Evolutionary topology optimization using the extended finite element method and isolines

REFERENCES

• Allaire, G., F. Jouve, and A. M. Toader. 2004. “Structural Optimization Using Sensitivity Analysis and a Level Set Method.” Journal of Computational Physics 194: 363–393. doi: 10.1016/j.jcp.2003.09.032
   Web of Science ®Google Scholar
• Aremu, A., I. Ashcroft, R. Wildman, R. Hague, C. Tuck, and D. Brackett. 2013. “The Effects of BESO Parameters on an Industrial Designed Component for Additive Manufacture.” Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, in press.
   Google Scholar
• Belytschko, T. and Black, T, 1999. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 45:601–620. doi: 10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S
   Web of Science ®Google Scholar
• Bendsøe, M. P. 1989. “Optimal Shape Design as a Material Distribution Problem.” Structural Optimization 1: 193–202. doi: 10.1007/BF01650949
   Google Scholar
• Bendsøe, M. P., and N. Kikuchi. 1988. “Generating Optimal Topologies in Structural Design Using a Homogenization Method.” Computer Methods in Applied Mechanics and Engineering 71: 197–224. doi: 10.1016/0045-7825(88)90086-2
   Web of Science ®Google Scholar
• Canann, S., Stephenson, M. and Blacker, T., 1993. Optismoothing: An optimization-driven approach to mesh Smoothing. Finite Elements in Analysis and Design, 13: 185–190. doi: 10.1016/0168-874X(93)90056-V
   Google Scholar
• Dunning, P., H. A. Kim, and G. Mullineux. 2008. “Error Analysis of Fixed Grid Formulation for Boundary Based Structural Optimization.” In 7th ASMO UK/ISSMO Conference on Engineering Design Optimization, July 7–8 2008, Bath, UK.
   Google Scholar
• Freitag, L., 1997. On combining Laplacian and optimization based mesh smoothing techniques. Proceedings of the 1997 Joint Summer Meeting of American Society of Mechanical Engineers (ASME) American Society of Civil Engineers (ASCE) and Society of Engineers Science (SES), pp. 37–44.
   Google Scholar
• Gerstenberger, A., and W. A. Wall. 2008. “An Extended Finite Element Method/Lagrange Multiplier Based Approach for Fluid-Structure Interaction.” Computer Methods in Applied Mechanics and Engineering 197: 1699–714. doi: 10.1016/j.cma.2007.07.002
   Web of Science ®Google Scholar
• Huang, X., and Y. M. Xie. 2007. “Convergent and Mesh-Independent Solutions for Bi-Directional Evolutionary Structural Optimization Method.” Finite Elements in Analysis and Design 43 (14): 1039–1049. doi: 10.1016/j.finel.2007.06.006
   Web of Science ®Google Scholar
• Huang, X., and Y. M. Xie. 2009. Evolutionary Topology Optimization of Continuum Structures. New Delhi, India: John Wiley & Sons.
   Google Scholar
• Jog, C. S., and R. B. Harber. 1996. “Stability of Finite Element Models for Distributed-Parameter Optimization and Topology Design.” Computer Methods in Applied Mechanics and Engineering 130: 1951–1965. doi: 10.1016/0045-7825(95)00928-0
   Web of Science ®Google Scholar
• Lee, D., S. Park, and S. Shin. 2007. “Node-Wise Topological Shape Optimum Design for Structural Reinforced Modeling of Michell-Type Concrete Deep Beams.” Journal of Solid Mechanics and Materials Engineering 1 (9): 1085–1096. doi: 10.1299/jmmp.1.1085
   Google Scholar
• Maute, K., and E. Ramm. 1995. “Adaptive Topology Optimization.” Structural Optimization 10: 100–112. doi: 10.1007/BF01743537
   Web of Science ®Google Scholar
• Melenk, J.M., and Babuška, I., 1996. The partition of unity finite element method: Basic theory and applications. Computer Methods in Applied Mechanics and Engineering, 139: 289–314. doi: 10.1016/S0045-7825(96)01087-0
   Web of Science ®Google Scholar
• Miegroet, L. V., and P. Duysinx. 2007. “Stress Concentration Minimization of 2D Filets Using X-FEM and Level Set Description.” Structural and Multidisciplinary Optimization 33: 425–438. doi: 10.1007/s00158-006-0091-1
   Web of Science ®Google Scholar
• Moës, N., J. Dolbow, and T. Belytschko. 1999. “A Finite Element Method for Crack Growth Without Remeshing.” International Journal for Numerical Methods in Engineering 46: 131–150. doi: 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J
   Web of Science ®Google Scholar
• Querin, O. M., G. P. Steven, and Y. M. Xie. 1998. “Evolutionary Structural Optimization (ESO) Using a Bidirectional Algorithm.” Engineering Computations 15 (8): 1031–1048. doi: 10.1108/02644409810244129
   Web of Science ®Google Scholar
• Sukumar, N., D. L. Chopp, N. Moës, and T. Belytschko. 2001. “Modeling Holes and Inclusions by Level Sets in the Extended Finite Element Method.” Computer Methods in Applied Mechanics and Engineering 190: 6183–6200. doi: 10.1016/S0045-7825(01)00215-8
   Web of Science ®Google Scholar
• Victoria, M., P. Martí, and O. M. Querin. 2009. “Topology Design of Two-Dimensional Continuum Structures Using Isolines.” Computer and Structures 87: 101–109. doi: 10.1016/j.compstruc.2008.08.001
   Web of Science ®Google Scholar
• Victoria, M., O. M. Querin, and P. Martí. 2010. “Topology Design for Multiple Loading Conditions of Continuum Structures Using Isolines and Isosurfaces.” Finite Elements in Analysis and Design 46: 229–237. doi: 10.1016/j.finel.2009.09.003
   Web of Science ®Google Scholar
• Vollmer, J., Mencl, R. and Müller, H., 2001. Improved Laplacian Smoothing of Noisy Surface Meshes. Computer Graphic Forum 18: 131–138. doi: 10.1111/1467-8659.00334
   Web of Science ®Google Scholar
• Wang, M. Y., X. Wang, and D. Guo. 2003. “A Level Set Method for Structural Topology Optimization.” Computer Methods in Applied Mechanics and Engineering 192: 227–246. doi: 10.1016/S0045-7825(02)00559-5
   Web of Science ®Google Scholar
• Wei, P., M. Y. Wang, and X. Xing. 2010. “A Study on X-FEM in Continuum Structural Optimization Using Level Set Method.” Computer-Aided Design 42: 708–719. doi: 10.1016/j.cad.2009.12.001
   Web of Science ®Google Scholar
• Xie, Y. M., and G. P. Steven. 1993. “A Simple Evolutionary Procedure for Structural Optimization.” Computers & Structures 49: 885–896. doi: 10.1016/0045-7949(93)90035-C
   Web of Science ®Google Scholar
• Yang, X. Y., Y. M. Xie, G. P. Steven, and O. M. Querin. 1999. “Bidirectional Evolutionary Method for Stiffness Optimization.” AIAA Journal 37 (11): 1483–1488. doi: 10.2514/2.626
   Web of Science ®Google Scholar
• Zhou, M., and G. I. N. Rozvany. 1991. “The COG Algorithm, Part II: Topological, Geometrical and General Shape Optimization.” Computer Methods in Applied Mechanics and Engineering 89: 309–336.
   Google Scholar