On the structural stiffness maximisation of anisotropic continua under inhomogeneous Neumann–Dirichlet boundary conditions

Bendsøe, 1988, Generating optimal topologies in structural design using a homogenization method, Comput Methods Appl Mech Eng, 71, 197, 10.1016/0045-7825(88)90086-2 Bendsøe, 2004 Sethian, 1999 Allaire, 2004, Structural optimization using sensitivity analysis and a level-set method, J Comput Phys, 194, 363, 10.1016/j.jcp.2003.09.032 Wang, 2003, A level set method for structural topology optimization, Comput Methods Appl Mech Eng, 192, 227, 10.1016/S0045-7825(02)00559-5 de Ruiter, 2004, Topology optimization using a topology description function, Struct Multidiscip Optim, 26, 406, 10.1007/s00158-003-0375-7 Xie, 1993, A simple evolutionary procedure for structural optimization, Comput Struct, 49, 885, 10.1016/0045-7949(93)90035-C Yang, 1999, Bidirectional evolutionary method for stiffness optimization, AIAA J, 37, 1483, 10.2514/2.626 Huang, 2009, Evolutionary topology optimization of continuum structures with an additional displacement constraint, Struct Multidiscip Optim, 40, 409, 10.1007/s00158-009-0382-4 Huang, 2010 Guo, 2014, Doing topology optimization explicitly and geometrically—A new moving morphable components based framework, J Appl Mech, 81, 10.1115/1.4027609 Zhang, 2017, Explicit three dimensional topology optimization via moving morphable void (MMV) approach, Comput Methods Appl Mech Eng, 322, 590, 10.1016/j.cma.2017.05.002 Costa, 2018, A 2D topology optimisation algorithm in NURBS framework with geometric constraints, Int J Mech Mater Design, 14, 669, 10.1007/s10999-017-9396-z Costa, 2021, NURBS hypersurfaces for 3D topology optimisation problems, Mech Adv Mater Struct, 28, 665, 10.1080/15376494.2019.1582826 Rodriguez, 2020, Structural displacement requirement in a topology optimization algorithm based on isogeometric entities, J Optim Theory Appl, 184, 250, 10.1007/s10957-019-01622-8 Costa, 2019, Minimum length scale control in a NURBS-based SIMP method, Comput Methods Appl Mech Eng, 354, 63, 10.1016/j.cma.2019.05.026 Costa, 2019, Maximum length scale requirement in a topology optimisation method based on NURBS hyper-surfaces, CIRP Annals, 68, 153, 10.1016/j.cirp.2019.04.048 Costa, 2020, Eigen-frequencies and harmonic responses in topology optimisation: a CAD-compatible algorithm, Eng Struct, 214, 10.1016/j.engstruct.2020.110602 Montemurro, 2021, A topology optimization method based on non-uniform rational basis spline hyper-surfaces for heat conduction problems, Symmetry, 13, 888, 10.3390/sym13050888 Montemurro, 2021, A general multi-scale topology optimisation method for lightweight lattice structures obtained through additive manufacturing technology, Compos Struct, 258, 10.1016/j.compstruct.2020.113360 Roiné, 2021, Stress-based topology optimization through non-uniform rational basis spline hyper-surfaces, Mech Adv Mater Struct Costa, 2017, A general hybrid optimization strategy for curve fitting in the non-uniform rational basis spline framework, J Optim Theory Appl, 176, 225, 10.1007/s10957-017-1192-2 Bertolino, 2021, An efficient hybrid optimisation strategy for surface reconstruction, Comput Graphics Forum, 40, 215, 10.1111/cgf.14269 Pedersen, 2011, Design objectives with non-zero prescribed support displacements, Struct Multidiscip Optim, 43, 205, 10.1007/s00158-010-0577-8 Niu, 2011, A general formulation of structural topology optimization for maximizing structural stiffness, Struct Multidiscip Optim, 43, 561, 10.1007/s00158-010-0585-8 Klarbring, 2012, A note on the min-max formulation of stiffness optimization including non-zero prescribed displacements, Struct Multidiscip Optim, 45, 147, 10.1007/s00158-011-0674-3 Barbarosie, 2011, A generalized notion of compliance, Compte Rendus Méc, 339, 641, 10.1016/j.crme.2011.07.002 Piegl, 1997 Svanberg, 2002, A class of globally convergent optimization methods based on conservative convex separable approximations, SIAM J Optim, 12, 555, 10.1137/S1052623499362822 Jones, 1975 Errico, 1997, What is an adjoint model?, Bull Amer Meteorol Soc, 78, 2577, 10.1175/1520-0477(1997)078<2577:WIAAM>2.0.CO;2