In this section, we'll cover the following:

• Deriving the element stiffness matrix using the principle of virtual work for a plate element.
• The theoretical origin of the stiffness matrix formulation.
• Recapping and applying Gauss quadrature for numerical integration.
• Implementing numerical integration to evaluate the stiffness matrix.
• Developing a Python function to compute and store the element stiffness matrix for later use.

In this section, we explore where the element stiffness matrix equation comes from by applying the principle of virtual work to a plate element, filling an important gap in the theoretical development. We then shift towards practical implementation, introducing Gauss quadrature as the numerical integration method used to evaluate the stiffness matrix.

We then focus on showing how this integration process can be translated into code. By building a Python function to compute the element stiffness matrix, we create a reusable tool that will support the development of a full solver in the next section. By the end of this section, you will have both a solid theoretical grounding and a clear computational approach to calculating stiffness matrices for plate elements.

Next up

In the next lecture, we will work through the derivation in detail, seeing exactly how virtual work leads to the element stiffness matrix and equivalent nodal force vector.