# Book of the Week: Introduction to Finite Element Analysis and Design

By on May 26th, 2020 in book

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This week’s selection is “Introduction to Finite Element Analysis and Design” by Nam H. Kim, Bhavani V. Sankar, and Ashok V. Kumar.

“FEA” is something you hear frequently in the world of 3D printing, and with very good reason. It’s the not-so-secret method that will power the technology forward in ways that cannot be done with other making processes.

“FEA” is “Finite Element Analysis”, a result obtained by investigating the properties of a physical scenario. It uses what’s called the “Finite Element Method”, which is defined by Wikipedia as:

“The finite element method (FEM) is the most widely used method for solving problems of engineering and mathematical models. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a particular numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretisation in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points. ”

As you might imagine, FEA involves a significant amount of mathematics, both in concept and in processing. This book, however, attempts to explain the concepts behind the technology in a manner understandable by many people.

The book covers multiple different analysis scenarios, ranging from the relatively straightforward “direct method”, where springs, bars and truss elements are mechanically examined, to complex scenarios involving dynamic motion and vibration.

Topics discussed include not only mechanical stress, but also heat transfer, two-dimensional scenarios, isoparametric elements, and more.

It’s my thought that FEA will play an incredibly important role in the future of 3D printing because it is an important way to enable the design of highly complex, yet functional parts. These parts are often made with far less material and yet still provide requirements-meeting properties.

If we did not have FEA, we would not have a new design space to explore using advanced generative software. And without these new designs, there would be less interest in 3D printing as a whole.