Nguyen-Xuan, H.[Department of Mechanics, Faculty of Mathematics and Computer Science, University of Science, VNU, HCM, Viet Nam, Division of Computational Mechanics, Ton Duc Thang University, HCM, Viet Nam]
Bordas, Stéphane[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
[en] Isogeometric analysis ; PHT-spline ; T-meshes ; T-spline ; Complex geometries ; Elastic solids ; Finite Element ; Local refinement ; Local support ; Non-negativity ; Numerical example ; Partition of unity ; Polynomial splines ; Shape functions ; Standard finite element ; T-splines ; Function evaluation ; Numerical methods ; Polynomial approximation ; Splines
[en] Isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries. One of the major drawbacks of NURBS-based isogeometric finite elements is the inefficiency of local refinement. In this study, we present an alternative to NURBS-based isogeometric analysis that allows for local refinement. The idea is based on polynomial splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support and partition of unity. Several numerical examples are used to demonstrate the reliability of the present method.
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