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.
Continue reading “Topics in Computational Mechanics: Part 4”
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.
Continue reading “Topics in Computational Mechanics: Part 3”
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 .
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 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”
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”
In 2018, the Ember core teams asked for community input in laying out a vision of what we need to achieve over the next year. In response, they received over 50 blog posts and several direct tweets. I read all in preparation for this post and smiled throughout, because we did achieve, and are actively working on, the following goals:
In 2019, in addition to continuing work on the items above, I’d like to see us work on building a larger community. Our community, while truly amazing and supportive, is yet small. To flourish, we need support from developers who don’t work with Ember daily. These developers may professionally work with React, Angular, or Vue. They may be self-taught or attending school, looking to enter tech with minimal risk in career trajectory and minimal time to create showcase projects.
I believe we can do 3 things to welcome these developers:
- Publish better website (address design and content)
- Promote Octane heavily
- Teach Ember at local and remote Meetups
I will explain what I mean by these and highlight our action items in (Ember) orange.
Continue reading “#EmberJS2019: Build a Larger Community”