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Isogeometric Analysis: Recent Developments

Friday, February 24, 10AM – 11AM
ACE 6.304

Thomas J.R. Hughes

Designs are encapsulated in CAD (Computer Aided Design) Systems and simulation is performed in FEA (Finite Element Analysis) systems. FEA requires the conversions of CAD descriptions to analysis-suitable formats, leading to finite element meshes. The conversion process involves many steps, is tedious and labor intensive, and is the major bottleneck in the engineering design-through-analysis process, accounting for more than 80% of overall analysis time. This is a major impediment to the product development cycle. The technical objectives are to create a new framework, simultaneously suitable for both design and analysis, and eliminate the bottleneck thereby, and leverage this framework to develop fundamentally new and improved computational mechanics methodologies to efficiently solve vexing problems.

The key concept utilized is a new paradigm for Finite Element Analysis (FEA), termed Isogeometric Analysis (IGA), based on rich geometric descriptions originating in CAD, resulting in one geometric model that is suitable for both design and analysis. In the few short years since its inception [1], Isogeometric Analysis has become a focus of research within both the fields of FEA and CAD.

Since the publication of he first text on IGA [2], significant progress has been made on a number of fronts, some of which are:

1) Development and characterization of Analysis Suitable T-splines as an isogeometric design-through-analysis methodology;

2) Development of new and canonical data structures that facilitate the incorporation of NURBS and T-splines in existing FEA computer programs with minimal disruption;

3) Development of new material modeling capabilities for discrete and distributed damage utilizing higher-order gradient-enhanced damage models, and a powerful methodology for dynamic brittle fracture based on phase-field representations;

4) Demonstration that smooth NURBS discretizations are superior to traditional FEA in modeling contact phenomena in general and especially in cases exhibiting large sliding, with and without friction;

5) Demonstratiion that isogeometric discretizations of Kirchhoff-Love shells (i.e., “thin” shells), which eliminate the need for rotational degrees-of-freedom, are accurate and efficient on nonlinear test problems, opening the way to much more economical shell modeling procedures than have existed heretofore;

6) Development of more efficient quadrature rules for NURBS, and stable and higher-order, minimal function-evaluation, NURBS-based collocation methods for explicit dynamic analysis;

7) Development of procedures to convert unstructured bilinear quadrilateral and trilinear hexahedral finite element and finite volume meshes to surface and volume T-splines, respectively.

8) Demonstration that higher-order isogeometric discretizations exhibit improved robustness in analysis;

9) Continuation of the development of phase-field theories for problems encountered in engieering design and análisis;

10) Development of div- and curl-conforming B-splines for vector-field problems.

The purpose of this talk is to review recent progress toward developing IGA procedures that do not involve traditional mesh generation and geometry clean-up steps, that is, the CAD file is directly utilized as the analysis input file, to summarize some of the mathematical developments within IGA that confirm the superior accuracy and robustness of spline-based approximations compared with traditional FEA, and to present some applications of IGA technology to problems of solids, structures and fluids that illustrate its advantages.

References

[1] T.J.R. Hughes, J.A. Cottrell and Y. Bazilevs, Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry and Mesh Refinement, Computer Methods in Applied Mechanics and Engineering, 194, (2005) 4135-4195.

[2] J.A. Cottrell, T.J.R. Hughes and Y. Bazilevs, Isogeometric Analysis: Toward Integration of CAD and FEA, Wiley, Chichester, U.K., 2009.

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