Traditional finite element methods use low degree, piecewise continuous polynomials to model the geometry of a structure. Modern computer aided design uses non-uniform rational B-splines (NURBS) to represent the geometry of a structure exactly. Isogeometric analysis is an extension of the finite element method that also uses NURBS and related functions. Among the advantages are few equations to solve than traditional finite element methods combined with better accuracy.
The figure shows the final state of an initially square tube that has been crushed in an accordion mode, a type of collapse engineered into modern cars to absorb energy to protect its occupants. It was performed using isogeometric elements with less than half the unknowns of typical conventional analyses and is faster than the standard elements in most commercial finite element codes.
This work is a collaborative effort with Professor Yuri Bazilevs (UC San Diego) and Professor T. J. R. Hughes (U Texas, Austin).