In the previous section, we built up everything we need to calculate the element stiffness matrix. But before we jump right into calculating the stiffness matrix, it’s worth spending one lecture exploring where the equation for the stiffness matrix itself comes from. We can do this by considering the Principle of Virtual Work, applied to our plate element.

With this gap in the theoretical development covered, we can move on to more practical matters, such as how we actually perform the integration required to calculate the stiffness matrix and equivalent force vector. We’ll implement a numerical integration technique known as Gauss quadrature or Gauss-Legendre numerical integration.

This was covered in some depth in the prerequisite course, so in this course, we’ll start with a primer to recap the core idea and how it’s implemented, but we won’t go over every step of what we did in the previous course. In truth, this is quite a formulaic and straightforward procedure to implement.

Once we’ve covered how we can apply Gauss quadrature integration to our element, the second half of this section focuses on implementing this in Python. Our goal here is to build a function for calculating the element stiffness matrix that we can store in a utilities file. We’ll use this function in the next section when we start building our full solver code.

By the end of this section, you’ll have a good understanding of the theoretical and practical aspects of calculating element stiffness matrices and we’ll be well on our way to conquering plate elements.

The first few lectures (14-16) focus on theory (level 3) while the remaining lectures switch over to Python implementation (level 2 and 3).