Academic Journal
A consistent relaxation of optimal design problems for coupling shape and topological derivatives
| العنوان: | A consistent relaxation of optimal design problems for coupling shape and topological derivatives |
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| المؤلفون: | Amstutz, Samuel, Dapogny, Charles, Ferrer Ferré, Àlex |
| المساهمون: | Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental, Universitat Politècnica de Catalunya. DECA - Grup de Recerca del Departament d'Enginyeria Civil i Ambiental |
| سنة النشر: | 2018 |
| المجموعة: | Universitat Politècnica de Catalunya (UPC): Tesis Doctorals en Xarxa (TDX) / Theses and Dissertations Online |
| مصطلحات موضوعية: | Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia, Structural optimization -- Mathematics, Multiscale modeling--Computer simulation, Level set method, Material interpolation, Shape derivative, Relaxation, Optimal design, topological derivative, Optimització d'estructures, Modelització multiescala, Classificació AMS::74 Mechanics of deformable solids::74P Optimization, Classificació AMS::35 Partial differential equations::35Q Equations of mathematical physics and other areas of application, Classificació AMS::49 Calculus of variations and optimal control, optimization::49Q Manifolds, Classificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problems, optimization::49M Methods of successive approximations |
| الوصف: | In this article, we introduce and analyze a general procedure for approximating a ‘black and white’ shape and topology optimization problem with a density optimization problem, allowing for the presence of ‘grayscale’ regions. Our construction relies on a regularizing operator for smearing the characteristic functions involved in the exact optimization problem, and on an interpolation scheme, which endows the intermediate density regions with fictitious material properties. Under mild hypotheses on the smoothing operator and on the interpolation scheme, we prove that the features of the approximate density optimization problem (material properties, objective function, etc.) converge to their exact counterparts as the smoothing parameter vanishes. In particular, the gradient of the approximate objective functional with respect to the density function converges to either the shape or the topological derivative of the exact objective. These results shed new light on the connections between these two different notions of sensitivities for functions of the domain, and they give rise to different numerical algorithms which are illustrated by several experiments ; Peer Reviewed ; Postprint (author's final draft) |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| تدمد: | 0029-599X |
| Relation: | https://link.springer.com/article/10.1007%2Fs00211-018-0964-4; Amstutz, S., Dapogny, C., Ferrer, A. A consistent relaxation of optimal design problems for coupling shape and topological derivatives. "Numerische mathematik", setembre 2018, vol. 140, núm. 1, p. 35-94; http://hdl.handle.net/2117/118037 |
| DOI: | 10.1007/s00211-018-0964-4 |
| الاتاحة: | http://hdl.handle.net/2117/118037 https://doi.org/10.1007/s00211-018-0964-4 |
| Rights: | Open Access |
| رقم الانضمام: | edsbas.698746B0 |
| قاعدة البيانات: | BASE |
| تدمد: | 0029599X |
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| DOI: | 10.1007/s00211-018-0964-4 |