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Robust topology optimization with interval field model: on the spatially varied non-probabilistic uncertainty of material property, loading and geometry
Shape Optimization Under a Constraint on the Worst-Case Scenario
Fabien Caubet, Marc Dambrine, Giulio Gargantini and Jérôme Maynadier SIAM Journal on Scientific Computing 46(6) A3703 (2024) https://doi.org/10.1137/24M1648818
Adaptive topology optimization for enhancing resistance to brittle fracture using the phase field model
Qi Zhang, Yang Liu, Nhon Nguyen-Thanh, Weidong Li, Shaofan Li and Kun Zhou Computer Methods in Applied Mechanics and Engineering 431 117237 (2024) https://doi.org/10.1016/j.cma.2024.117237
Adaptive density-based robust topology optimization under uncertain loads using parallel computing
Geometric Partial Differential Equations - Part II
Grégoire Allaire, Charles Dapogny and François Jouve Handbook of Numerical Analysis, Geometric Partial Differential Equations - Part II 22 1 (2021) https://doi.org/10.1016/bs.hna.2020.10.004
An optimization algorithm for automatic structural design
Nicola Ferro, Stefano Micheletti and Simona Perotto Computer Methods in Applied Mechanics and Engineering 372 113335 (2020) https://doi.org/10.1016/j.cma.2020.113335
Parametric topology optimization with multiresolution finite element models
Vahid Keshavarzzadeh, Robert M. Kirby and Akil Narayan International Journal for Numerical Methods in Engineering 119(7) 567 (2019) https://doi.org/10.1002/nme.6063
Large-scale stochastic topology optimization using adaptive mesh refinement and coarsening through a two-level parallelization scheme
Joan Baiges, Jesús Martínez-Frutos, David Herrero-Pérez, Fermin Otero and Alex Ferrer Computer Methods in Applied Mechanics and Engineering 343 186 (2019) https://doi.org/10.1016/j.cma.2018.08.028
Robust compliance topology optimization using the first-order second-moment method
Microstructural topology optimization for minimizing the sound pressure level of structural–acoustic coupled systems with multi-scale random parameters
Integrated method for performance analysis of reliability-based topologically optimized components
Arshad Javed, Joshua Amrith Raj and BK Rout Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233(19-20) 7019 (2019) https://doi.org/10.1177/0954406219865757
Risk-averse structural topology optimization under random fields using stochastic expansion methods
Jesús Martínez-Frutos, David Herrero-Pérez, Mathieu Kessler and Francisco Periago Computer Methods in Applied Mechanics and Engineering 330 180 (2018) https://doi.org/10.1016/j.cma.2017.10.026
Robust truss topology optimization via semidefinite programming with complementarity constraints: a difference-of-convex programming approach
A critical analysis of expected-compliance model in volume-constrained robust topology optimization with normally distributed loading directions, using a minimax-compliance approach alternatively
Topology optimization under uncertainty via non-intrusive polynomial chaos expansion
Vahid Keshavarzzadeh, Felipe Fernandez and Daniel A. Tortorelli Computer Methods in Applied Mechanics and Engineering 318 120 (2017) https://doi.org/10.1016/j.cma.2017.01.019
A general framework for robust topology optimization under load-uncertainty including stress constraints
Robust shape optimization of continuous structures via the level set method
Jesús Martínez-Frutos, David Herrero-Pérez, Mathieu Kessler and Francisco Periago Computer Methods in Applied Mechanics and Engineering 305 271 (2016) https://doi.org/10.1016/j.cma.2016.03.003
Topology optimization of structures with interval random parameters
Grégoire Allaire, François Jouve and Georgios Michailidis Springer Optimization and Its Applications, Variational Analysis and Aerospace Engineering 116 1 (2016) https://doi.org/10.1007/978-3-319-45680-5_1
Robust shape optimization method for a linear elastic structure with unknown loadings
Masatoshi SHIMODA, Tomohiro NAGANO, Kohei SHINTANI and Satoshi ITO Transactions of the JSME (in Japanese) 81(832) 15-00353 (2015) https://doi.org/10.1299/transjsme.15-00353
Topology optimization applied to 2D elasticity problems considering the geometrical nonlinearity
Shape Optimization for Stokes flows: a finite element convergence analysis
Ivan Fumagalli, Nicola Parolini and Marco Verani ESAIM: Mathematical Modelling and Numerical Analysis 49(4) 921 (2015) https://doi.org/10.1051/m2an/2014060
Robust Topology Optimization Based on Stochastic Collocation Methods under Loading Uncertainties
Combined shape and topology optimization of 3D structures
Asger Nyman Christiansen, J. Andreas Bærentzen, Morten Nobel-Jørgensen, Niels Aage and Ole Sigmund Computers & Graphics 46 25 (2015) https://doi.org/10.1016/j.cag.2014.09.021
A NOTE ON FORMULATIONS OF ROBUST COMPLIANCE OPTIMIZATION UNDER UNCERTAIN LOADS
Yoshihiro KANNO Journal of Structural and Construction Engineering (Transactions of AIJ) 80(710) 601 (2015) https://doi.org/10.3130/aijs.80.601
A semidefinite programming approach to robust truss topology optimization under uncertainty in locations of nodes
Robust optimal shape design for an elliptic PDE with uncertainty in its input data
Jesús Martínez-Frutos, Mathieu Kessler and Francisco Periago ESAIM: Control, Optimisation and Calculus of Variations 21(4) 901 (2015) https://doi.org/10.1051/cocv/2014049
Robust topology optimization of truss structures with random loading and material properties: A multiobjective perspective
Tolerance range selection of topologically optimized structures with the effects of uncertainties of manufacturing process
Arshad Javed and BK Rout Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 228(18) 3441 (2014) https://doi.org/10.1177/0954406214528484
A survey of structural and multidisciplinary continuum topology optimization: post 2000
Sergio Conti, Benedict Geihe, Martin Rumpf and Rüdiger Schultz International Series of Numerical Mathematics, Trends in PDE Constrained Optimization 165 193 (2014) https://doi.org/10.1007/978-3-319-05083-6_13
Tolerance range section of topologically optimized structure using combined array design of experiments approach
Arshad Javed and BK Rout Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227(9) 2023 (2013) https://doi.org/10.1177/0954406212468652
Level-set methods for structural topology optimization: a review
An Explicit Formula for Computing the Sensitivity of the Effective Conductivity of Heterogeneous Composite Materials to Local Inclusion Transport Properties and Geometry
Constrained Optimization and Optimal Control for Partial Differential Equations
Pradeep Atwal, Sergio Conti, Benedict Geihe, et al. International Series of Numerical Mathematics, Constrained Optimization and Optimal Control for Partial Differential Equations 160 215 (2012) https://doi.org/10.1007/978-3-0348-0133-1_12
Investigation on parametric sensitivity of topologically optimized structures
Arshad Javed and BK Rout Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 226(11) 2791 (2012) https://doi.org/10.1177/0954406212437513
Topology optimization with geometric uncertainties by perturbation techniques
B. S. Lazarov, M. Schevenels and O. Sigmund International Journal for Numerical Methods in Engineering 90(11) 1321 (2012) https://doi.org/10.1002/nme.3361
Introducing Loading Uncertainty in Topology Optimization
Topology optimization for worst load conditions based on the eigenvalue analysis of an aggregated linear system
Akihiro Takezawa, Satoru Nii, Mitsuru Kitamura and Nozomu Kogiso Computer Methods in Applied Mechanics and Engineering 200(25-28) 2268 (2011) https://doi.org/10.1016/j.cma.2011.03.008
Risk Averse Shape Optimization
Sergio Conti, Harald Held, Martin Pach, Martin Rumpf and Rüdiger Schultz SIAM Journal on Control and Optimization 49(3) 927 (2011) https://doi.org/10.1137/090754315
Optimal distribution of the internal null control for the one-dimensional heat equation