A Nitsche-based non-intrusive coupling strategy for global/local isogeometric structural analysis

In this work, we propose a new non-intrusive coupling algorithm for global/local isogeometric structural analysis. In contrast to the existing non-intrusive strategies that rely on a Lagrange multiplier coupling, the algorithm makes use of the non-symmetric Nitsche method. It results in an accurate and efficient tool to compute any evolution of a local model within a fixed global NURBS one. The reason for this is the robustness and simplicity of the coupling (no auxiliary fields, no dual space approximation, no stabilization parameters), which enables to directly handle all the non-conforming coupling scenarios encountered through the global/local multiresolution process. The performance of the methodology is numerically demonstrated through a series of two-dimensional elastic benchmarks involving conforming and non-conforming couplings, along straight, curved, and bi-material interfaces. In all examined problems, the proposed Nitsche algorithm provides optimal accuracy. Conversely, reaching the same accuracy with Lagrange multipliers would imply to use a difficult to implement dual space. It is shown that using a practical choice for the dual space leads to less robustness for the Lagrange multiplier version. Finally, to illustrate both the efficiency in a multiple query context and the robustness of the method to arbitrary non-conforming scenarios, a simple structural optimization problem is carried out using the developed non-intrusive solver, which simplifies the process and ensures computational time saving.