After graduating from RPI in 2012 I began working as a finite element analyst in support of my employer’s manufacturing mission. In 2016 I began investigating a flavor of the finite element method called isogeometric analysis (IGA), which eventually led to a full-fledged research project into the method. The project consisted primarily of a collaboration with the IGA research group headed by Prof. Michael Scott at Brigham Young University (BYU) in Provo, Utah. In 2019 my employer granted me a two-year technical fellowship to attend BYU and study under Prof. Scott in order to gain a deeper technical understanding of IGA.
One strong opinion that I’ve developed over the duration of my investigations is that IGA is a misleading moniker for the technology; a more precise name for the technology is simply spline-based finite element analysis. Splines are a rich mathematical construct that were first formally described in the 1940s and by the end of the 1970s the contemporary description of splines was complete. Their use in interpolation and approximation has been well documented, but while splines have been highly successful in interpolation they have almost no utility (outside of fundamental research) in approximations – largely due to the limitations of our spline descriptions.
In the 2000s new research into splines began to change the way we describe and utilize splines, especially in finite element methods. In fact, it appears that these new spline descriptions may change the way we view, teach, and apply the finite element method. A purpose of this blog is to try to explain some of these new spline technologies, pedantically breaking them down and demystifying them for other FEA analysts.
My thesis will focus on applying a commercial spline-based FEA software to solve various classes of structural mechanics problems and compare the workflow and results to those attained by a conventional FEA software package. Thus a second purpose of this blog will be to track the progress on these problems and share interesting results with my coworkers, graduate committee, and the FEA community at-large.