Isogeometric analysis research is being published at an exponential rate. These key themes are emerging.

Better simulation through better geometry.

IGA has matured significantly since the first IGA paper was introduced in 2005 by T.J.R. Hughes, J.A. Cottrell, and Y. Bazilevs, becoming one of the hottest research fields in FEA and computer graphics. Many key breakthroughs and benchmarks have been established both in industry and academia.

Five key descriptions of IGA are emerging from the research: accurate, robust, efficient, adaptive, and all-purpose. Below is a list of just some of the significant IGA papers grouped by these themes. We will continue to flesh out this list, please contact us if there are papers you’d like to make sure we include.

Accurate

Higher-order smooth basis functions — Smooth higher-order basis functions improve the accuracy of the entire simulation process.

Exact analysis-suitable geometry — Exact analysis-suitable CAD geometry outperforms faceted meshes for many classes of problems (i.e., contact, interface problems, etc.) and can be used in a simulation without any geometry clean-up or mesh generation steps.

Robust

Accommodates severe mesh deformation without remeshing — Smooth higher-order basis functions can withstand larger mesh deformations than traditional FEA without failing.

Superior non-linear behavior — Several important features of IGA lead to improved behavior for hard non-linear problems. These include

  1. improved spectral behavior lead to smaller time steps
  2. well conditioned, analysis-suitable basis functions reduce the number of nonlinear iterations required for convergence
  3. exact representation of contact surfaces and interfaces eliminates spurious pressure oscillations
  4. smaller linear system sizes for a given level of accuracy

Efficient

Greater accuracy per degree of freedom — For many classes of problems, smooth higher-order basis functions lead to improved accuracy per degree of freedom (DOF) and highly optimized solution strategies (i.e., collocation, reduced quadrature schemes, etc.)

Lean geometry representation — Curved geometry can be captured with few degrees of freedom, leading to compact, analysis-suitable CAD representations.

Adaptive

Geometrically exact local mesh adaptivity — Analysis-suitable CAD possesses a wide range of localized, geometrically exact, mesh adaptivity algorithms (e.g., in h (element size), p (polynomial degree), and k (smoothness)) to enable the user to tailor the geometry for the simulation at hand and reduce compute costs.

Integrated design iteration — Leveraging analysis-suitable CAD opens the door to a fully integrated CAD-CAE process without the traditional time-intensive and error-prone data translation steps, like mesh generation and geometry cleanup.

All-purpose

IGA can be used for everything FEA can be used for — IGA is a generalization of FEA, so problems that can be solved with FEA can be solved with IGA. In fact, IGA has already been successfully applied across many areas of engineering application with great success.

IGA opens up new frontiers in simulation — The unique attributes of IGA and analysis-suitable CAD make it possible to attack next generation problems which are currently out of reach for traditional FEA tools.

 

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