6. Generic hexahedral (HE) elements

HE elements define hexahedral 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.

HE8 element connectivity

Figure 29. HE8 element connectivity


HE20 element connectivity

Figure 30. HE20 element connectivity


HE27 element connectivity

Figure 31. HE27 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.

HE element face numbering and orientation

Figure 32. HE element face numbering and orientation


Table 8. HE element face node connectivity

  HE8 HE20 HE27
Face 1: n4 n1 n5 n8 n4 n1 n5 n8 n12 n17 n16 n20 n4 n1 n5 n8 n12 n17 n16 n20 n21
Face 2: n2 n3 n7 n6 n2 n3 n7 n6 n10 n19 n14 n18 n2 n3 n7 n6 n10 n19 n14 n18 n22
Face 3: n1 n2 n6 n5 n1 n2 n6 n5 n9 n18 n13 n17 n1 n2 n6 n5 n9 n18 n13 n17 n23
Face 4: n3 n4 n8 n7 n3 n4 n8 n7 n11 n20 n1c5 n19 n3 n4 n8 n7 n11 n20 n15 n19 n24
Face 5: n2 n1 n4 n3 n2 n1 n4 n3 n9 n12 n11 n10 n2 n1 n4 n3 n9 n12 n11 n10 n25
Face 6: n5 n6 n7 n8 n5 n6 n7 n8 n13 n14 n15 n16 n5 n6 n7 n8 n13 n14 n15 n16 n26


The element edge node connectivity of HE 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.

HE element edge numbering and orientation

Figure 33. HE element edge numbering and orientation


Table 9. HE element edge node connectivity

  HE8 HE20/HE27
Edge 1: n1 n2 n1 n2 n9
Edge 2: n2 n3 n2 n3 n10
Edge 3: n3 n4 n3 n4 n11
Edge 4: n4 n1 n4 n1 n12
Edge 5: n5 n6 n5 n6 n13
Edge 6: n6 n7 n6 n7 n14
Edge 7: n7 n8 n7 n8 n15
Edge 8: n8 n5 n8 n5 n16
Edge 9: n1 n5 n1 n5 n17
Edge 10: n2 n6 n2 n6 n18
Edge 11: n3 n7 n3 n7 n19
Edge 12: n4 n8 n4 n8 n20