Table of Contents
Triangular semi-loof
Shell element with possible reinforcements along edges. Thickness is generally variable.
Nodes
The element has 6 nodes. Midside nodes must not be omitted.
Corner nodes have displacements $[u,v,w].$ Midside nodes have 5 degrees of freedom $[u,v,w,\alpha,\beta],$ where $\alpha$ and $\beta$ are the angles of rotation of the edge. All nodes have temperatures $[T,\Delta T],$ where $\Delta T$ is the temperature difference between the bottom and top sides.
Edges
The element has 3 edges, whose orientation depends on the particular mesh numbering.
Orientation of the edge
An edge has three nodes with global numbers N1, N2 and N3. In the figure, N1 < N3 is assumed. The angles of rotation $\alpha$ and $\beta$ are moved to the midside node, but they are actually calculated in the loof points $L_1,L_2.$ The angles $\alpha,\beta$ are positive for clockwise rotation about the axis $y_h$ in the points $L_1,L_2.$
An edge is oriented positively by the axis $y_h.$
Local coordinate system of the edge
The axis $x_h$ is such that the resulting coortinate system is right-handed and, generally, does not point outward from the element.
The axis $y_h$ coincides with the edge in the direction from N1 to N3, therefore, its orientation depends on the particular mesh numbering.
The axis $z_h$ coincides with the local surface normal $\zeta.$
Faces
The element has one (center-line) surface. This surface is oriented positively by the normal $\zeta,$ which is directed from the bottom side to the top side.
For heat transfer problems, there are two more surfaces defined, coinciding with the bottom side (face 2) and the top side (face 1).
Local coordinate system of the element
The axis $\xi$ coincides with the edge 1, which is defined by nodes 1 – 4 – 2.
The axis $\eta$ coincides with the edge 3, which is defined by nodes 1 – 6 – 3.
The axis $\zeta$ is such that the resulting coordinate system is right-handed.