Analysis of thin plates by a combination of isogeometric analysis and the Lagrange multiplier approach

The isogeometric analysis is increasingly used in various engineering problems. It is based on Non-Uniform Rational B-Splines (NURBS) basis function applied for the solution field approximation and the geometry description. One of the major concerns with this method is finding an efficient approach to impose essential boundary conditions, especially for inhomogeneous boundaries. The main contribution of this study is to use the well-known Lagrange multiplier method to impose essential boundary conditions for improving the accuracy of the isogeometric solution. Moreover, Dirichlet boundary conditions on the derivatives of the solution field (which are not directly defined as independent degrees of freedom) can be treated easily. The Lagrange multipliers must be interpolated on a set of boundary points. Among the different available choices for the boundary interpolation points, the Greville abscissas are considered in this work. Several plate problems have been solved, which demonstrate significant improvement in accuracy and rate of convergence in comparison with the direct imposition of essential boundary conditions.