Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids

By N. Nguyen‐Thanh, Hung Nguyen-Xuan, Stéphane P.A. Bordas, Timon Rabczuk. 2011

294 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/a173ca51cf0759862c135d0fc073c50a9244737f

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

In Mechanics of Materials

Citations in the corpus

Isogeometric analysis: An overview and computer implementation aspects (2012, background): “PHT-splines (polynomial spline over hierarchical T-meshes) have been extended to rational splines and applied in [94, 95] to problems in elasticity for continua and thin structures.”
Isogeometric collocation for large deformation elasticity and frictional contact problems (2015, background): “In so-called open knot vectors, the first p+ 1 knots and the last p+ 1 terms are equal, so that the basis is interpolatory at the ends.”
THB-splines: The truncated basis for hierarchical splines (2012, background): “cubic splines over hierarchical T–meshes with reduced C(1) regularity, no refinement propagation is observed — see for example the original papers [2, 12] or their recent application for the numerical solution of partial differential equations [9, 14].”
A hierarchical approach to adaptive local refinement in isogeometric analysis (2011, methodology): “bicubic rectangles) for FEM with hanging nodes, and recently, they were used for isogeometric simulation [15].”
A two-dimensional Isogeometric Boundary Element Method for elastostatic analysis (2012, background): “[6,13] which have the attractive property that refinement can be achieved locally compared to the expensive global refinement achieved with NURBS due to the tensor product nature of the approximation.”