Generalized Geometry Projection: A Unified Approach for Geometric Feature Based Topology Optimization

摘要

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.