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An immersed boundary approach for shape and topology optimization of stationary fluid-structure interaction problems.

Nicholas Jenkins and Kurt Maute

Journal of Structural and Multidisciplinary Optimization,  May 2016.

This paper presents an approach to shape and topology optimization of fluid-structure interaction (FSI) problems at steady state. The overall approach builds on an immersed boundary method that couples a Lagrangian formulation of the structure to an Eulerian fluid model, discretized on a deforming mesh. The geometry of the fluid-structure boundary is manipulated by varying the nodal parameters of a discretized level set field. This approach allows for topological changes of the fluid-structure interface, but free-floating volumes of solid material can emerge in the course of the optimization process. The free-floating volumes are tracked and modeled as fluid in the FSI analysis. To sense the isolated solid volumes, an indicator field described by linear, isotropic diffusion is computed prior to analyzing the FSI response of a design. The fluid is modeled with the incompressible Navier-Stokes equations, and the structure is assumed linear elastic. The FSI model is discretized by an extended finite element method, and the fluid-structure coupling conditions are enforced weakly. The resulting nonlinear system of equations is solved monolithically with Newton’s method. The design sensitivities are computed by the adjoint method and the optimization problem is solved by a gradient-based algorithm. The characteristics of this optimization framework are studied with two-dimensional problems at steady state. Numerical results indicate that the proposed treatment of free-floating volumes introduces a discontinuity in the design evolution, yet the method is still successful in converging to meaningful designs.

Level set topology optimization of stationary fluid-structure interaction problems

Nicholas Jenkins and Kurt Maute

Journal of Structural and Multidisciplinary Optimization,  March 2015.

3D Level Set internal topology optimization of FSI problems. 


This paper introduces a topology optimization approach that combines an explicit level set method (LSM) and the extended finite element method (XFEM) for designing the internal structural layout of fluid-structure interaction (FSI) problems. The FSI response is predicted by a monolithic solver that couples an incompressible Navier-Stokes flow model with a small-deformation solid model. The fluid mesh is modeled as an elastic continuum that deforms with the structure. The fluid model is discretized with stabilized finite elements and the structural model by a generalized formulation of the XFEM. The nodal parameters of the discretized level set field are defined as explicit functions of the optimization variables. The optimization problem is solved by a nonlinear programming method. The LSM-XFEM approach is studied for two- and three-dimensional FSI problems at steady-state and compared against a density topology optimization approach. The numerical examples illustrate that the LSM-XFEM approach convergences to well-defined geometries even on coarse meshes, regardless of the choice of objective and constraints. In contrast, the density method requires refined grids and a mass penalization to yield smooth and crisp designs. The numerical studies show that the LSM-XFEM approach can suffer from a discontinuous evolution of the design in the optimization process as thin structural members disconnect. This issue is caused by the interpolation of the level set field and the inability to represent particular geometric configurations in the XFEM model. While this deficiency is generic to the LSM-XFEM approach used here, it is pronounced by the nonlinear response of FSI problems.

Generalized Level Set Method for Optimization of Fluid-Structure Interaction Problems

Immersed boundary FSI optimization.

Nicholas Jenkins and Kurt Maute

17th National Congress of Theoretical and Applied Mechanics. Lansing, MI. June, 2014.


The extended finite element method (XFEM) has emerged as a powerful tool for analysis and optimization of multi-physics systems. To this end, we have developed a framework to perform topology optimization of fluid-structure systems with a Level Set field describing the boundary between each discipline. The XFEM is used to enrich the shape functions to accurately represent and integrate the governing equations in intersected elements. We employ stabilized Lagrange multipliers to couple fluid and structure at the interface. Further, we perform topology optimization by allowing the optimization algorithm to work directly on the Level Set field which in turn generates variable internal structure topology and outer (fluid-structure interface) shape. We aim to show the advantages of the new method over traditional density based methods due to a looser requirement on mesh resolution, and a more robust and accurate coupling compared to existing porosity penalization approaches. 

The Level Set Method for Topology Optimization of Fluid-Structure Interaction Problems

Optimization result for beam FSI.

Nicholas Jenkins and Kurt Maute

10th World Congress of Structural and Multidisciplinary Optimization. Orlando, Florida. May, 2013. 


Topology optimization of coupled multi-physics systems is an appealing approach as intuitive solutions are often suboptimal due to strong nonlinearities dominating the system response. This paper focuses on topology optimization of fluid-structure interaction problems. Recently, density methods using a SIMP (Solid Isotropic Material Penalization) interpolation approach have been applied to find the optimal geometry of the internal structure for a given mold-line body design (Maute and Allen, 2004; Stanford and Ifju, 2009; James and Martins, 2008). To allow for changes of the overall topology, Kreissl and Maute (2010) and Yoon (2010) apply a density approach simultaneously to both the fluid and structure domain. All current methods suffer typically from the presence of large volumes of material with intermediate densities, and the lack of a clearly defined structural layout. In addition, the methods manipulating just the internal structure as well as the approach of Yoon are limited to rather small structural deformation due to mesh distortion issues. In this paper we present an alternative approach combining a level-set method to describe the structural geometry and the extended (or general) finite element method (XFEM) to predict the coupled fluid-structure response. This approach leads inherently to a well described definition of the fluid-structure interfaces and the internal structural layout. The optimization problem is solved by the GCMMA algorithm operating directly on the parameters of the discretized level-set field. We will compare this level-set/XFEM approach to SIMP approaches. Results will be presented for a flexible (hyperelastic) structure immersed in an incompressible flow. Our results will show that SIMP approaches require a highly refined mesh to mitigate the occurrence of large volumes of intermediate densities. Utilizing level-sets and XFEM allows a coarser resolution while retaining the ability to describe detailed geometric features. 

Preshot Calculations for the Ortega Experiment (U)

Nicholas Jenkins, Bruce C. Trent, Marvin A. Zocher, Michael R. Furlanetto.

17th American Physical Society: Shock Compression and Condensed Matter. Chicago, IL. June 26 - July 1, 2011.


The purpose of the calculations of the Ortega Experiment is to bound the expected results of the VISAR and PDV velocimetry readings from the experiment. In addition, the purpose is to benchmark predictive simulation capabilities. Material models, shocked media, multi-phase coupled interactions, and large strains and strain rates are all complex attributes of the Ortega experiment. The calculations measured up well to a similar experiment using radiographs, and many characteristics of the model were verified before the high explosives were detonated for the experiment.