Isogeometric analysis [1] has become the subject of intensive research due to its promise of providing a unified design and analysis approach. It features exact domain representation and high accuracy and regularity provided by the spine basis functions used in Computer Aided Design (CAD). Due to the higher smoothness of the basis function, collocation methods can be efficiently implemented and can result in a significant computational savings. In particular, superconvergent and Gaussian-based collocation have been shown have optimal convergence and offer possibilities of adaptive local refinement [2].

In this work, we propose to use isogeometric collocation methods for the efficient simulation of complex geometries such as honeycomb and cellular structures. Analysis on such domains can be demanding, particularly in contexts such as structural optimization, where many simulations on different domains need to be conducted iteratively. A method for parametrically generating structures with many voids and coupling the resulting spline patches will be presented. Moreover, we will investigate the application of machine learning models, such as deep neural networks [3], to further accelerate the design of optimal structures by constructing a suitable computational surrogates.

References

[1] Hughes, T. J., Cottrell, J. A., & Bazilevs, Y. (2005). Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer methods in applied mechanics and engineering, 194(39-41), 4135-4195.
[2] Jia, Y., Anitescu, C., Zhang, Y. J., & Rabczuk, T. (2019). An adaptive isogeometric analysis collocation method with a recovery-based error estimator. Computer Methods in Applied Mechanics and Engineering, 345, 52-74.
[3] Ma, C., Zhang, Z., Luce, B., Pusateri, S., Xie, B., Rafiei, M. H., & Hu, N. (2020). Accelerated design and characterization of non-uniform cellular materials via a machine-learning based framework. npj Computational Materials, 6(1), 1-8.