Circular element: Isogeometric elements of smooth boundary

This article introduces a family of elements of smooth, curved geometry. Unlike traditional approaches based on finite element geometry, the proposed method employs rational Bezier functions for boundary description and, as a result, common shapes such as circles and ellipses can be exactly described. The interior of the element is parameterized in terms of the boundary control points via basis functions that are smooth extensions of the boundary Bezier bases. The interior basis functions are constructed over the unit circular domain, and applied in an isoparametric setting to other convex domains that are topologically circular. This family of elements is particularly suited for analyzing discrete bodies undergoing more or less uniform or regular deformations. An example involving the compression of a circular elastic disk, in which the disk is modeled as a single 16-point element, is presented to demonstrate the application.