Immersogeometric Analysis using B-Rep CAD Models

Immersogeometric analysis (IMGA) is a geometrically flexible technique for solving computational fluid–structure interaction (FSI) problems involving large, complex structural deformations. The method analyzes a surface representation of the structure by immersing it into a non-boundary-fitted discretization of the background fluid domain and focuses on accurately capturing the immersed geometry within non-boundary-fitted analysis meshes. The method is further extended in the context of a tetrahedral finite cell approach for the simulation of incompressible flow, both laminar and turbulent, around geometrically complex objects. The motivation is to alleviate the difficulties associated with computational fluid dynamics (CFD) mesh generation around complex design geometries. Creating a boundary-fitted fluid-domain mesh that accurately captures all the features of the B-rep computer-aided design (CAD) model is often time consuming and labor intensive. Very often, small and thin geometric features are hard to discretize and require extensive geometry cleanup, defeaturing, and mesh manipulation. The immersogeometric method is proposed to eliminate these labor-intensive mesh generation procedures from the CFD simulation pipeline while still maintaining high accuracy of the simulation results. The flexibility of the immersogeometric approach also allows it to be easily automated and placed in an optimization loop that searches for better designs.







Immersogeometric flow analysis of a semi-trailer truck directly using its B-rep model.


Optimizing Fluid–Structure Interaction Systems with Immersogeometric Analysis

This work presents an FSI design optimization framework and applies it to improving the structural performance of a water brake used to stop aircraft landing on short runways. Inside the water brake, a dissipative torque is exerted on a rotor through interactions between rotor blades and a surrounding fluid. We seek to optimize blade shape over a parameterized design space, to prevent potentially-damaging stress concentrations without compromising performance. To avoid excessive numbers of costly simulations while exploring the design space, we use a surrogate management framework that combines derivative-free pattern search optimization with automated construction of a low-fidelity surrogate model, requiring only a handful of high-fidelity FSI simulations. We avoid the difficult problem of generating fluid and structure meshes at new points in the design space by using immersogeometric FSI analysis. The structure is analyzed isogeometrically––its design geometry also serves as a computational mesh. This geometry is then immersed in an unfitted fluid mesh that does not depend on the structure’s design parameters. We use this framework to make significant improvements to the baseline design.












Top: The NURBS-based parametric model of the water twister and a cut through the unfitted fluid mesh used in immersogeometric analysis. Note that changes to the structural design do not require any fluid mesh regeneration. Bottom: Design modification strategy used for rotor blades and stator vanes. x1, x2 and x3 are the design variables.

The immersogeometric simulation results are in excellent agreement with the reference boundary-fitted simulation results as well as the experimental data.




By performing immersogeometric FSI simulations and searching through the design space, a new design which reduces the stress variance by 35% is found.

Contours of von Mises stress on FSI-based optimization result. The deflection is scaled by 100 times.


References - Immersogeometric Analysis

  1. Wu MCH, Kamensky D, Wang C, Herrema AJ, Xu F, Pigazzinic MS, Verma A, Marsden AL, Bazilevs Y, Hsu M-C* (2017) Optimizing fluid–structure interaction systems with immersogeometric analysis and surrogate modeling: application to a hydraulic arresting gearComputer Methods in Applied Mechanics and Engineering, 316:668–693.
  2. Wang C, Xu F, Hsu M-C, Krishnamurthy A* (2017) Rapid B-rep model preprocessing for immersogeometric analysis using analytic surfacesComputer Aided Geometric Design, 52–53:190–204.
  3. Hsu M-C*, Wang C, Xu F, Herrema AJ, Krishnamurthy A (2016) Direct immersogeometric fluid flow analysis using B-rep CAD modelsComputer Aided Geometric Design, 43:143-158.
  4. Xu F, Schillinger D, Kamensky D, Varduhn V, Wang C, Hsu M-C* (2016) The tetrahedral finite cell method for fluids: Immersogeometric analysis of turbulent flow around complex geometriesComputers & Fluids, 141:135–154.
  5. Varduhn V*, Hsu M-C, Ruess M, Schillinger D (2016) The tetrahedral finite cell method: Higher-order immersogeometric analysis on adaptive non-boundary-fitted meshesInternational Journal for Numerical Methods in Engineering, 107:1054–1079.
  6. Kamensky D, Hsu M-C*, Schillinger D, Evans JA, Aggarwal A, Bazilevs Y, Sacks MS, Hughes TJR (2015) An immersogeometric variational framework for fluid–structure interaction: application to bioprosthetic heart valvesComputer Methods in Applied Mechanics and Engineering, 284:1005-1053(Web of Science Highly Cited Paper) 


Parametric Design and Optimization using Isogeometric Analysis

Isogeometric analysis (IGA) fundamentally seeks to bridge the gap between engineering design and high-fidelity computational analysis by using spline functions that are typically used in CAD as finite element bases. In this work, we propose a novel approach that employs IGA methodologies while still rigorously abiding by the paradigms of advanced design parameterization, analysis model validity, and interactivity. The entire design lifecycle utilizes a consistent geometry description and is contained within a single platform. Because of this unified workflow, iterative design optimization can be naturally integrated. The proposed methodology is demonstrated through an IGA-based parametric design optimization framework implemented using the Grasshopper algorithmic modeling interface for Rhinoceros 3D. The framework is capable of performing IGA-based design optimization of realistic engineering structures that are practically constructed through the use of complex geometric operations. In addition to inherently featuring the advantageous characteristics of IGA, the seamless nature of the workflow instantiated in this framework diminishes the obstacles traditionally encountered when performing FEA-based design optimization. The effectiveness of the framework is demonstrated on a wind turbine blade design.









Parametric design and optimization of wind turbine blades using isogeometric analysis.

An interactive geometry modeling and parametric design platform for isogeometric analysis.


References - Isogeometric Analysis

  1. Herrema AJ, Wiese NM, Darling CN, Ganapathysubramanian B, Krishnamurthy A, Hsu M-C* (2017) A framework for parametric design optimization using isogeometric analysisComputer Methods in Applied Mechanics and Engineering, 316:944–965.
  2. Hsu M-C*, Wang C, Herrema AJ, Schillinger D, Ghoshal A, Bazilevs Y (2015) An interactive geometry modeling and parametric design platform for isogeometric analysisComputers & Mathematics with Applications, 70:1481-1500.
© Ming-Chen Hsu 2020