Shape optimisation with the level set method for contact problems in linearised elasticity

Maury, Aymeric; Allaire, Grégoire; Jouve, François

doi:10.5802/smai-jcm.27

Cited by 19 publications

(20 citation statements)

References 56 publications

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“…Other objective functions or mechanical constraints for which shape derivatives are available (see e.g. [22]) could be optimized, particularly the contact pressure. Different models could be accommodated in our setting, like free or forced vibrations.…”

Section: Discussionmentioning

confidence: 99%

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Coupled topology optimization of structure and connections for bolted mechanical systems

Rakotondrainibe

Desai

Orval

et al. 2022

European Journal of Mechanics - A/Solids

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Section: Discussionmentioning

confidence: 99%

“…The derivation of the above adjoint equation has been performed in [22]. The weak form of ( 17) reads: find p ∈ V such that…”

Section: Adjoint Statementioning

confidence: 99%

Coupled topology optimization of structure and connections for bolted mechanical systems

Rakotondrainibe

Desai

Orval

et al. 2022

European Journal of Mechanics - A/Solids

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“…Gradient-based optimisation is used for the optimisation. Considering contact problems, the problem of TO has been addressed in a quasi-static context in [30][31][32]. The objective of this study is to perform TO for the optimisation of nonlinear dynamic systems in the presence of a friction interface, which has never been done before according to the knowledge of the authors.…”

Section: Introductionmentioning

confidence: 99%

Topological Optimization of Under-Platform Dampers With Moving Morphable Components and Global Optimization Algorithm for Nonlinear Frequency Response

Denimal

Haddad

Wong

et al. 2021

Journal of Engineering for Gas Turbines and Power

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To limit the risk of high cycle fatigue, underplatform dampers (UDPs) are traditionally used in aircraft engines to control the level of vibration. Many studies demonstrate the impact of the geometry of the damper on its efficiency, thus the consideration of topological optimization (TO) to find the best layout of the damper seems natural. Because of the nonlinear behavior of the structure due to the friction contact interface, classical methods of TO are not usable. This study proposes to optimize the layout of an UDP to reduce the level of nonlinear vibrations computed with the multiharmonic balance method (MHBM). The approach of TO employed is based on the moving morphable components (MMC) framework together with the Kriging and the efficient global optimization algorithm to solve the optimization problem. The results show that the level of vibration of the structure can be reduced to 30% and allow for the identification of different efficient geometries.

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“…Challenging scenarios are the ones in which the geometry of the domain can vary and it is potentially the unknown of the problem to be solved. This is common to several fields of research such as shape optimisation ( [10,11,12]), inverse scattering problems ( [13]), geometry morphometrics ( [14,15]). Moreover, a variable domain is challenging for projection based ROM for which, typically, a basis of space functions is defined on a given domain.…”

Section: Introductionmentioning

confidence: 99%

State Estimation with Model Reduction and Shape Variability. Application to biomedical problems

Galarce,

Lombardi,

Mula

2021

Preprint

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We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems are posed on certain organs or portions of the body which inevitably involve morphological variations. If one wants to provide fast reconstruction methods, the algorithms must take into account the geometric variability. We develop and analyze a method which allows to take this variability into account without needing any a priori knowledge on a parametrization of the geometrical variations. For this, we rely on morphometric techniques involving Multidimensional Scaling, and couple them with reconstruction algorithms that make use of reduced model spaces precomputed on a database of geometries. We prove the potential of the method on a synthetic test problem inspired from the reconstruction of blood flows and quantities of medical interest with Doppler ultrasound imaging.

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Shape optimisation with the level set method for contact problems in linearised elasticity

Cited by 19 publications

References 56 publications

Coupled topology optimization of structure and connections for bolted mechanical systems

Coupled topology optimization of structure and connections for bolted mechanical systems

Topological Optimization of Under-Platform Dampers With Moving Morphable Components and Global Optimization Algorithm for Nonlinear Frequency Response

State Estimation with Model Reduction and Shape Variability. Application to biomedical problems

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