In this lecture, we'll cover the following:

• Defining plate geometry, material properties, and mesh parameters
• Generating a structured rectangular mesh using NumPy
• Constructing nodal coordinates and organising them into a node array
• Developing element connectivity with consistent node ordering
• Visualising nodes and elements, including numbering and layout checks

In this lecture, we focus on building the foundation of a finite element plate solver by working with a simple rectangular plate and a regular mesh. We begin by defining the plate geometry, material properties, and mesh spacing, then use NumPy tools such as linspace and meshgrid to efficiently generate a structured grid of nodal coordinates. From this grid, we construct a node array that systematically stores the coordinates of every point in the mesh.

We then move on to establishing element connectivity, which is where the mesh becomes a true finite element model. By looping through the grid, we identify groups of four nodes that form each plate element, ensuring that their ordering is consistent with the formulation (counterclockwise starting from the top right). We also implement and verify indexing logic to reliably determine neighbouring nodes. Finally, we visualise the mesh, plotting both nodes and elements with clear numbering, which helps confirm correctness and provides a solid platform for further development.

Next up

With the mesh in place, the next lecture focuses on defining boundary conditions by identifying and constraining the appropriate degrees of freedom.