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2016 | OriginalPaper | Chapter

Molding Direction Constraints in Structural Optimization via a Level-Set Method

Authors : Grégoire Allaire, François Jouve, Georgios Michailidis

Published in: Variational Analysis and Aerospace Engineering

Publisher: Springer International Publishing

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Abstract

In the framework of structural optimization via a level-set method, we develop an approach to handle the directional molding constraint for cast parts. A novel molding condition is formulated and a penalization method is used to enforce the constraint. A first advantage of our new approach is that it does not require to start from a feasible initialization, but it guarantees the convergence to a castable shape. A second advantage is that our approach can incorporate thickness constraints too. We do not address the optimization of the casting system, which is considered a priori defined. We show several 3d examples of compliance minimization in linearized elasticity under molding and minimal or maximal thickness constraints. We also compare our results with formulations already existing in the literature.

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Literature
1.
Ahn, H.K., De Berg, M., Bose, P., Cheng, S.W., Halperin, D., Matoušek, J., Schwarzkopf, O.: Separating an object from its cast. Comput. Aided Des. 34 (8), 547–559 (2002)CrossRef
2.
Allaire, G.: Conception Optimale de Structures. Mathématiques & Applications, vol. 58. Springer, Berlin (2007)
3.
Allaire, G., Jouve, F.: A level-set method for vibration and multiple loads structural optimization. Comput. Methods Appl. Mech. Eng. 194 (30), 3269–3290 (2005)MathSciNetCrossRefMATH
4.
Allaire, G., Kohn, R.V.: Optimal design for minimum weight and compliance in plane stress using extremal microstructures. Eur. J. Mech. A: Solids 12 (6), 839–878 (1993)MathSciNetMATH
5.
Allaire, G., Bonnetier, E., Francfort, G., Jouve, F.: Shape optimization by the homogenization method. Numer. Math. 76 (1), 27–68 (1997)MathSciNetCrossRefMATH
6.
Allaire, G., Jouve, F., Toader, A.-M.: A level-set method for shape optimization. C. R. Acad. Sci. Paris, Série I 334, 1125–1130 (2002)MathSciNetMATH
7.
Allaire, G., Jouve, F., Toader, A.-M.: Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 194 (1), 363–393 (2004)MathSciNetCrossRefMATH
8.
Allaire, G., Dapogny, C., Frey, P.: Topology and geometry optimization of elastic structures by exact deformation of simplicial mesh. C. R. Math. 349 (17), 999–1003 (2011)MathSciNetCrossRefMATH
9.
Allaire, G., Jouve, F., Van Goethem, N.: Damage and fracture evolution in brittle materials by shape optimization methods. J. Comput. Phys. 230 (12), 5010–5044 (2011)MathSciNetCrossRefMATH
10.
Allaire, G., Jouve, F., Michailidis, G.: Casting constraints in structural optimization via a level-set method. In: WCSMO-10, Orlando, FL (2013)
11.
Allaire, G., Dapogny, C., Delgado, G., Michailidis, G.: Multi-phase structural optimization via a level-set method. ESAIM Control Optim. Calc. Var. 20, 576–611 (2014)MathSciNetCrossRefMATH
12.
Allaire, G., Dapogny, C., Frey, P.: Shape optimization with a level set based mesh evolution method. Comput. Methods Appl. Mech. Eng. 282, 22–53 (2014)MathSciNetCrossRef
13.
Allaire, G., Jouve, F., Michailidis, G.: Thickness control in structural optimization via a level set method (2014). HAL preprint: hal-00985000v1 (to appear in SMO)
14.
Bendsøe, M.P.: Optimal shape design as a material distribution problem. Struct. Multidiscip. Optim. 1 (4), 193–202 (1989)CrossRef
15.
Bendsøe, M.P., Kikuchi, N.: Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Eng. 71 (2), 197–224 (1988)MathSciNetCrossRefMATH
16.
Bendsoe, M.P., Sigmund, O.: Topology Optimization: Theory, Methods and Applications. Springer, Berlin (2004)CrossRefMATH
17.
Blank, L., Farshbaf-Shaker, H., Garcke, H., Styles, V.: Relating phase field and sharp interface approaches to structural topology optimization. ESAIM Control Optim. Calc. Var. 20 (4), 1025–1058 (2014)MathSciNetCrossRefMATH
18.
19.
Campbell, J.: Castings, 1991. Butterworth Heinemann, Great Britain (1964)
20.
de Gournay, F.: Velocity extension for the level-set method and multiple eigenvalues in shape optimization. SIAM J. Control. Optim. 45 (1), 343–367 (2006)MathSciNetCrossRefMATH
21.
de Gournay, F., Allaire, G., Jouve, F.: Shape and topology optimization of the robust compliance via the level set method. ESAIM Control Optim. Calc. Var. 14 (01), 43–70 (2008)MathSciNetCrossRefMATH
22.
Fu, M.W., Nee, A.Y.C., Fuh, J.Y.H.: The application of surface visibility and moldability to parting line generation. Comput. Aided Des. 34 (6), 469–480 (2002)CrossRef
23.
Harzheim, L., Graf, G.: Optimization of engineering components with the SKO method. SAE Technical Paper, 951104 (1995)
24.
Harzheim, L., Graf, G.: Topshape: an attempt to create design proposals including manufacturing constraints. Int. J. Veh. Des. 28 (4), 389–409 (2002)CrossRef
25.
Harzheim, L., Graf, G.: A review of optimization of cast parts using topology optimization: Ii - topology optimization without manufacturing constraints. Struct. Multidiscip. Optim. 30 (5), 491–497 (2005)CrossRef
26.
Harzheim, L., Graf, G.: A review of optimization of cast parts using topology optimization: I - topology optimization with manufacturing constraints. Struct. Multidiscip. Optim. 31 (5), 388–399 (2006)CrossRef
27.
Henrot, A., Pierre, M.: Variation et optimisation de formes: une analyse géométrique, vol. 48. Springer, Berlin (2005)
28.
Laadhari, A., Misbah, C., Saramito, P.: On the equilibrium equation for a generalized biological membrane energy by using a shape optimization approach. Physica D 239 (16), 1567–1572 (2010)MathSciNetCrossRefMATH
29.
Leiva, J.P., Watson, B.C., Kosaka, I.: An analytical directional growth topology parameterization to enforce manufacturing requirements. In: Proceedings of 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Material Conference, Palm Springs, CA (2004)
30.
Lewis, R.W., Manzari, M.T., Gethin, D.T.: Thermal optimisation in the sand casting process. Eng. Comput. 18 (3/4), 392–417 (2001)CrossRefMATH
31.
Mattheck, C.: Design and growth rules for biological structures and their application to engineering. Fatigue Fract. Eng. Mater. Struct. 13 (5), 535–550 (1990)CrossRef
32.
33.
Mohammadi, B., Pironneau, O.: Applied Shape Optimization for Fluids, vol. 28. Oxford University Press, Oxford (2001)MATH
34.
Murat, F., Simon, J.: Etude de problèmes d’optimal design. In: Optimization Techniques Modeling and Optimization in the Service of Man Part 2, pp. 54–62 (1976)MATH
35.
Osher, S.J., Santosa, F.: Level set methods for optimization problems involving geometry and constraints: I. frequencies of a two-density inhomogeneous drum. J. Comput. Phys. 171 (1), 272–288 (2001)
36.
Osher, S.J., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys. 79 (1), 12–49 (1988)MathSciNetCrossRefMATH
37.
Sethian, J.A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge University Press, Cambridge (1999)MATH
38.
Sethian, J.A., Wiegmann, A.: Structural boundary design via level set and immersed interface methods. J. Comput. Phys. 163 (2), 489–528 (2000)MathSciNetCrossRefMATH
39.
Sokołowski, J., Zolésio, J.-P.: Introduction to Shape Optimization. Springer, Berlin (1992)CrossRefMATH
40.
SYSTUS2014, SYSWELD2014, User’s manual, SYSTUS International (2014)
41.
Takezawa, A., Nishiwaki, S., Kitamura, M.: Shape and topology optimization based on the phase field method and sensitivity analysis. J. Comput. Phys. 229 (7), 2697–2718 (2010)MathSciNetCrossRefMATH
42.
Tavakoli, R., Davami, P.: Optimal riser design in sand casting process by topology optimization with SIMP method I: Poisson approximation of nonlinear heat transfer equation. Struct. Multidiscip. Optim. 36 (2), 193–202 (2008)CrossRef
43.
Tortorelli, D.A., Tiller, M.M., Dantzig, J.A.: Optimal design of nonlinear parabolic systems. Part I: fixed spatial domain with applications to process optimization. Comput. Methods Appl. Mech. Eng. 113 (1), 141–155 (1994)MathSciNetMATH
44.
Wang, X., Wang, M.Y., Guo, D.: Structural shape and topology optimization in a level-set-based framework of region representation. Struct. Multidiscip. Optim. 27 (1), 1–19 (2004)CrossRef
45.
Xia, Q., Shi, T., Wang, M.Y., Liu, S.: A level set based method for the optimization of cast part. Struct. Multidiscip. Optim. 41 (5), 735–747 (2010)MathSciNetCrossRef
46.
Xia, Q., Shi, T., Wang, M.Y., Liu, S.: Simultaneous optimization of cast part and parting direction using level set method. Struct. Multidiscip. Optim. 44 (6), 751–759 (2011)MathSciNetCrossRefMATH
47.
Xia, Q., Shi, T., Liu, S., Wang, M.Y.: A level set solution to the stress-based structural shape and topology optimization. Comput. Struct. 90–91, 55–64 (2012)CrossRef
48.
Yamada, T., Izui, K., Nishiwaki, S., Takezawa, A.: A topology optimization method based on the level set method incorporating a fictitious interface energy. Comput. Methods Appl. Mech. Eng. 199 (45), 2876–2891 (2010)MathSciNetCrossRefMATH
49.
Zhou, M., Rozvany, G.I.N.: The COC algorithm, Part II: topological, geometrical and generalized shape optimization. Comput. Methods Appl. Mech. Eng. 89 (1), 309–336 (1991)CrossRef
50.
Zhou, S., Wang, M.Y.: Multimaterial structural topology optimization with a generalized Cahn–Hilliard model of multiphase transition. Struct. Multidiscip. Optim. 33 (2), 89–111 (2007)MathSciNetCrossRefMATH
51.
Zhou, M., Shyy, Y.K., Thomas, H.L.: Topology optimization with manufacturing constraints. In: Proceedings of the 4th World Congress of Structural and Multidisciplinary Optimization (2001)
Metadata
Title
Molding Direction Constraints in Structural Optimization via a Level-Set Method
Authors
Grégoire Allaire
François Jouve
Georgios Michailidis
Copyright Year
2016
Book
Variational Analysis and Aerospace Engineering

Print ISBN: 978-3-319-45679-9

Electronic ISBN: 978-3-319-45680-5

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-45680-5_1

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