Isogeometric Analysis of Structural Mechanics
Summary
Isogeometric analysis (IGA) represents a unification of computer-aided design and numerical simulation, employing spline-based representations such as non-uniform rational B-splines (NURBS) both for geometric description and for the approximation of mechanical fields. In structural mechanics this approach delivers exact geometry handling, higher-order continuity and smooth basis functions that are intrinsic to advanced shell and solid formulations. By preserving CAD data throughout the simulation pipeline, IGA reduces geometric approximation error and facilitates seamless design iterations. Its capacity for C1‐continuous discretisations is particularly beneficial for thin-shell theories such as Kirchhoff–Love formulations, while robust algorithms for contact, large deformations and multiphysics coupling expand its reach to fluid–structure interaction, composite materials and dynamic analyses. Moreover, IGA supports local refinement strategies and direct integration with optimisation frameworks, enabling lightweight design and improved performance in aerospace, automotive and civil engineering applications on a global scale.
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Isogeometric Analysis of Structural Mechanics publication trend
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Technical terms
Isogeometric analysis (IGA): A simulation approach that uses the same spline basis for CAD geometry and numerical solution fields.
NURBS: Non-Uniform Rational B-Splines, versatile spline functions for exact representation of CAD geometries.
Kirchhoff–Love shell: A classical thin-shell theory requiring C1 continuity to model bending-dominated structural behaviour.
Free-Form Deformation (FFD): A parametrisation technique that smoothly modifies geometry through a control lattice during optimisation.
Nitsche’s method: A weak enforcement technique for imposing boundary or interface conditions in finite element discretisations.
References
- Isogeometric analysis for multi-patch structured Kirchhoff–Love shells. Computer Methods in Applied Mechanics and Engineering (2023).
- Automated shape and thickness optimization for non-matching isogeometric shells using free-form deformation. Engineering with Computers (2024).
- Immersed boundary-conformal isogeometric method for linear elliptic problems. Computational Mechanics (2021).
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