Hierarchically refined isogeometric analysis of trimmed shells

Abstract

This work focuses on the study of several computational challenges arising when trimmed surfaces are directly employed for the isogeometric analysis of Kirchhoff-Love shells. To cope with these issues and to resolve mechanical and/or geometrical features of interest, we exploit the local refinement capabilities of hierarchical B-Splines. In particular, we show numerically that local refinement is suited to effectively impose Dirichlet-type boundary conditions in a weak sense, where this easily allows to overcome the issue of over-constraining of trimmed elements. Moreover, we highlight how refinement can alleviate the spurious coupling stemming from disjoint supports of basis functions in the presence of "small" trimmed geometrical features such as thin holes. These phenomena are particularly pronounced in surface models defined by complex trimming patterns and with details at different scales, where we show through several numerical examples the benefits and computational efficiency of the proposed methodology.

Fast and multiscale formation of isogeometric matrices of microstructured geometric models

“…This simple spline model can be enriched in many ways: e.g., geometries can be described as a collections of spline patches (multipatch geometries), or via NURBS in the case of conic sections. We refer the interested readers to the following non-exhaustive list of works which deal with key points regarding the modeling with splines: theoretical description and practical use of B-Spline and NURBS [22,25,32,59], the issue of trimming procedures and boundary representation [1,14,21,24,52], and the generation of analysis-suitable geometric models for complex structures [4,23,51,54].…”

Finite Cell Method for functionally graded materials based onV-models and homogenized microstructures

“…This is addressed in the following Examples 3.3.4, and 3.3.5. Note, since the shape functions are badly suited to represent holes inside one finite cell, meaning 'material-void-material' [17], the microstructure needs to be resolved with many finite cells. A remedy can be local enrichment as presented in [50].…”

Finite Cell Method for functionally graded materials based on V-models and homogenized microstructures

“…Homogenization is addressed in the following Examples 3.3.4, and 3.3.5. Note, since the shape functions are badly suited to represent holes inside one finite cell, meaning 'material-voidmaterial' [83], the microstructure needs to be resolved with many finite cells. A remedy can be local enrichment, as presented in [84].…”