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http://dx.doi.org/10.7734/COSEIK.2012.25.6.559

Level Set Based Topological Shape Optimization of Hyper-elastic Nonlinear Structures using Topological Derivatives  

Kim, Min-Geun (WTG development team1, Samsung Heavy Industries)
Ha, Seung-Hyun (Department of Civil Engineering, Jones Hopkins University)
Cho, Seonho (Department of Naval Architecture and Ocean Engineering)
Publication Information
Journal of the Computational Structural Engineering Institute of Korea / v.25, no.6, 2012 , pp. 559-567 More about this Journal
Abstract
A level set based topological shape optimization method for nonlinear structure considering hyper-elastic problems is developed. To relieve significant convergence difficulty in topology optimization of nonlinear structure due to inaccurate tangent stiffness which comes from material penalization of whole domain, explicit boundary for exact tangent stiffness is used by taking advantage of level set function for arbitrary boundary shape. For given arbitrary boundary which is represented by level set function, a Delaunay triangulation scheme is used for current structure discretization instead of using implicit fixed grid. The required velocity field in the actual domain to update the level set equation is determined from the descent direction of Lagrangian derived from optimality conditions. The velocity field outside the actual domain is determined through a velocity extension scheme based on the method suggested by Adalsteinsson and Sethian(1999). The topological derivatives are incorporated into the level set based framework to enable to create holes whenever and wherever necessary during the optimization.
Keywords
topological shape optimization; level set method; topological derivatives; hyper-elastic material; adjoint variable method; velocity extension scheme;
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1 Adalsteinsson, D., Sethian, J.A. (1999) The Fast Construction of Extension Velocities in Level Set Methods, Journal of Computational Physics, 148, pp.2-22.   DOI   ScienceOn
2 Allaire, G., Jouve, F., Toader, A.M. (2004) Structural Optimization using Sensitivity Analysis and a Level-Set Method, Journal of Computational Physics, 194, pp.363-393.   DOI
3 Bendsoe, M.P., Kikuchi, N. (1988) Generating Optimal Topologies in Structural Design using a Homogenization Method, Computer Methods in Applied Mechanics and Engineering, 71, pp. 197-224. Bendso̸e   DOI   ScienceOn
4 Bendsoe, M.P., Sigmund, O. (2003) Topology Optimization: Theory, Methods and Applications, Springer-Verlag, Berlin, pp.370.
5 Buhl, T., Petersen, C.B.W., Sigmund, O. (2000) Stiffness Design of Geometrically Nonlinear Structures using Topology Optimization, Structural Multidisciplinary Optimization, 19, pp.93-104.   DOI   ScienceOn
6 Cho, S., Jung, H. (2003) Design Sensitivity Analysis and Topology Optimization of Displacement-Loaded Nonlinear Structures, Computer Methods in Applied Mechanics and Engineering, 192, pp.2539-2553.   DOI
7 Ha, S.H, Cho, S. (2009) Level Set Based Topological Shape Optimization of Geometrically Nonlinear Structures using Unstructured Mesh, Computers & Structures, 86, pp.1447-1455.
8 Kim, M.G., Ha, S.H, Cho, S. (2009) Level Set-Based Topological Shape Optimization of Nonlinear Heat Conduction Problems using Topological Derivatives, Mechanics Based Design of Structures and Machines, 37, pp.550-582.   DOI
9 Kwak, J., Cho, S. (2005) Topological Shape Optimization of Geometrically Nonlinear Structures using Level Set Method, Computers & Structures, 83, pp.2257-2268.   DOI
10 Mooney, M. (1940) A Theory of Large Elastic Deformation, Journal of Applied Physics, 11 pp.582-592.   DOI
11 Novotny, A.A., Feijoo, R.A., Taroco, E., Padra, C. (2000) Topological Sensitivity Analysis, Computational Methods in Applied Mechanics and Engineering, 188 pp.713-726.   DOI
12 Osher, S., Sethian, J.A. (1988) Front Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations, Journal of Computational Physics, 79, pp.12-49.   DOI   ScienceOn
13 Persson, P., Strang, G. (2004) A Simple Mesh Henerator in Matlab, SIAM Review, 46(2), pp.329-345.   DOI
14 Sokolowski, J., Zochowski, A. (1999) A. On Topological Derivative in Shape Optimization, SIAM Journal of Control and Optimization, 37, 1251-1272.   DOI
15 Wang, M.Y., Wang, X., Guo, D. (2003) A Level Set Method for Structural Topology Optimization, Computational Methods in Applied Mechanics and Engineering, 192, pp.227-24.   DOI   ScienceOn