In this section, we'll cover:

• How to move from a local element reference frame to a common global reference frame,
• How to define and use the transformation matrix,
• How to define the local element reference frame in a couple of different ways,
• How to code these ideas up and visualise them with 3D plots,
• How to build the element transformation matrix from the element axes.
• How to use the transformation matrix to convert the local element stiffness matrix into a global element stiffness matrix.

In this section, we will take the next step after establishing the local element stiffness matrix by working out how to express forces, stiffnesses and displacements in a shared global frame. To do that, we first revisit the transformation matrix carefully and build up a clear understanding of what it does and how it is defined. We then consider different ways of defining the local element reference frame.

Once we have the element axes and transformation matrix in place, we will use them to convert the local element stiffness matrix from the previous section into a global element stiffness matrix. This global form is the one we need before we can combine individual element contributions into the overall structure stiffness matrix in the next section of the course.

Next up

In the next lecture, we will define the transformation matrix. We will also see how to use the transformation matrix to transform quantities defined in a local element reference frame into quantities defined in a global reference frame.