In this lecture, we'll cover:

• How to visualise a 3D shell element using Plotly,
• How to define a local reference frame for an element in global coordinates,
• How to build unit vectors aligned with an element edge and within the element plane,
• How to use cross products to construct mutually orthogonal local axes,
• How to plot the local axes at different origins, such as a node or the element centroid.

We begin by setting up a simple quadrilateral shell element in a global reference frame and then plotting it in 3D. We then construct one version of the local element axes, where the local x-axis is aligned with one edge of the element. To do this, we calculate a direction vector between two nodes, normalise it to obtain a unit vector, and then use another in-plane vector and the cross product to generate the remaining orthogonal axes. This gives a local coordinate system that captures the element’s orientation in space.

We also write a reusable function to draw these axes on the plot, allowing us to visualise the local reference frame at different locations, such as the centroid or a node. By the end of the lecture, you have one practical way of defining an element’s local axes and a visual check that confirms the axes are oriented correctly.

Next up

In the next lecture, we will build a global axis-aligned local element axes system using a similar approach.