A POINTWISE APPROACH FOR ENFORCEMENT OF ESSENTIAL BOUNDARY CONDITIONS IN THE ISOGEOMETRIC ANALYSIS

10.22099/ijstm.2014.1963

Abstract

Isogeometric analysis is a recently developed numerical technique that uses NURBS
basis functions instead of Lagrange polynomial basis functions used in standard finite element
method. This allows the analysis to be done with the exact CAD geometry that it is based on.
However, the non interpolatory property of NURBS basis functions makes the essential boundary
condition imposition to be no longer applicable, directly on the control values. Therefore, a
technique such as penalty method or fitting of the boundary data onto the span of the basis
functions is needed. Such techniques usually lead to additional computational complexity or cost.
In the present paper, a simple pointwise approach is proposed to accurately impose essential
boundary conditions in the isogeometric analysis. The method is based on the collocation of
boundary conditions in distinct points on the boundary using NURBS basis functions. Some
numerical examples in heat conduction and linear elasticity are used to evaluate applicability and
accuracy of the proposed method. It is shown, through demonstrative numerical examples, that the
present method can improve the accuracy of the isogeometric analysis.

Keywords