- Volume 27 Issue 5
DOI QR Code
Shape Design Optimization of Crack Propagation Problems Using Meshfree Methods
무요소법을 이용한 균열진전 문제의 형상 최적설계
- Kim, Jae-Hyun (National Creative Research Initiatives(NCRI) Center for Isogeometric Optimal Design, Department of Naval Architecture and Ocean Engineering, Seoul National University) ;
- Ha, Seung-Hyun (Department of Ocean Engineering, Korea Maritime and Ocean University) ;
- Cho, Seonho (National Creative Research Initiatives(NCRI) Center for Isogeometric Optimal Design, Department of Naval Architecture and Ocean Engineering, Seoul National University)
- Received : 2014.03.04
- Accepted : 2014.09.24
- Published : 2014.10.31
This paper presents a continuum-based shape design sensitivity analysis(DSA) method for crack propagation problems using a reproducing kernel method(RKM), which facilitates the remeshing problem required for finite element analysis(FEA) and provides the higher order shape functions by increasing the continuity of the kernel functions. A linear elasticity is considered to obtain the required stress field around the crack tip for the evaluation of J-integral. The sensitivity of displacement field and stress intensity factor(SIF) with respect to shape design variables are derived using a material derivative approach. For efficient computation of design sensitivity, an adjoint variable method is employed tather than the direct differentiation method. Through numerical examples, The mesh-free and the DSA methods show excellent agreement with finite difference results. The DSA results are further extended to a shape optimization of crack propagation problems to control the propagation path.
Supported by : 한국연구재단
- Chen, J.S., Pan, C., Wu, C.T. (1997) Large Deformation Analysis of Rubber Based on a Reproducing Kernel Particle Method, Comput. Mech.., 19, pp.211-217. https://doi.org/10.1007/s004660050170
- Ha, S.H., Cho, S. (2008) Level Set Based Topological Shape Optimization of Geometrically Nonlienar Structures using Unstructured Mesh, Comput. & Struct., 86, pp.1447-1455. https://doi.org/10.1016/j.compstruc.2007.05.025
- Ha, Y., Cho, S. (2006) Design Sensitivity Analysis and Topology Optimization of Eigenvalue Problems for Piezoelectric Resonators, Smart Mater. & Struct., 15, pp.1513-1524. https://doi.org/10.1088/0964-1726/15/6/002
- Haber, R.B., Koh, H.M. (1985) Explicit Expressions for Energy Release Rates Using Virtual Crack Extensions, International, J. Numer. Method in Eng., 21, pp.301-315. https://doi.org/10.1002/nme.1620210208
- Haug, E.J., Choi, K.K., Komkov, V. (1986) Design Sensitivity Analysis of Structural System, Academic Press, New York, NY.
- Kim, M.-G., Ha, S.H., Cho, S. (2012) Level Set Based Topological Shape Optimization of Hyper-Elastic Nonlinear Structures using Topological Derivatives, J. Comput. Struct. Eng. Inst. Korea, 25(6), pp.559-567. https://doi.org/10.7734/COSEIK.2012.25.6.559
- Park, S.M. (2004) Crack Propagation Analysis using Reproducing Kernel Method, Master Thesis, Seoul National University.