Abstract
This study investigates the sensitivity filtering properties of the Mortar Mapping method and correlates it to the Vertex Morphing method in order to demonstrate the advantages of such a procedure in the context of shape optimization. It points out the importance of a common design control approach in a Multi-Disciplinary Optimization (MDO) environment. In particular, individual components of MDO have nonmatching interfaces when Fluid-Structure Interaction (FSI) problems are of interest. Since the numerical models of dissimilar discretizations deliver nonconforming sensitivity fields with respect to the design variables defined at their interfaces, the shape optimization of the common surfaces necessitates a third field which unifies the optimization variables and acts as a control field. This approach not only covers this necessity by facilitating the Mortar Mapping method but also reveals that such a procedure acts as a sensitivity filter similar to the Vertex Morphing method without altering the optimality of the solution.
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Notes
- 1.
EMPIRE is a research tool for co-simulation in the context of field and signal coupling. http://empire.st.bv.tum.de/.
- 2.
OpenFOAM® is an open-source toolbox for CFD simulations. http://www.openfoam.com/.
- 3.
Python® is a programming language. https://www.python.org/.
References
M. Hojjat, E. Stavropoulou, K.-U. Bletzinger, The vertex morphing method for node-based shape optimization. Comput. Methods Appl Mech. Eng. (2014). https://doi.org/10.1016/j.cma.2013.10.015
K.-U. Bletzinger, A consistent frame for sensitivity filtering and the vertex assigned morphing of optimal shape. Struct. Multidisc. Optim. (2014). https://doi.org/10.1007/s00158-013-1031-5
R.B. Bapat, Linear Algebra and Linear Models (Springer, London, 2012)
T. Wang, R. Wüchner, S. Sicklinger, K.-U. Bletzinger, Assessment and improvement of mapping algorithms for non-matching meshes and geometries in computational FSI. Comput. Mech. (2016). https://doi.org/10.1007/s00466-016-1262-6
B.I. Wohlmuth, Discretization techniques based on domain decomposition, in Discretization Methods and Iterative Solvers Based on Domain Decomposition, vol. 17, Lecture Notes in Computational Science and Engineering, ed. by M. Griebel, D.E. Keyes, R.M. Nieminen, D. Roose, T. Schlick (Springer, Berlin, 2001), pp. 1–84
C. Farhat, M. Lesoinne, P. LeTallec, Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: momentum and energy conservation, optimal discretization and application to aeroelasticity. Comput. Methods Appl. Mech. Eng. (1998). https://doi.org/10.1016/S0045-7825(97)00216-8
J.R.R.A. Martins, A.B. Lambe, Multidisciplinary design optimization: a survey of architectures. AIAA J. (2013). https://doi.org/10.2514/1,J051895
R. Najian-Asl, D. Baumgärtner, K.-U. Bletzinger, Towards shape optimization of steady-state fluid-structure interaction problems using vertex morphing, in 16th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Dallas, TX, 22–26 June 2015. https://doi.org/10.2514/6.2015-3356
E.M. Papoutsis-Kiachagias, K.C. Giannakoglou, Continuous adjoint methods for turbulent flows, applied to shape and topology optimization: industrial applications. Arch. Comput. Methods Eng. (2014). https://doi.org/10.1007/s11831-014-9141-9
A. Fazzolari, An Aero-Structure Adjoint Formulation for Efficient Multidisciplinary Wing Optimization. Dissertation, Technische Universität Braunschweig (2005)
C. Othmer, A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows. Int. J. Numer. Methods Fluids (2008). https://doi.org/10.1002/fld.1770
J.R.R.A. Martins, J.J. Alonso, J.J. Reuther, Complete configuration aero-structural optimization using a coupled sensitivity analysis method, in Proceedings of the 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Atlanta, GA, 46 Sept 2002, https://doi.org/10.2514/6.2002-5402
A.B. Lambe, J.R.R.A. Martins, Extensions to the design structure matrix for the description of multidisciplinary design, analysis, and optimization processes. Struct. Multidisc. Optim. (2014). https://doi.org/10.1007/s00158-012-0763-y
G. Schuhmache, F. Daoud, Ö. Petersson, M. Wagner, Multidisciplinary airframe design optimization, in 28th International Congress of the Aeronautical Sciences, Brisbane, Australia, 23–28 Sept 2012
B. Irons, R.C. Tuck, A version of the Aitken accelerator for computer implementation. Int. J. Numer. Methods Eng. 1, 275277 (1969)
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Emiroğlu, A., Wüchner, R., Bletzinger, KU. (2018). Treating Non-conforming Sensitivity Fields by Mortar Mapping and Vertex Morphing for Multi-disciplinary Shape Optimization. In: Heinrich, R. (eds) AeroStruct: Enable and Learn How to Integrate Flexibility in Design. AeroStruct 2015. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 138. Springer, Cham. https://doi.org/10.1007/978-3-319-72020-3_9
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