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.

Generic Q4 element connectivity

Figure 21. Generic Q4 element connectivity


Generic Q8 element connectivity

Figure 22. Generic Q8 element connectivity


Generic Q9 element connectivity

Figure 23. Generic Q9 element connectivity


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.

Q element edge orientation

Figure 24. Q element edge orientation


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