IMPOSING DISPLACEMENT BOUNDARY CONDITIONS WITH NITSCHE'S METHOD IN ISOGEOMETRIC ANALYSIS

Isogeometric analysis uses the exact geometric representations for the modeling and numerical simulations by NURBS basis functions. It eliminates the geometric approximation errors during the mesh discretization, and the high-order conforming NURBS elements can be conveniently constructed. In the structural analysis, smooth stress fields can be directly computed without the stress recovery procedure as in the finite element method. Due to the lack of the interpolation properties for the NURBS basis functions, it is difficult to enforce the displacement boundary conditions in isogeometric analysis. The imposition of prescribed values is not as straightforward as the conventional approaches. In order to solve this issue, a weak imposition method was proposed basing on the Nitsche's variational principle. It has some attractive advantages: (i) the consistent and stabilized weak form, (ii) the degree-of-freedoms are not increased, (iii) the resulting system is symmetric and positive, (iv) the matrix condition number is not very large in order to ensure convergence. Meantime, the stability conditions were derived for the structural analysis. The stability parameters were evaluated by solving a generalized eigenvalue problem. Through several numerical examples, the optimal rates of convergence were observed under the h-refinement of the NURBS meshes. Contrasting with directly imposing into the control points, the better results were obtained by the proposed method.