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N. Nguyen-Thanh, H. Nguyen-Xuan, S. Bordas, T. Rabczuk, Isogeometric analysis using polynimial splines over hierarchical for two-dimensional elastic solids, Computer Methods in Applied Mechanics and Engineering, Vol. 200, p. 1892–1908, 2011, Doi: 10.1016/j.cma.2011.01.018, 2011.
Abstract: 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.
Keywords: Isogeometric analysis; T-spline; T-meshes; PHT-spline