## 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. Figure 29. HE8 element connectivity Figure 30. HE20 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. 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. 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