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.

TE4 element connectivity

Figure 25. TE4 element connectivity


TE10 element connectivity

Figure 26. TE10 element connectivity


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.

TE element face numbering

Figure 27. TE element face numbering


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.

TE element edge numbering and orientation

Figure 28. TE element edge numbering and orientation


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