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Formulation de Nouvelles Fonctionnalités dans la Méthode d’Optimisation Topologique Basée sur la Méthode SIMP et les Hyper-surfaces NURBS

Abstract : Topology Optimization (TO) is of paramount importance in a design process of components obtained through additive manufacturing technology. The goal of the TO is to determine the optimal distribution of the material within the design domain in order to satisfy the requirements of the problem at hand. Currently, in TO methods based on pseudo-density field, e.g., the strategies making use of the SIMP (Solid Isotropic Material with Penalization) approach the final topology is available only in a discretized form (i.e., in terms of the active mesh elements retained at the end of the process), thus it is not compatible with CAD software. Geometry quality and performances are, consequently, highly dependent on the discretization (i.e., mesh-dependent); of course, the higher the number of elements, the better the final performances but also the higher the number of design variables and, accordingly, the higher the computational costs.To overcome the above issues, a new TO method, named NURBS-based SIMP, has been developed at the I2M laboratory making use of NURBS geometry as topological descriptor in the context of the classical density-based TO algorithms.The NURBS entity is used to describe the pseudo-density field of the material within the design domain. The continuous parameters of the NURBS entity (i.e., the pseudo-density at the control points and the associated weights) are the variables of the TO problem. Moreover, the NURBS integer parameters (i.e., number of control points and degrees of the basis function), influencing the local support property of the NURBS entity, are set to obtain mesh-independent solutions.In this background, this Ph.D. Thesis presents a new version of the NURBS-based SIMP TO algorithm developed in Python programming environment, by proposing new features, which render the algorithm more versatile. Specifically, these features are: a structural displacement criterion formulated in linear elasticity framework; an adaptation of a multi-material interpolation function in the NURBS-based SIMP framework giving a new multi-material TO method.
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Submitted on : Thursday, June 16, 2022 - 9:50:49 AM
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Thibaut Rodriguez. Formulation de Nouvelles Fonctionnalités dans la Méthode d’Optimisation Topologique Basée sur la Méthode SIMP et les Hyper-surfaces NURBS. Mécanique [physics]. HESAM Université, 2022. Français. ⟨NNT : 2022HESAE020⟩. ⟨tel-03696581⟩

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