The last part of this series is short. You can check out the Matlab code for implementing FEM today! I encourage you to see how the code demonstrates ideas that we studied. These include pullback to parent domain, Gauss quadrature for numerical integration, and postprocessing for visualization.
The geometries that we considered so far are simple. If we are to analyze a complex, real-world structure, we need a way to accurately model its geometry. Not to worry, we can map a simple element to a complex one using a function.
Today, we will study the isoparametric approach. It tells us how to define the function so that we can evaluate integrals fast and achieve optimal rate of convergence. It is key to making FEM practical and powerful.
Recall the continuum approach to mechanics. We view the body, the structure of our interest, as a continuous region in the vector space of . Then, we can completely describe the structure’s state by finding the set of fields that satisfies the force and moment equilibriums, the stress-strain relation (constitutive equation), and the strain-displacement relation (kinematics).
The problem is, finding the fields exactly is impossible for all but simple structures. Today, we will look at how to make the problem simpler so that we can analyze real-life structures.