In this lecture, we'll cover the following:

• Setting up a Jupyter Notebook environment.
• Defining material and geometric constants for a finite element.
• Representing nodal coordinates and element connectivity using NumPy arrays.
• Constructing the generalised constitutive matrix from previously derived theory.
• Visualising a four-noded quadrilateral element and enforcing node ordering.
• Introducing a reusable coding workflow using utility functions.

In this lecture, we begin translating finite element theory into Python code by setting up a basic computational environment and defining the key inputs required for a single element. We establish material properties such as Young’s modulus, shear modulus, and Poisson’s ratio, along with the element thickness. We then define how nodal coordinates and element connectivity are stored using structured NumPy arrays, emphasising that this approach will scale to much larger meshes. A key conceptual point is the importance of consistent node ordering, as it directly affects the formulation of shape functions used later.

We then construct the generalised constitutive matrix by assembling bending and shear components derived from earlier theory, demonstrating how these are combined into a single matrix representation. Finally, we visualise the element using Matplotlib, labelling nodes to reinforce their ordering and spatial arrangement. The lecture concludes by introducing a clean coding workflow, where reusable functionality, such as plotting, is moved into a separate utilities file.

Next up

In the next lecture, we will use these inputs to compute a complete element stiffness matrix using Gauss quadrature.