Bezier (B)over-bar projection

作者：Miao Di^*; Borden Michael J; Scott Michael A; Thomas Derek C

来源：Computer Methods in Applied Mechanics and Engineering, 2018, 335: 273-297.

DOI：10.1016/j.cma.2018.02.019

• Isogeometric analysis
• Bezier extraction
• Bezier dual basis
• Bezier projection
• (B)over-bar-projection
• Locking

In this paper we demonstrate the use of Bezier projection to alleviate locking phenomena in structural mechanics applications of isogeometric analysis. Interpreting the well-known (B) over bar projection in two different ways we develop two formulations for locking problems in beams and nearly incompressible elastic solids. One formulation leads to a sparse symmetric system and the other leads to a sparse non-symmetric system. To demonstrate the utility of Bezier projection for both geometry and material locking phenomena we focus on transverse shear locking in Timoshenko beams and volumetric locking in nearly compressible linear elasticity although the approach can be applied generally to other types of locking phenomena as well. Bezier projection is a local projection technique with optimal approximation properties, which in many cases produces solutions that are comparable to global L-2 projection. In the context of (B) over bar methods, the use of Bezier projection produces sparse stiffness matrices with only a slight increase in bandwidth when compared to standard displacement-based methods. Of particular importance is that the approach is applicable to any spline representation that can be written in Bezier form like NURBS, T-splines, LR-splines, etc. We discuss in detail how to integrate this approach into an existing finite element framework with minimal disruption through the use of Bezier extraction operators and a newly introduced dual basis for the Bezier projection operator. We then demonstrate the behavior of the two proposed formulations through several challenging benchmark problems.

• 出版日期2018-6-15