## 4. Generic quadrilateral (Q) elements

Q elements define quadrilateral elements in R2 and 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 Q element face connectivity is the same as the element connectivity. The element faces are numbered in counter-clockwise direction, as seen from above, i.e. in the positive element z-axis quadrant. 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 . xfaceelement. The first 2 nodes of the element edge connectivity list define the element edge local x-axis.

Table 5. Q element edge connectivity

 Q4 element Q8/Q9 element Edge 1: n1 n2 n1 n2 n5 Edge 2: n2 n3 n2 n3 n6 Edge 3: n3 n4 n3 n4 n7 Edge 4: n4 n1 n4 n1 n8