An isogeometric approach to coupled thermomechanics in 3D via hierarchical adaptivity
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A complete numerical scheme to perform adaptive re nement and coarsening in the context of isogeometric analysis applied to thermomechanics is introduced. In particular, truncated hierarchical B-splines (THB-splines) [1] are considered as a basis for the analysis and suitably graded isogeometric meshes are constructed to guarantee admissible con gurations [2] at each re nement and coarsening iteration [3]. The algorithms are developed and implemented in a full three-dimensional framework and applied to solve coupled problems with localized features. The proposed numerical framework is veri ed on numerical examples with respect to overkill solutions, obtained either with a commercial nite element software or with uniform isogeometric meshes. Numerical results demonstrate the ability of the THB-spline-based admissible adaptive scheme to deliver robust discretizations guaranteeing an optimal trade-o between computational accuracy and number of degrees of freedom. Further outlooks are the extension of the proposed framework to even more complex physical models and experimental validation, toward the development of an isogeometric framework suitable for multi-physics applications with localized problem features.
