Application of isogeometric analysis in structural shape optimization

Haftka, 1986, Structural shape optimization—a survey, Comput. Methods Appl. Mech. Engrg., 57, 91, 10.1016/0045-7825(86)90072-1 Zienkiewicz, 1973, Shape optimization and sequential linear programming, 109 Francavilla, 1975, Optimization of shape to minimize stress concentration, J. Strain Anal. Eng. Des., 10, 63, 10.1243/03093247V102063 Haftka, 1992 Olhoff, 1991, On CAD-integrated structural topology and design optimization, Comput. Methods Appl. Mech. Engrg., 89, 259, 10.1016/0045-7825(91)90044-7 Imam, 1982, Three-dimensional shape optimization, Internat. J. Numer. Methods Engrg., 18, 661, 10.1002/nme.1620180504 Yao, 1989, 3-D shape optimal design and automatic finite element regridding, Internat. J. Numer. Methods Engrg., 28, 369, 10.1002/nme.1620280209 Botkin, 1992, Three-dimensional shape optimization using fully automatic mesh generation, AIAA J., 30, 1932, 10.2514/3.11162 Younsi, 1996, Multi-mesh and adaptivity in 3D shape optimization, Comput. Struct., 61, 1125, 10.1016/0045-7949(96)00117-4 Lindby, 1997, 2-D and 3-D shape optimization using mesh velocities to integrate analytical sensitivities with associative CAD, Struct. Optim., 13, 213, 10.1007/BF01197449 Shi, 1999, Shape optimization in three-dimensional linear elasticity by the boundary contour method, Eng. Anal. Bound. Elem., 23, 627, 10.1016/S0955-7997(99)00022-3 Annicchiarico, 2001, Structural shape optimization 3D finite-element models based on genetic algorithms and geometric modeling, Finite Elem. Anal. Des., 37, 403, 10.1016/S0168-874X(00)00041-X Cervera, 2005, Evolutionary structural optimization based on boundary representation of NURBS. Part II: 3D algorithms, Comput. Struct., 83, 1917, 10.1016/j.compstruc.2005.02.017 Braibant, 1984, Shape optimal design using B-splines, Comput. Methods Appl. Mech. Engrg., 44, 247, 10.1016/0045-7825(84)90132-4 Braibant, V., Fleury, C. and Beckers, P. “Shape optimal design: an approach matching CAD and optimization concepts”, Technical Report Rep. SA-109, Aerospace Laboratory of the University of Liege, Belgium (1983). Bletzinger, 1991, Efficient modeling in shape optimal design, Comput. Syst. Eng., 2, 483, 10.1016/0956-0521(91)90051-6 Bletzinger, 1999, A general finite element approach to the form finding of tensile structures by the updated reference strategy, Int. J. Space Struct., 14, 131, 10.1260/0266351991494759 Bletzinger, 2001, Structural optimization and form finding of light weight structures, Comput. Struct., 79, 2053, 10.1016/S0045-7949(01)00052-9 Haftka, 1992, vol. 2 Hughes, 2005, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Engrg., 194, 4135, 10.1016/j.cma.2004.10.008 Bazilevs, 2006, Isogeometric analysis: approximation, stability and error estimates for h-refined meshes, Math. Models Methods Appl. Sci., 16, 1031, 10.1142/S0218202506001455 Bazilevs, 2007, Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows, Comput. Methods Appl. Mech. Engrg., 197, 173, 10.1016/j.cma.2007.07.016 Bazilevs, 2006, Isogeometric fluid structure interaction analysis with applications to arterial blood flow, Comput. Mech., 38, 310, 10.1007/s00466-006-0084-3 Cottrell, 2006, Isogeometric analysis of structural vibrations, Comput. Methods Appl. Mech. Engrg., 195, 5257, 10.1016/j.cma.2005.09.027 Piegl, 1997 Wall, 2008, Isogeometric structural shape optimization, Comput. Methods Appl. Mech. Engrg., 197, 2976, 10.1016/j.cma.2008.01.025 Cho, 2009, Isogeometric shape design optimization: exact geometry and enhanced sensitivity, Struct. Multidiscip. Optim., 38, 53, 10.1007/s00158-008-0266-z Qian, 2010, Full analytical sensitivities in NURBS based isogeometric shape optimization, Comput. Methods Appl. Mech. Engrg., 199, 2059, 10.1016/j.cma.2010.03.005 Nagy, 2010, Isogeometric sizing and shape optimization of beam structures, Comput. Methods Appl. Mech. Engrg., 199, 1216, 10.1016/j.cma.2009.12.010 Manh, 2011, Isogeometric shape optimization of vibrating membranes, Comput. Methods Appl. Mech. Engrg., 200, 1343, 10.1016/j.cma.2010.12.015 Hassani, 1999 Kirsch, 1993 Arora, 2004 Svanberg, 1987, The method of moving asymptotes—a new method for structural optimization, Internat. J. Numer. Methods Engrg., 24, 359, 10.1002/nme.1620240207 Hassani, B. and Moghadam, N.Z. “Development of a new numerical method for solution of ordinary differential equations by using spine basis functions”, Technical Report No. 1015, Shahrood University of Technology, Iran (2009) (in Farsi). Hassani, 2009, Isogeometric solution of Laplace equation, Asian J. Civ. Eng., 10, 579 Sienz, J. Integrated structural modeling, adaptive analysis and shape optimization, Ph.D. Thesis, Civil Engineering Dept., University of Swansea, UK (1994).