Generalized Geometry Projection: A Unified Approach for Geometric Feature Based Topology Optimization
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ORIGINAL PAPER
Generalized Geometry Projection: A Unified Approach for Geometric Feature Based Topology Optimization Simone Coniglio1 · Joseph Morlier2 · Christian Gogu2 · Rémi Amargier1 Received: 19 February 2019 / Accepted: 30 September 2019 © CIMNE, Barcelona, Spain 2019
Abstract Structural topology optimization has seen many methodological advances in the past few decades. In this work we focus on continuum-based structural topology optimization and more specifically on geometric feature based approaches, also known as explicit topology optimization, in which a design is described as the assembly of simple geometric components that can change position, size and orientation in the considered design space. We first review various recent developments in explicit topology optimization. We then describe in details three of the reviewed frameworks, which are the Geometry Projection method, the Moving Morphable Components with Esartz material method and Moving Node Approach. Our main contribution then resides in the proposal of a theoretical framework, called Generalized Geometry Projection, aimed at unifying into a single formulation these three existing approaches. While analyzing the features of the proposed framework we also provide a review of smooth approximations of the maximum operator for the assembly of geometric features. In this context we propose a saturation strategy in order to solve common difficulties encountered by all reviewed approaches. We also explore the limits of our proposed strategy in terms of both simulation accuracy and optimization performance on some numerical benchmark examples. This leads us to recommendations for our proposed approach in order to attenuate common discretization induced effects that can alter optimization convergence.
1 Introduction
Simone Coniglio [email protected]
non-conventional solutions or derive design principles for similar problems. Since the pioneering work of [5], topology optimization has received considerable research attention. Numerous topology optimization approaches such as SIMP (Solid Isotropic Material with Penalization) approach [4, 76], level set approach [1, 50], and evolutionary approach [54, 56] have been successfully proposed and implemented. Direct density based approaches [4, 6, 76], which are currently among the most popular ones, can reach organic or free form designs, defining the local presence or absence of material. In Zhu et al. [81], the interested reader can find a review of this family of approaches in the Aerospace design applications. The exploration power of these approaches, their freedom and their ease in handling large changes in the design configuration without re-meshing come however at the cost of some drawbacks as well:
Joseph Morlier j.morlier@isae‑supaero.fr
• The number of design variables and of degrees of free-
The manufacturing industry is faced with multiple challenges in both cost reduction and product performance improvement in order to stay competitive in the market. In this context, struct
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