5. Generic tetrahedral (TE) elements

TE elements define tetrahedral elements in R3. B2000++ node indices are positive integers and they must belong to the same branch. The element local x-axis xelement is defined by r21 = p2 - p1, with p2 being the coordinate of the vertex n2, and p1 the coordinate of the vertex n1. The element local z-axis zelement is defined by the vector product r21 . r31, with r31 = p3 - p1, and p3 being the coordinate of the vertex n3. The element local y-axis yelement is then obtained by the vector product zelement . xelement.

The element faces are numbered in counter-clockwise direction, as seen from outside the element. Thus, the element face normals (and the element face local z-axis) always point out from the element. The first 2 nodes of the element face connectivity list define the element face local x-axis xface. The element face local y-axis is defined by yface = r21 . r31, with r21 = p2 - p1 and r31 = p3 - p1, p1 being the coordinate of the element face connectivity node 1, p2 of node 2, and p3 of node 3. The element face local y-axis yface is then defined by zface . xface.

Table 6. TE element face node connectivity

 TE4 faces TE10 faces Face 1: n1 n3 n2 n1 n3 n2 n7 n6 n5 Face 2: n1 n2 n4 n1 n2 n4 n5 n9 n8 Face 3: n2 n3 n4 n2 n3 n4 n6 n10 n9 Face 4: n3 n1 n4 n3 n1 n4 n7 n8 n10

The element edge node connectivity of TE elements are defined as follows: The first 2 nodes of an element edge connectivity list also define the element edge local x-axis xedge, the axis running from the first to the second node. The figure and table below display the element local edge numbering, the orientation (direction) of the edge local x-axis, as well as the element nodes defining the edges.

Table 7. TE element edge node connectivity

 TE4 TE10 Edge 1: n1 n2 n1 n2 n5 Edge 2: n2 n3 n2 n3 n6 Edge 3: n3 n1 n3 n1 n7 Edge 4: n1 n4 n1 n4 n8 Edge 5: n2 n4 n2 n4 n9 Edge 6: n3 n4 n3 n4 n10