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Three-dimensional elastoplastic solids simulation by an effective IGA based on Bézier extraction of NURBS

  • Tiantang YuEmail author
  • Wenjiang Lai
  • Tinh Quoc BuiEmail author
Article

Abstract

The isogeometric analysis (IGA), which employs non-uniform rational B-splines (NURBS) basis as shape functions for both representation of geometry and approximation of the field variables, owns several inherent advantages to become an effective numerical method such as an exact geometry description with fewer control points, high-order continuity, and high accuracy. Unlike the C0-continuity shape functions in the conventional finite element method (FEM), the high-order basis functions in IGA are not confined to one element, but span on several elements instead. This property makes the programming task difficult, and more importantly they cannot be straightforwardly embedded into the existing FEM framework. In this paper, we provide an effective numerical scheme by further extending the IGA based on the Bézier extraction of NURBS to study mechanical behavior of elasto-plastic problems in three-dimension (3D). The Bézier extraction operator decomposes NURBS functions into a set of Bernstein polynomials and provides C0-continuity Bézier elements for the IGA, which are similar to Lagrange elements structure. Consequently, the implementation of IGA is now similar to that of conventional FEM, and can easily be embedded in most existing FEM codes. The merits of the proposed formulation are also demonstrated by its convergence and validation studies against reference solutions considering both simple and complicated configurations.

Keywords

3D elasto-plastic problems Isogeometric analysis NURBS Bézier extraction FEM Numerical methods 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. 1.Department of Engineering MechanicsHohai UniversityNanjingPeople’s Republic of China
  2. 2.Institute for Research and DevelopmentDuy Tan UniversityDa Nang CityVietnam
  3. 3.Department of Civil and Environmental EngineeringTokyo Institute of TechnologyMeguro-ku, TokyoJapan

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