Imposing Essential Boundary Conditions in Isogeometric Analysis with Nitsche’s Method
Isogeometric Analysis combines the NURBS technology and finite element approaches into a unified framework. Regrettably, the NURBS basis functions don’t interpolate at the control points, which lead to the difficulty for imposing the essential boundary conditions. A new approach inspired by Nitsche’s notion was proposed in order to remedy this issue. The essential boundary constraints are enforced by the consistent penalty terms. It has some notable advantages than the other methods, such as (i) the symmetric and positive definite bilinear formulation when the stiffness matrix is symmetric and the stabilization parameter is large enough; (ii) the well-conditioning coefficient matrix of the linear system. Finally, the numerical experiment was performed to verify the optimal rate of convergence of the present method.
Dongye Sun, Wen-Pei Sung and Ran Chen
T. Chen et al., "Imposing Essential Boundary Conditions in Isogeometric Analysis with Nitsche’s Method", Applied Mechanics and Materials, Vols. 121-126, pp. 2779-2783, 2012