Topology Optimization for Polymeric Foam Shock-Absorbing Structure Using Hybrid Cellular Automata
Wonho Lee, Jinhoon Kim, and Changbae Park
R&D Solution Lab., Digital Media Communication R&D Center, Samsung Electronics Co., Ltd., 129, Samsung-Ro, Yeongtong-gu, Suwon-si, Gyeonggi-do 443-742, Korea
Foam shock-absorbing structures such as cushioned packages are often utilized to protect various products from mechanical shock and vibration during transportation. The goal of packaging design engineers is to design a cushioned package structure that improves the shock-absorbing performance and minimizes the volume of the package. Some optimization techniques, combined with computational simulation, provide engineers with a way to design an optimal structure. In this paper, we propose a modified topology optimization method suitable for a polymeric foam shock-absorbing structure under dynamic drop loads in multiple directions. Our approach uses a heuristic topology optimization method, known as the Hybrid Cellular Automata (HCA). The HCA algorithm uniformly distributes internal energy density and controls the relative density of Cellular Automata (CAs) making up the design space. This allows the algorithm to maintain or increase the performance of shock absorption and to decrease the amount of material. In particular, this paper presents a modified Solid IsotropicMaterial with Penalization (SIMP) model for foam materials, which parameterizes the design region and interpolates the material properties. We attempt to optimize a simple bottom-cushioned package for a refrigerator by using the proposed foam SIMP model with commercial software: LS-DYNA for drop dynamic simulation and LS-OPT/Topology for the HCA algorithm. Drop simulation and topology optimization are performed considering multiple drop-directions. As a result, our method removes elements that are not related to the shock-absorption performance and provide an optimal cushioning structure using foam material.
-  M. Avalle, G. Belingardi, and R. Montanini, “Characterization of polymeric structural foams under compressive impact loading by means of energy-absorption diagram,” Int. J. of Impact Engineering, Vol.25, pp. 455-472, 2001.
-  “Packaging with Styropor,” BASF, 2006.
-  B. Croop and H. Lobo, “Selecting Material Models for the Simulation of Foams in LS-DYNA,” 7th European LS-DYNA Conf., 2009.
-  S.W. Booh, K. T. Kim, and W. J. Chung, “Drop/Impact Analysis of Electronic Products with Packaging Materials,” Trans. of the KSME (A), pp. 228-234, 1995.
-  K. Y. Seok, K. W. Yoon, J. M. Na, and C. B. Park, “Analysis of Package Drop and its Application for Optical Disc Drives,” Proc. of the KSNV Engineering Conf., pp. 177-182, 2004.
-  D. H. Kum, W. J. Kim, S. D. Kim, and S. H. Park, “Optimal Design for Cushioned package of a Heavy Electronic Product Using Mechanical Drop Analysis,” Trans. of the KSNV, Vol.14, No.2, pp. 128-135, Feb. 2004.
-  C. S. Kim, B. K. Base, and D. Y. Sung, “Drop Analysis of a Package and Cushion Performance of Drum Washing Machine,” Trans. of the KSME (A), Vol.34, No.11, pp. 1733-1740, Nov. 2010.
-  J. W. Yi, D. Y. Ha, S. W. Lee, J. M. Lim, G. J. Park, “Development of Design System for EPS Cushioned package of Monitor Using Axiomatic Design,” Trans. of the KSME (A), Vol.27, No.10, pp. 228-234, Oct. 2003.
-  Y. Y. Wang, C. Lu, J. Li, X. M. Tan, and T. C. Tse, “Simulation of drop/impact reliability for electronic devices,” Finite Element in Analysis and Design, Vol.41, Issue 6, Mar. 2005.
-  M. P. Bensøe and O. Sigmund, “Topology Optimization, Theory: Methods and Applications,” Springer-Verlag, Berlin, 2003.
-  T. Goel, W. Roux, and N. Stander, “A Topology Optimization Tool for LS-DYNA Users: LS-OPT/Topology,” 7th European LS-DYNA Conf., 2009.
-  M. M. Abdalla, S. Setoodeh, and Z. Gürdal, “Cellular automata paradigm for topology optimisation,” IUTAM Symp. on Topological Design Optimization of Structures, Machines and Materials: Status and Perspectives, pp. 169-180, 2006.
-  G. H. Yoon and Y. Y. Kim, “Element connectivity parameterization for topology optimization of geometrically nonlinear structures,” Int. J. of Solids and Structures, Vol.42, Issue 7, pp. 1983-2009, Apr. 2005.
-  A. Erhart, P. Schumacher, N. Lazarov, H. Műllerschön, “Topology optimization with LS-TaSC and Genesis/ESL for crash-loading,” LS-DYNA Forum, Germany, 2012.
-  M. K. Shin, K. J. Park, and G. J. Park, “Optimization of structures with nonlinear behavior using equivalent load,” Computer Methods in Applied Mechanics and Engineering, Vol.196, Issue 4-6, pp. 1154-1167, Jan. 2007.
-  A. Tovar, N. M. Pater, AK. Kaushik, G. A. Letona, and J. E. Renaud, “Hybrid cellular automata: a biologically-inspired structural optimization technique,” In Proc. of the 10th AIAA/ISSMO Symp. on Multidisciplinary Analysis and Optimization, AIAA 2004-4558, 2004.
-  A. Tovar, N. M. Patel, G. L. Niebur, M. Sen, and JE. Renaud, “Topology Optimization Using a Hybrid Cellular Automaton Method With Local Control Rules,” J. of Mechanical Design of ASME, Vol.128, pp. 1205-1216, 2006.
-  N. M. Patel, “Crashworthiness design using topology optimization,” Dissertation, University of Notre Dame, 2007.
-  W. Roux, LS-OPT/Tolopology 1.0, Livermore Software Technology Corporation, 2010.
-  J. O. Hallquist, “LS-DYNA Theory Manual,” Livermore Software Technology Corporation, 2006.
-  JC. Goetz, H. Tan, J. E. Renaud, and A. Tovar, “Structural topology optimization for blast mitigation using hybrid cellular automata,” Proc. of the GVSETS, 2009.
-  M. P. Bendsøe and O. Sigmund, “Material interpolation schemes in topology optimization,” Archive of Appied Mechanics, Vol.69, pp. 635-654, 1999.
-  WESTPAK, “Cushion Material Testing,” Technical Papers,
http://www.westpak.com. [accessed Apr. 16, 2012]
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