- Volume 26 Issue 4
DOI QR Code
Isogeometric Shape Design Sensitivity Analysis of Mindlin Plates
민들린 평판의 아이소-지오메트릭 형상 설계민감도 해석
- Lee, Seung-Wook (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)
- Received : 2013.06.28
- Accepted : 2013.07.31
- Published : 2013.08.30
In this paper, a shape design sensitivity analysis(DSA) method is presented for Mindlin plates using an isogeometric approach. The isogeometric method possesses desirable advantages; the representation of exact geometry and the higher order inter-element continuity, which lead to the fast convergence of solution as well as accurate sensitivity results. Unlike the finite element methods using linear shape functions, the isogeometric method considers the exact normal vector and curvature of the CAD geometry, taking advantages of higher order NURBS basis functions. A selective reduced integration(SRI) technique is incorporated to overcome the difficulty of 'shear locking' phenomenon. This simple technique is surprisingly helpful for the accuracy of the isogeometric shape sensitivity without complicated formulation. Through the numerical examples of plate bending problems, the accuracy of the proposed isogeometric analysis method is compared with that of finite element one. Also, the isogeometric shape sensitivity turns out to be very accurate when compared with finite difference sensitivity.
Supported by : 한국연구재단
- Ahn, S., Kim, M.G., Cho, S. (2010) Isogeometric Shape Design Optimization of Structures under Stress Constraints, Journal of Computational Structural Engineering Institute of Korea, 23(4), pp.275 -282.
- Bazilevs, Y., Hughes, T.J.R (2007) Weak Imposition of Direchlet Boundary Conditions in Fluid Mechanics, Computers and Fluids, 36(1), pp.12-26. https://doi.org/10.1016/j.compfluid.2005.07.012
- Cho, S., Ha, S.-H. (2009) Isogeometric Shape Design Optimization :Exact Geometry, Enhanced Sensitivity, Structural and Multidisciplinary Optimization, 38(1), pp.53-70. https://doi.org/10.1007/s00158-008-0266-z
- Cottrell, J.A., RealiA, Bazileves, Y., Hughes, T.J.R (2006) Isogeometric Analysis of Structureal Vibrations, Computer Method in Applied Mechanics and Engineering, 195, pp.5257-5296. https://doi.org/10.1016/j.cma.2005.09.027
- Hughes, T.J.R., Cottrell, J.A., Bazileves, Y. (2005) Isogeometric Analysis : CAD, FInite Elements NURBS, Exact Geometry and Mesh Refinement, Computer Method in Applied Mechanics and Engineering, 194, pp.4135-4195. https://doi.org/10.1016/j.cma.2004.10.008
- Kim, N.H., Choi, K.K., Chen, J-S., Botkin, M.E. (2002) Meshfree Analysis and Design Sensitivity Analysis for Shell Structures, International Journal for Numerical Methods in Engineering, S, 53(9), pp.2087-2116. https://doi.org/10.1002/nme.385
- Oral, S. (2000) Mindlin Plate Finite Element with Semianalytical Shape Design Sensitivities, Computer and Structures, 78(1), pp.467-472. https://doi.org/10.1016/S0045-7949(00)00068-7
- Timoshenko, Stehan, P. Woinowsky-Kringer, S. (1961) Theory of Plates and Shells, Mcgraw-Hill Book Company, p.580.
- Isogeometric Shape Design Optimization of Power Flow Problems at High Frequencies vol.27, pp.3, 2014, https://doi.org/10.7734/COSEIK.2014.27.3.155