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

Abstract

Isogeometric analysis is a recently developed numerical technique that uses NURBSbasis functions instead of Lagrange polynomial basis functions used in standard finite elementmethod. 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the non interpolatory property of NURBS basis functions makes the essential boundarycondition imposition to be no longer applicable, directly on the control values. Therefore, atechnique such as penalty method or fitting of the boundary data onto the span of the basisfunctions 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 essentialboundary conditions in the isogeometric analysis. The method is based on the collocation ofboundary conditions in distinct points on the boundary using NURBS basis functions. Somenumerical examples in heat conduction and linear elasticity are used to evaluate applicability andaccuracy of the proposed method. It is shown, through demonstrative numerical examples, that thepresent method can improve the accuracy of the isogeometric analysis.