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On multi-material topology optimisation problems under inhomogeneous Neumann–Dirichlet boundary conditions

Article dans une revue avec comité de lecture
Auteur
ccMONTEMURRO, Marco
1002421 Institut de Mécanique et d'Ingénierie [I2M]
RODRIGUEZ, Thibaut
300016 Commissariat à l'énergie atomique et aux énergies alternatives [CEA]
ccPAILHES, Jerome
1002421 Institut de Mécanique et d'Ingénierie [I2M]
LE TEXIER, Paul
300016 Commissariat à l'énergie atomique et aux énergies alternatives [CEA]

URI
http://hdl.handle.net/10985/25067
DOI
10.1016/j.finel.2022.103867
Date
2023-02
Journal
Finite Elements in Analysis and Design

Résumé

This work deals with the topology optimisation of structures made of multiple material phases. The proposed approach is based on non-uniform rational basis spline (NURBS) hyper-surfaces to represent the geometric descriptor related to each material phase composing the continuum, and an improved multiphase material interpolation (MMI) scheme to penalise the stiffness tensor of the structure. In this context, the problem is formulated in the most general case by considering inhomogeneous Neumann–Dirichlet boundary conditions and by highlighting the differences between two different problem formulations. The first one uses the work of applied forces and displacements as cost function and the resulting optimisation problem is not self-adjoint. The second one considers the generalised compliance (related to the total potential energy), and the resulting optimisation problem is self-adjoint. Moreover, the improved MMI scheme proposed here does not require the introduction of artificial filtering techniques to smooth the boundary of the topological descriptors of the material phases composing the structure. The effectiveness of the method is proven on both 2D and 3D problems. Specifically, an extensive campaign of numerical analyses is conducted to investigate the influence of the type of geometric descriptor, of the integer parameters involved in the definition of the NURBS entity, of the type of cost function, of the type of lightness requirement, of the number and type of material phases, of the applied boundary conditions on the optimised topology.

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  • Institut de Mécanique et d’Ingénierie de Bordeaux (I2M)

Documents liés

Visualiser des documents liés par titre, auteur, créateur et sujet.

  • Determination of the effective thermoelastic properties of cork-based agglomerates 
    Article dans une revue avec comité de lecture
    DELUCIA, Marco; ccCATAPANO, Anita; ccMONTEMURRO, Marco; ccPAILHES, Jerome (SAGE Publications, 2019)
    In this paper, a general numerical homogenisation scheme coupled with an efficient modelling strategy for predicting the effective thermoelastic properties of cork-based agglomerates is presented. In order to generate a ...
  • Thermo-mechanical homogenisation of cork-based composites: variability in materials properties and propagation of uncertainty 
    Conférence invitée
    DELUCIA, Marco; ccCATAPANO, Anita; ccMONTEMURRO, Marco; ccPAILHES, Jerome (2019)
    The last decades have been characterized by a growth of raw material demand, in particular due to the consumerism in developed countries and to the fast industrialization of emerging economies. Nowadays, with the aim to ...
  • A NURBS-BASED TOPOLOGY OPTIMIZATION METHOD INCLUDING ADDITIVE MANUFACTURING CONSTRAINTS 
    Communication avec acte
    COSTA, Giulio; ccMONTEMURRO, Marco; ccPAILHES, Jerome (J.F. Silva Gomes and Shaker A. Meguid editors, 2017)
    In this work, the Solid Isotropic Material with Penalization (SIMP) topology optimization (TO) method is revisited and reformulated within the mathematical framework of NURBS functions. This implies several advantages: ...
  • Multi-scale optimisation of thin-walled structures by considering a global/local modelling approach 
    Article dans une revue avec comité de lecture
    IZZI, Michele Iacopo; ccMONTEMURRO, Marco; ccCATAPANO, Anita; FANTERIA, Daniele; ccPAILHES, Jerome (SAGE Publications, 2020)
    In this work, a design strategy for optimising thin-walled structures based on a global-local finite element (FE) modelling approach is presented. The preliminary design of thin-walled structures can be stated in the form ...
  • On the integration of additive manufacturing constraints in the framework of a NURBS-based topology optimisation method 
    Communication sans acte
    COSTA, Giulio; ccMONTEMURRO, Marco; ccPAILHES, Jerome (2017)
    This work focuses on the topology optimization (TO) of 2D structures: the Solid Isotropic Material with Penalisation (SIMP) method is revisited and reformulated within the mathematical framework of Non-Uniform Rational ...

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