P. Antolin, A. Buffa, F. Calabrò, M. Martinelli, and G. Sangalli, Efficient matrix computation for tensor-product isogeometric analysis: The use of sum factorization, Computer Methods in Applied Mechanics and Engineering, vol.285, pp.817-828, 2015.

P. Antolin, A. Buffa, and L. Coradello, A hierarchical approach to the a posteriori error estimation of isogeometric Kirchhoff plates and Kirchhoff-Love shells, Computer Methods in Applied Mechanics and Engineering, vol.363, p.112919, 2020.

S. Arnout, M. Firl, and K. U. Bletzinger, Parameter free shape and thickness optimisation considering stress response. Structural and Multidisciplinary Optimization, vol.45, pp.801-814, 2012.

F. Bandara-k-&-cirak, Isogeometric shape optimisation of shell structures using multiresolution subdivision surfaces, Computer-Aided Design, vol.95, pp.62-71, 2018.

M. Bischoff, E. Ramm, and J. Irslinger, Encyclopedia of Computational Mechanics Second Edition 1859, pp.1-86, 2017.

L. Blanchard, R. Duvigneau, A. V. Vuong, and B. Simeon, Shape Gradient for Isogeometric Structural Design, Journal of Optimization Theory and Applications, vol.161, pp.361-367, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00998594

K. U. Bletzinger, S. Kimmich, and E. Ramm, Efficient modeling in shape optimal design, Computing Systems in Engineering, vol.2, pp.483-495, 1991.

K. U. Bletzinger, Encyclopedia of Computational Mechanics, 2017.

K. U. Bletzinger and F. Daoud, Approximation of derivatives in semi-analytical structural optimization, Computers & Structures, vol.86, pp.1404-1416, 2008.

E. Bletzinger-ku-&-ramm, Shell Structures for Architecture, pp.45-55, 2014.

K. U. Bletzinger, R. Reitinger, S. Kimmich, and E. Ramm, Software Systems for Structural Optimization 97-124, 1993.

K. U. Bletzinger, R. Wüchner, F. Daoud, and N. Camprubí, Computational methods for form finding and optimization of shells and membranes, Computer Methods in Applied Mechanics and Engineering, vol.194, pp.3438-3452, 2005.

V. Braibant and C. Fleury, Shape optimal design using B-splines, Computer Methods in Applied Mechanics and Engineering, vol.44, pp.247-267, 1984.

H. Chamoin-l-&-thai, Certified real-time shape optimization using isogeometric analysis, PGD model reduction, and a posteriori error estimation, International Journal for Numerical Methods in Engineering, vol.119, pp.151-176, 2019.

M. J. Choi and S. Cho, Constrained isogeometric design optimization of lattice structures on curved surfaces: computation of design velocity field. Structural and Multidisciplinary Optimization, vol.58, pp.17-34, 2018.

E. Cohen, R. F. Riesenfeld, and G. Elber, Geometric Modeling with Splines: An Introduction (A. K. Peters, Ltd, 2001.

S. Coniglio, C. Gogu, and J. Amargier-r-&-morlier, Engine Pylon Topology Optimization Framework Based on Performance and Stress Criteria, AIAA Journal, vol.57, pp.5514-5526, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02302631

J. A. Cottrell and A. Hughes-tjr-&-reali, Studies of refinement and continuity in isogeometric structural analysis, Computer Methods in Applied Mechanics and Engineering, vol.196, pp.4160-4183, 2007.

J. A. Cottrell, T. Hughes, and Y. Bazilevs, Isogeometric Analysis: Toward Integration of CAD and FEA 1st, 2009.

N. Dang-manh, A. Evgrafov, J. Gravesen, and D. Lahaye, Iso-geometric shape optimization of magnetic density separators. COMPEL -The international journal for computation and mathematics in electrical and electronic engineering, vol.33, pp.1416-1433, 2014.

S. D. Daxini and J. M. Prajapati, Parametric shape optimization techniques based on Meshless methods: A review. Structural and Multidisciplinary Optimization, vol.56, pp.1197-1214, 2017.

C. Ding, X. Cui, G. Huang, G. Li, and K. K. Tamma, Exact and efficient isogeometric reanalysis of accurate shape and boundary modifications, Computer Methods in Applied Mechanics and Engineering, vol.318, pp.619-635, 2017.

C. Ding, A gradient-based shape optimization scheme via isogeometric exact reanalysis. Engineering Computations, 2018.

P. Duysinx and O. Sigmund, New developments in handling stress constraints in optimal material distribution in, 7th AIAA / USAF / NASA / ISSMO Symposium on Multidisciplinary Analysis and Optimization (American Institute of Aeronautics and Astronautics, pp.1501-1509, 1998.

R. Echter, B. Oesterle, and M. Bischoff, A hierarchic family of isogeometric shell finite elements, Computer Methods in Applied Mechanics and Engineering, vol.254, pp.170-180, 2013.

R. Echter, Isogeometric Analysis of Shells PhD thesis, 2013.

F. J. Ertl, G. Dhondt, and K. U. Bletzinger, Vertex assigned morphing for parameter free shape optimization of 3-dimensional solid structures, Computer Methods in Applied Mechanics and Engineering, vol.353, pp.86-106, 2019.

E. Evans, M. Scott, X. Li, and D. Thomas, Hierarchical T-splines: Analysis-suitability, Bézier extraction, and application as an adaptive basis for isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, vol.284, pp.1-20, 2015.

J. A. Evans, Y. Bazilevs, I. Babu?ka, and T. J. Hughes, n-Widths, sup-infs, and optimality ratios for the k-version of the isogeometric finite element method, Computer Methods in Applied Mechanics and Engineering, vol.198, pp.1726-1741, 2009.

G. Farin, Curves and Surfaces for CAGD: A Practical Guide 5th, 2002.

M. Firl, Optimal shape design of shell structures PhD thesis, 2010.

D. Fußeder, B. Simeon, and A. V. Vuong, Fundamental aspects of shape optimization in the context of isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, vol.286, pp.313-331, 2015.

C. Gígola and S. Gomez, A Regularization Method for Solving the Finite Convex Min-Max Problem, SIAM Journal on Numerical Analysis, vol.27, pp.1621-1634, 1990.

J. Gravesen, A. Evgrafov, and D. M. Nguyen, On the sensitivities of multiple eigenvalues. Structural and Multidisciplinary Optimization, vol.44, pp.583-587, 2011.

R. T. Haftka and R. V. Grandhi, Structural shape optimization-A survey, Computer Methods in Applied Mechanics and Engineering, vol.57, pp.91-106, 1986.

B. Hassani, S. Tavakkoli, and N. Moghadam, Application of isogeometric analysis in structural shape optimization, Scientia Iranica, vol.18, pp.846-852, 2011.

R. R. Hiemstra, G. Sangalli, M. Tani, F. Calabrò, and T. J. Hughes, Fast formation and assembly of finite element matrices with application to isogeometric linear elasticity, Computer Methods in Applied Mechanics and Engineering, vol.355, pp.234-260, 2019.

T. Hirschler, R. Bouclier, A. Duval, T. Elguedj, and J. Morlier, The embedded isogeometric Kirchhoff-Love shell: From design to shape optimization of non-conforming stiffened multipatch structures, Computer Methods in Applied Mechanics and Engineering, vol.349, pp.774-797, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02055622

T. Hirschler, R. Bouclier, A. Duval, T. Elguedj, and J. Morlier, Isogeometric sizing and shape optimization of thin structures with a solid-shell approach. Structural and Multidisciplinary Optimization 59, pp.767-785, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01898851

M. Hojjat, E. Stavropoulou, and K. U. Bletzinger, The Vertex Morphing method for node-based shape optimization, Computer Methods in Applied Mechanics and Engineering, vol.268, pp.494-513, 2014.

Y. L. Hsu, A review of structural shape optimization, Computers in Industry, vol.25, pp.3-13, 1994.

T. Hughes, J. A. Cottrell, and Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer Methods in Applied Mechanics and Engineering, vol.194, pp.4135-4195, 2005.
URL : https://hal.archives-ouvertes.fr/hal-01513346

M. H. Imam, Three-dimensional shape optimization, International Journal for Numerical Methods in Engineering, vol.18, pp.661-673, 1982.

S. G. Johnson, The NLopt nonlinear

D. Kamensky, Immersogeometric cardiovascular fluid-structure interaction analysis with divergence-conforming B-splines, Computer Methods in Applied Mechanics and Engineering, vol.314, pp.408-472, 2017.

P. Kang and S. K. Youn, Isogeometric shape optimization of trimmed shell structures. Structural and Multidisciplinary Optimization, vol.53, pp.825-845, 2016.

B. Kegl-m-&-brank, Shape optimization of truss-stiffened shell structures with variable thickness, Computer Methods in Applied Mechanics and Engineering, vol.195, pp.2611-2634, 2006.

J. Kiendl, K. U. Bletzinger, J. Linhard, and R. Wüchner, Isogeometric shell analysis with Kirchhoff-Love elements, Computer Methods in Applied Mechanics and Engineering, vol.198, pp.3902-3914, 2009.

J. Kiendl, Isogeometric Analysis and Shape Optimal Design of Shell Structures PhD thesis, 2011.

J. Kiendl, R. Schmidt, R. Wuchner, and K. U. Bletzinger, Isogeometric shape optimization of shells using semi-analytical sensitivity analysis and sensitivity weighting, Computer Methods in Applied Mechanics and Engineering, vol.274, pp.148-167, 2014.

G. Kirchhoff, Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. ger, Journal für die reine und angewandte Mathematik, vol.40, pp.51-88, 1850.

U. Kirsch, A unified reanalysis approach for structural analysis, design, and optimization, pp.67-85, 2003.

D. Kraft, A Software Package for Sequential Quadratic Programming (Wiss, 1988.

C. Le, T. Bruns, and D. Tortorelli, A gradient-based, parameter-free approach to shape optimization, Computer Methods in Applied Mechanics and Engineering, vol.200, pp.985-996, 2011.

. Lee and Y. Park, Degree elevation of nurbs curves by weighted blossom, Korean Journal of Computational & Applied Mathematics, vol.9, pp.151-165, 2002.

Z. Lei, F. Gillot, and L. Jezequel, Shape Optimization for Natural Frequency with Isogeometric Kirchhoff-Love Shell and Sensitivity Mapping, Mathematical Problems in Engineering, pp.1-11, 2018.

K. Li and X. Qian, Isogeometric analysis and shape optimization via boundary integral, Computer-Aided Design, vol.43, pp.1427-1437, 2011.

X. S. Li and S. C. Fang, On the entropic regularization method for solving min-max problems with applications, Mathematical Methods of Operations Research, vol.46, pp.119-130, 1997.

H. Lian, P. Kerfriden, and S. Bordas, Shape optimization directly from CAD: An isogeometric boundary element approach using T-splines, Computer Methods in Applied Mechanics and Engineering, vol.317, pp.1-41, 2017.

S. Lipton, J. Evans, Y. Bazilevs, T. Elguedj, and T. Hughes, Robustness of isogeometric structural discretizations under severe T. Hirschler et al. mesh distortion, Computer Methods in Applied Mechanics and Engineering, vol.199, pp.357-373, 2010.

A. Love and . Xvi, The small free vibrations and deformation of a thin elastic shell. Philosophical Transactions of the Royal Society of London, pp.491-546, 1888.

J. Lund-e-&-stegmann, IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials, pp.147-156, 2006.

N. D. Manh, A. Evgrafov, and J. Gersborg-ar-&-gravesen, Isogeometric shape optimization of vibrating membranes, Computer Methods in Applied Mechanics and Engineering, vol.200, pp.1343-1353, 2011.

S. Morganti, Patient-specific isogeometric structural analysis of aortic valve closure, Computer Methods in Applied Mechanics and Engineering, vol.284, pp.508-520, 2015.

A. P. Nagy, M. M. Abdalla, and Z. Gürdal, Isogeometric sizing and shape optimisation of beam structures, Computer Methods in Applied Mechanics and Engineering, vol.199, pp.1216-1230, 2010.

A. P. Nagy, M. M. Abdalla, and Z. Gürdal, Isogeometric design of elastic arches for maximum fundamental frequency. Structural and Multidisciplinary Optimization, vol.43, pp.135-149, 2011.

A. P. Nagy, S. T. Ijsselmuiden, and M. M. Abdalla, Isogeometric design of anisotropic shells: Optimal form and material distribution, Computer Methods in Applied Mechanics and Engineering, vol.264, pp.145-162, 2013.

D. M. Nguyen and J. Evgrafov-a-&-gravesen, Isogeometric Shape Optimization for Electromagnetic Scattering problems, Progress In Electromagnetics Research B, vol.45, pp.117-146, 2012.

M. Occelli, T. Elguedj, S. Bouabdallah, L. Morançay, and . Lr-b-, Splines implementation in the Altair RadiossTM solver for explicit dynamics IsoGeometric Analysis, Advances in Engineering Software, vol.131, pp.166-185, 2019.

N. Olhoff, Multicriterion structural optimization via bound formulation and mathematical programming, Structural Optimization, vol.1, pp.11-17, 1989.

N. Olhoff, J. Rasmussen, E. Lund, and . Method-of, Exact" Numerical Differentiation for Error Elimination in Finite-Element-Based Semi-Analytical Shape Sensitivity Analyses*, Mechanics of Structures and Machines, vol.21, pp.1-66, 1993.

M. Papadrakakis, N. D. Lagaros, Y. Tsompanakis, and V. Plevris, Large scale structural optimization: Computational methods and optimization algorithms, Archives of Computational Methods in Engineering, vol.8, pp.239-301, 2001.

B. U. Park, Y. D. Seo, O. Sigmund, and S. K. Youn, Shape optimization of the stokes flow problem based on isogeometric analysis. Structural and Multidisciplinary Optimization, vol.48, pp.965-977, 2013.

L. Piegl and W. Tiller, The NURBS Book, vol.2, 1997.

X. Qian, Full analytical sensitivities in NURBS based isogeometric shape optimization, Computer Methods in Applied Mechanics and Engineering, vol.199, pp.2059-2071, 2010.

A. P. Seyranian, E. Lund, and N. Olhoff, Multiple eigenvalues in structural optimization problems, Structural Optimization, vol.8, pp.207-227, 1994.

A. Shamanskiy, M. H. Gfrerer, J. Hinz, and B. Simeon, Isogeometric parametrization inspired by large elastic deformation, Computer Methods in Applied Mechanics and Engineering, vol.363, p.112920, 2020.

M. Shimoda and Y. Liu, A non-parametric free-form optimization method for shell structures. Structural and Multidisciplinary Optimization, vol.50, pp.409-423, 2014.

M. Shimoda and Y. Liu, Node-based free-form optimization method for vibration problems of shell structures, Computers & Structures, vol.177, pp.91-102, 2016.

M. Shimoda, T. Nagano, T. Morimoto, Y. Liu, and J. X. Shi, Nonparametric free-form optimal design of frame structures in natural frequency problem, International Journal of Mechanical Sciences, vol.117, pp.334-345, 2016.

O. Sigmund, On the Design of Compliant Mechanisms Using Topology Optimization*. Mechanics of Structures and Machines, vol.25, pp.493-524, 1997.

B. Stanford, P. Beran, and M. Bhatia, Aeroelastic Topology Optimization of Blade-Stiffened Panels, Journal of Aircraft, vol.51, pp.938-944, 2014.

B. Taheri-a-&-hassani, Simultaneous isogeometrical shape and material design of functionally graded structures for optimal eigenfrequencies, Computer Methods in Applied Mechanics and Engineering, vol.277, pp.46-80, 2014.

J. Tomlow, Gaudí's reluctant attitude towards the inverted catenary, Proceedings of the Institution of Civil Engineers -Engineering History and Heritage, vol.164, pp.219-233, 2011.

F. Van-keulen, R. Haftka, and N. Kim, Review of options for structural design sensitivity analysis. Part 1: Linear systems, Computer Methods in Applied Mechanics and Engineering, vol.194, pp.3213-3243, 2005.

A. Verbart, M. Langelaar, and F. Van-keulen, A unified aggregation and relaxation approach for stress-constrained topology optimization. Structural and Multidisciplinary Optimization, vol.55, pp.663-679, 2017.

W. A. Wall, M. A. Frenzel, and C. Cyron, Isogeometric structural shape optimization, Computer Methods in Applied Mechanics and Engineering, vol.197, pp.2976-2988, 2008.

W. Wang, P. M. Clausen, and K. U. Bletzinger, Improved semi-analytical sensitivity analysis using a secant stiffness matrix for geometric nonlinear shape optimization, Computers & Structures, vol.146, pp.143-151, 2015.

Y. Wang, Z. Wang, Z. Xia, and L. Poh, Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review, Computer Modeling in Engineering & Sciences, vol.117, pp.455-507, 2018.

Z. P. Wang, M. Abdalla, and S. Turteltaub, Normalization approaches for the descent search direction in isogeometric shape optimization, Computer-Aided Design, vol.82, pp.68-78, 2017.

. Wang and S. Turteltaub, Isogeometric shape optimization for quasi-static processes, International Journal for Numerical Methods in Engineering, vol.104, pp.347-371, 2015.

Z. P. Wang, S. Turteltaub, and M. Abdalla, Shape optimization and optimal control for transient heat conduction problems using an isogeometric approach, Computers & Structures, vol.185, pp.59-74, 2017.

O. Weeger, B. Narayanan, and M. L. Dunn, Isogeometric shape optimization of nonlinear, curved 3D beams and beam structures, Computer Methods in Applied Mechanics and Engineering, 2018.

C. Williams, Shell Structures for Architecture, pp.21-31, 2014.

Q. Xia, T. Shi, and M. Y. Wang, A level set based shape and topology optimization method for maximizing the simple or repeated first eigenvalue of structure vibration. Structural and Multidisciplinary Optimization, vol.43, pp.473-485, 2011.

M. Xu, S. Wang, and X. Xie, Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency, Frontiers of Mechanical Engineering, vol.14, pp.222-234, 2019.

R. Yang and C. J. Chen, Stress-based topology optimization. Structural Optimization, vol.12, pp.98-105, 1996.

B. Zhu, Design of compliant mechanisms using continuum topology optimization: A review. Mechanism and Machine Theory, vol.143, p.103622, 2020.