Topics in Computational Mechanics: Part 2

In continuum mechanics, we view the body—the structure (solid or fluid) that is of our interest—as a continuous region that lives in the three-dimensional space \mathbb{R}^{3}.

The word continuous means, we assume the body to be made up of infinitely many, infinitely small points, with no space in-between (like the cloud of paint seen above), rather than discrete, finitely small atoms, with an atomistic space in-between.

The space \mathbb{R}^{3} is special in many ways (mathematically, that is), and allows us to set up and solve problems in mechanics in a rigorous manner. To keep things interesting and concise, we will replace some definitions with layman, more intuitive explanations.

Continue reading “Topics in Computational Mechanics: Part 2”

Topics in Computational Mechanics: Part 1

Over the next few posts, I will share the writings and programs that I had created for a class in computational structural analysis—how we efficiently analyze a structure using numerical methods. The field is a subset of computational mechanics, which combines the disciplines of mathematics, computer science, and engineering.

The class consisted of juniors and seniors in mechanical or aerospace engineering. In other words, for brevity, I will assume that you have some familiarity with statics, linear algebra, and calculus. If time permits in future, I will upload my class notes to fill gaps and share more drawings.

Continue reading “Topics in Computational Mechanics: Part 1”

Isogeometric Analysis Library

Today, I make my Isogeometric Analysis library available to you.

Written in Matlab, it reflects the time and effort that I spent in graduate school. It also shows unfortunate age, as B-splines and NURBS are fully supported, but not T-splines and other basis that are state-of-the-art. One day, I hope to return.

You can find my Isogeometric Analysis library here:
Download from GitHub

If you like regular, vanilla Finite Element Analysis:
Download from GitHub