at mid laminate thickness so that if $t$ is the laminate total thickness and the laminate has $N$ plies, top surface of the laminate is located at $z_N=+t∕2$ and bottom surface at $z_0=-t∕2$. (The plies are numbered from 1 to $N$.)

Figure II.1.1: Conventions for the numbering of plies in a laminate and for the definition of the laminate coordinate system. (A six plies laminate is represented.)

In the laminate, the plies are characterized by their material, thickness and by their angle in the laminate. Figure II.1.2 shows the convention for the orientation of a ply in a laminate. $1$, $2$ and $3$ are the ply axes; $x$, $y$ and $z$ are the laminate axes. Of course, because only 2D laminates are considered here, one has always $z=3$. If $\xi$ is the angle of the ply in the laminate, this angle is as represented in Figure II.1.2: a positive angle corresponds to a rotation from axis $x$ to axis $y$. If the angle is $0^{\circ }$, the first ply axis 1 is parallel to the first laminate axis $x$.

Figure II.1.2: Conventions for the orientation of plies in the laminate.)