Shell elements, unlike continuum elements, use material directions local to each element. Anisotropic material data, such as that for fiber reinforced composites, and element output variables, such as stress and strain, are defined in terms of these local material directions. In large-displacement analyses the local material axes on a shell surface rotate with the average motion of the material at each integration point.
The local material 1- and 2-directions lie in the plane of the shell. The default local 1-direction is the projection of the global 1-axis onto the shell surface. If the global 1-axis is normal to the shell surface, the local 1-direction is the projection of the global 3-axis onto the shell surface. The local 2-direction is perpendicular to the local 1-direction in the surface of the shell, so that the local 1-direction, local 2-direction, and the positive normal to the surface form a right-handed set (see Figure 5–6).
The default set of local material directions can sometimes cause problems; a case in point is the cylinder shown in Figure 5–7.
For most of the elements in the figure the local 1-direction is circumferential. However, there is a line of elements that are normal to the global 1-axis. For these elements the local 1-direction is the projection of the global 3-axis onto the shell, making the local 1-direction axial instead of circumferential. A contour plot of the direct stress in the local 1-direction,
, looks very strange, since for most elements is the circumferential stress, whereas for some elements it is the axial stress. In such cases it is necessary to define more appropriate local directions for the model, as discussed in the next section.You can replace the global Cartesian coordinate system with a local rectangular, cylindrical, or spherical coordinate system, as shown in Figure 5–8.
You define the orientation of the local (
, 
, 
) coordinate system, as well as which of the local axes corresponds to which material direction. Thus, you must specify the local axis (1, 2, or 3) that is closest to being normal to the shell's 1 and 2 material directions and a rotation about that axis. ABAQUS follows a cyclic permutation (1, 2, 3) of the axes and projects the axis following your selection onto the shell region to form the material 1-direction. For example, if you choose the -axis, ABAQUS projects the -axis onto the shell to form the material 1-direction. The material 2-direction is defined by the cross product of the shell normal and the material 1-direction. Normally, the final material 2-direction and the projection of the other local axis, in this case the -axis, will not coincide for curved shells.If these local axes do not create the desired material directions, you can specify a rotation about the selected axis. The other two local axes are rotated by this amount before they are projected onto the shell's surface to give the final material directions. For the projections to be interpreted easily, the selected axis should be as close as possible to the shell normal.
For example, if the centerline of the cylinder shown in Figure 5–7 coincides with the global 3-axis, local material directions can be defined such that the local material 1-direction is always circumferential and the corresponding local material 2-direction is always axial. The procedure is described below.
To define local material directions:
From the main menu bar of the Property module, select Tools
Datum and define a cylindrical datum coordinate system.
Select AssignMaterial Orientation to assign a local material orientation to your part. When prompted to select a coordinate system, select the datum coordinate system defined in the previous step. The approximate shell normal direction is Axis–1; no additional rotation is necessary.
