1. How to define the local element axis

  • Define the reference vector

  • Then

    • The local z-axis is found as the cross product between the local x-axis and the reference vector.

    • The local y-axis is found as the cross product between the local z-axis and the local x-axis.

editor

2. Reference vector

  • Local x-axis goes from end 1 to end of the element

  • The reference vector define a point relative to end 1.

  • The reference vector is non-dimensional

  • Together the reference vector and the local x-axis define the local xy-plane

ref vector

3. Local Z

  • The local z-axis is found as the cross product between the local x-axis and the reference vector, i.e., Zloc = Xloc x R, where Xloc=[dx,dy,dz] and R=[Rnx,Rny,Rnz]

localZ

4. Local Y

  • The local y-axis is found as the cross product between the local z-axis and the local x-axis, i.e., Yloc = Zloc x Xloc, where Zloc =[dx,dy,dz] and Xloc=[dx,dy,dz]

localY

5. Example 1 - local x parallel along global x-axis

  • Reference point is R=[0,1,0]

  • Local z-axis will be parallel to global z-axis

  • Local y-axis will be parallel to global y-axis

ex1

6. Example 2 - local x parallel along global x-axis

  • Reference point is R=[2,2,0]

  • The point is in the same plane as in example 1

  • Local z-axis will be parallel to global z-axis

  • Local y-axis will be parallel to global y-axis

ex2

7. Example 3 - local x parallel along global x-axis

  • Reference point is R=[0,-1,0]

  • The point is in the same plane as in example 1 but on the other side of the element

  • Local z-axis will be parallel to global z-axis but in the opposite direction; i.e. downwards

ex3

8. Example 4 - local x parallel along global z-axis

  • Reference point is R=[0,1,0]

  • Local y-axis will be parallel to global y-axis

  • Local z-axis will be parallel to global x-axis but point in the negative direction

ex4

9. Example 5 - local x parallel along global z-axis

  • Reference point is R=[0,-1,0]

  • Local y-axis will be parallel to global, negative y-axis

  • Local z-axis will be parallel to global x-axis

ex5