A Method for Enforcement of Dirichlet Boundary Conditions in Isogeometric Analysis

Abstract

Isogeometric finite element analysis is a technique that substitutes NURBS basis functions for the Lagrange polynomial basis functions used in standard finite element analysis. This allows finite element analysis to exactly replicate the CAD geometry on which it is based. However, the non-interpolatory nature of NURBS basis functions used in CAD means that imposition of Dirichlet boundary conditions can no longer be accomplished by collocation of exact values at the control points. A technique such as a global least-squares fit of the prescribed boundary data onto the span of the basis functions is required; however, this requires solution of potentially large sets of equations, leading to unacceptable computational costs, particularly in problems with time-varying Dirichlet boundary data. This paper presents a method to weakly impose Dirichlet boundary conditions in isogeometric finite element analysis that is shown (via numerical examples) to be significantly more efficient than a global least-squares fit while attaining nearly the same accuracy.