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. ,
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. ,
Parameter free shape and thickness optimisation considering stress response. Structural and Multidisciplinary Optimization, vol.45, pp.801-814, 2012. ,
Isogeometric shape optimisation of shell structures using multiresolution subdivision surfaces, Computer-Aided Design, vol.95, pp.62-71, 2018. ,
, Encyclopedia of Computational Mechanics Second Edition 1859, pp.1-86, 2017.
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
Efficient modeling in shape optimal design, Computing Systems in Engineering, vol.2, pp.483-495, 1991. ,
, Encyclopedia of Computational Mechanics, 2017.
Approximation of derivatives in semi-analytical structural optimization, Computers & Structures, vol.86, pp.1404-1416, 2008. ,
, Shell Structures for Architecture, pp.45-55, 2014.
, Software Systems for Structural Optimization 97-124, 1993.
Computational methods for form finding and optimization of shells and membranes, Computer Methods in Applied Mechanics and Engineering, vol.194, pp.3438-3452, 2005. ,
Shape optimal design using B-splines, Computer Methods in Applied Mechanics and Engineering, vol.44, pp.247-267, 1984. ,
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. ,
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. ,
Geometric Modeling with Splines: An Introduction (A. K. Peters, Ltd, 2001. ,
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
Studies of refinement and continuity in isogeometric structural analysis, Computer Methods in Applied Mechanics and Engineering, vol.196, pp.4160-4183, 2007. ,
Isogeometric Analysis: Toward Integration of CAD and FEA 1st, 2009. ,
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. ,
Parametric shape optimization techniques based on Meshless methods: A review. Structural and Multidisciplinary Optimization, vol.56, pp.1197-1214, 2017. ,
Exact and efficient isogeometric reanalysis of accurate shape and boundary modifications, Computer Methods in Applied Mechanics and Engineering, vol.318, pp.619-635, 2017. ,
A gradient-based shape optimization scheme via isogeometric exact reanalysis. Engineering Computations, 2018. ,
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. ,
A hierarchic family of isogeometric shell finite elements, Computer Methods in Applied Mechanics and Engineering, vol.254, pp.170-180, 2013. ,
Isogeometric Analysis of Shells PhD thesis, 2013. ,
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. ,
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. ,
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. ,
Curves and Surfaces for CAGD: A Practical Guide 5th, 2002. ,
Optimal shape design of shell structures PhD thesis, 2010. ,
Fundamental aspects of shape optimization in the context of isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, vol.286, pp.313-331, 2015. ,
A Regularization Method for Solving the Finite Convex Min-Max Problem, SIAM Journal on Numerical Analysis, vol.27, pp.1621-1634, 1990. ,
On the sensitivities of multiple eigenvalues. Structural and Multidisciplinary Optimization, vol.44, pp.583-587, 2011. ,
Structural shape optimization-A survey, Computer Methods in Applied Mechanics and Engineering, vol.57, pp.91-106, 1986. ,
Application of isogeometric analysis in structural shape optimization, Scientia Iranica, vol.18, pp.846-852, 2011. ,
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. ,
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
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
The Vertex Morphing method for node-based shape optimization, Computer Methods in Applied Mechanics and Engineering, vol.268, pp.494-513, 2014. ,
A review of structural shape optimization, Computers in Industry, vol.25, pp.3-13, 1994. ,
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
Three-dimensional shape optimization, International Journal for Numerical Methods in Engineering, vol.18, pp.661-673, 1982. ,
The NLopt nonlinear ,
Immersogeometric cardiovascular fluid-structure interaction analysis with divergence-conforming B-splines, Computer Methods in Applied Mechanics and Engineering, vol.314, pp.408-472, 2017. ,
Isogeometric shape optimization of trimmed shell structures. Structural and Multidisciplinary Optimization, vol.53, pp.825-845, 2016. ,
Shape optimization of truss-stiffened shell structures with variable thickness, Computer Methods in Applied Mechanics and Engineering, vol.195, pp.2611-2634, 2006. ,
Isogeometric shell analysis with Kirchhoff-Love elements, Computer Methods in Applied Mechanics and Engineering, vol.198, pp.3902-3914, 2009. ,
Isogeometric Analysis and Shape Optimal Design of Shell Structures PhD thesis, 2011. ,
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. ,
Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. ger, Journal für die reine und angewandte Mathematik, vol.40, pp.51-88, 1850. ,
A unified reanalysis approach for structural analysis, design, and optimization, pp.67-85, 2003. ,
A Software Package for Sequential Quadratic Programming (Wiss, 1988. ,
A gradient-based, parameter-free approach to shape optimization, Computer Methods in Applied Mechanics and Engineering, vol.200, pp.985-996, 2011. ,
Degree elevation of nurbs curves by weighted blossom, Korean Journal of Computational & Applied Mathematics, vol.9, pp.151-165, 2002. ,
Shape Optimization for Natural Frequency with Isogeometric Kirchhoff-Love Shell and Sensitivity Mapping, Mathematical Problems in Engineering, pp.1-11, 2018. ,
Isogeometric analysis and shape optimization via boundary integral, Computer-Aided Design, vol.43, pp.1427-1437, 2011. ,
On the entropic regularization method for solving min-max problems with applications, Mathematical Methods of Operations Research, vol.46, pp.119-130, 1997. ,
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. ,
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. ,
The small free vibrations and deformation of a thin elastic shell. Philosophical Transactions of the Royal Society of London, pp.491-546, 1888. ,
, IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials, pp.147-156, 2006.
Isogeometric shape optimization of vibrating membranes, Computer Methods in Applied Mechanics and Engineering, vol.200, pp.1343-1353, 2011. ,
Patient-specific isogeometric structural analysis of aortic valve closure, Computer Methods in Applied Mechanics and Engineering, vol.284, pp.508-520, 2015. ,
Isogeometric sizing and shape optimisation of beam structures, Computer Methods in Applied Mechanics and Engineering, vol.199, pp.1216-1230, 2010. ,
Isogeometric design of elastic arches for maximum fundamental frequency. Structural and Multidisciplinary Optimization, vol.43, pp.135-149, 2011. ,
Isogeometric design of anisotropic shells: Optimal form and material distribution, Computer Methods in Applied Mechanics and Engineering, vol.264, pp.145-162, 2013. ,
Isogeometric Shape Optimization for Electromagnetic Scattering problems, Progress In Electromagnetics Research B, vol.45, pp.117-146, 2012. ,
Splines implementation in the Altair RadiossTM solver for explicit dynamics IsoGeometric Analysis, Advances in Engineering Software, vol.131, pp.166-185, 2019. ,
Multicriterion structural optimization via bound formulation and mathematical programming, Structural Optimization, vol.1, pp.11-17, 1989. ,
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. ,
Large scale structural optimization: Computational methods and optimization algorithms, Archives of Computational Methods in Engineering, vol.8, pp.239-301, 2001. ,
Shape optimization of the stokes flow problem based on isogeometric analysis. Structural and Multidisciplinary Optimization, vol.48, pp.965-977, 2013. ,
, The NURBS Book, vol.2, 1997.
Full analytical sensitivities in NURBS based isogeometric shape optimization, Computer Methods in Applied Mechanics and Engineering, vol.199, pp.2059-2071, 2010. ,
Multiple eigenvalues in structural optimization problems, Structural Optimization, vol.8, pp.207-227, 1994. ,
Isogeometric parametrization inspired by large elastic deformation, Computer Methods in Applied Mechanics and Engineering, vol.363, p.112920, 2020. ,
A non-parametric free-form optimization method for shell structures. Structural and Multidisciplinary Optimization, vol.50, pp.409-423, 2014. ,
Node-based free-form optimization method for vibration problems of shell structures, Computers & Structures, vol.177, pp.91-102, 2016. ,
Nonparametric free-form optimal design of frame structures in natural frequency problem, International Journal of Mechanical Sciences, vol.117, pp.334-345, 2016. ,
On the Design of Compliant Mechanisms Using Topology Optimization*. Mechanics of Structures and Machines, vol.25, pp.493-524, 1997. ,
Aeroelastic Topology Optimization of Blade-Stiffened Panels, Journal of Aircraft, vol.51, pp.938-944, 2014. ,
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. ,
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. ,
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 unified aggregation and relaxation approach for stress-constrained topology optimization. Structural and Multidisciplinary Optimization, vol.55, pp.663-679, 2017. ,
Isogeometric structural shape optimization, Computer Methods in Applied Mechanics and Engineering, vol.197, pp.2976-2988, 2008. ,
Improved semi-analytical sensitivity analysis using a secant stiffness matrix for geometric nonlinear shape optimization, Computers & Structures, vol.146, pp.143-151, 2015. ,
Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review, Computer Modeling in Engineering & Sciences, vol.117, pp.455-507, 2018. ,
Normalization approaches for the descent search direction in isogeometric shape optimization, Computer-Aided Design, vol.82, pp.68-78, 2017. ,
Isogeometric shape optimization for quasi-static processes, International Journal for Numerical Methods in Engineering, vol.104, pp.347-371, 2015. ,
Shape optimization and optimal control for transient heat conduction problems using an isogeometric approach, Computers & Structures, vol.185, pp.59-74, 2017. ,
Isogeometric shape optimization of nonlinear, curved 3D beams and beam structures, Computer Methods in Applied Mechanics and Engineering, 2018. ,
, Shell Structures for Architecture, pp.21-31, 2014.
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. ,
Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency, Frontiers of Mechanical Engineering, vol.14, pp.222-234, 2019. ,
, Stress-based topology optimization. Structural Optimization, vol.12, pp.98-105, 1996.
Design of compliant mechanisms using continuum topology optimization: A review. Mechanism and Machine Theory, vol.143, p.103622, 2020. ,