Browse > Article
http://dx.doi.org/10.7734/COSEIK.2014.27.1.1

Level Set Based Topological Shape Optimization Combined with Meshfree Method  

Ahn, Seung-Ho (National Creative Research Initiatives(NCRI) Center for Isogeometric Optimal Design, Department of Naval Architecture and Ocean Engineering, Seoul National University)
Ha, Seung-Hyun (National Creative Research Initiatives(NCRI) Center for Isogeometric Optimal Design, Department of Naval Architecture and Ocean Engineering, Seoul National University)
Cho, Seonho (National Creative Research Initiatives(NCRI) Center for Isogeometric Optimal Design, Department of Naval Architecture and Ocean Engineering, Seoul National University)
Publication Information
Journal of the Computational Structural Engineering Institute of Korea / v.27, no.1, 2014 , pp. 1-8 More about this Journal
Abstract
Using the level set and the meshfree methods, we develop a topological shape optimization method applied to linear elasticity problems. Design gradients are computed using an efficient adjoint design sensitivity analysis(DSA) method. The boundaries are represented by an implicit moving boundary(IMB) embedded in the level set function obtainable from the "Hamilton-Jacobi type" equation with the "Up-wind scheme". Then, using the implicit function, explicit boundaries are generated to obtain the response and sensitivity of the structures. Global nodal shape function derived on a basis of the reproducing kernel(RK) method is employed to discretize the displacement field in the governing continuum equation. Thus, the material points can be located everywhere in the continuum domain, which enables to generate the explicit boundaries and leads to a precise design result. The developed method defines a Lagrangian functional for the constrained optimization. It minimizes the compliance, satisfying the constraint of allowable volume through the variations of boundary. During the optimization, the velocity to integrate the Hamilton-Jacobi equation is obtained from the optimality condition for the Lagrangian functional. Compared with the conventional shape optimization method, the developed one can easily represent the topological shape variations.
Keywords
Shape optimization; level set method; reproducing kernel method; adjoint variable method;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Allaire, G., Jouve, F., Toader, A. (2002) A Level-set Method for Shape Optimization, C. R. Acad. Sci. Paris, Ser. I, 334, pp.1125-1130.   DOI
2 Belytschko, T., Krogauz, Y., Organ, D., Fleming, M., Krysl, P. (1996) Meshless Methods: An Overview and Recent Developments, Computer Methods in Applied Mechanics and Engineering, 139, pp.3-47.   DOI
3 Chen, J.S., Pan, C., Wu, C.T. (1997) Large Deformation Analysis of Rubber Based on Reproducing Kernel Particle Method, Computational Mechanics, 19, pp.211-227.   DOI   ScienceOn
4 Haug, E.J., Choi, K.K., Komkov, V. (1986) Design Sensitivity Analysis of Structural Systems, Academic Press, New York.
5 Kim, M.-G., Hashimoto, H., Abe, K., Cho, S. (2012) Level Set Based Topological Shape Optimization of Phononic Crystals for Sound Barriers, Computational Structural Engineering Institute of Korea, 25(6), pp.549-558.   DOI
6 Lancaster, P., Salkauskas, K. (1981) Surface Generated by Moving Least Squares Methods, Mathematics of Computation, 37, pp.141-158.   DOI   ScienceOn
7 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
8 Sethian, J.A., Wiegmann, A. (2000) Structural Boundary Design via Level Set and Immersed Interface Methods, Journal of Computational Physics, 163, pp.489-528.   DOI   ScienceOn
9 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.227-246.   DOI   ScienceOn