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A NURBS‐based interface‐enriched generalized finite element method for problems with complex discontinuous gradient fields

A non‐uniform rational B‐splines (NURBS)‐based interface‐enriched generalized finite element method is introduced to solve problems with complex discontinuous gradient fields observed in the structural and thermal analysis of the heterogeneous materials. The presented method utilizes generalized degrees of freedom and enrichment functions based on NURBS to capture the solution with non‐conforming meshes. A consistent method for the generation and application of the NURBS‐based enrichment functions is introduced. These enrichment functions offer various advantages including simplicity of the integration, possibility of different modes of local solution refinement, and ease of implementation. In addition, we show that these functions well capture weak discontinuities associated with highly curved material interfaces. The convergence, accuracy, and stability of the method in the solution of two‐dimensional elasto‐static problems are compared with the standard finite element scheme, showing improved accuracy. Finally, the performance of the method for solving problems with complex internal geometry is highlighted through a numerical example. Copyright © 2015 John Wiley & Sons, Ltd.