A MATLAB code for topology optimization using the geometry projection method
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EDUCATIONAL PAPER
A MATLAB code for topology optimization using the geometry projection method Hollis Smith 1 & Julián A. Norato 1 Received: 19 December 2019 / Revised: 29 January 2020 / Accepted: 14 February 2020 # The Author(s) 2020
Abstract This work introduces a MATLAB code to perform the topology optimization of structures made of bars using the geometry projection method. The primary objective of this code is to make available to the structural optimization community a simple implementation of the geometry projection method that illustrates the formulation and makes it possible to easily and efficiently reproduce results. A guiding principle in writing the code is modularity, so that researchers can easily modify the program for their own purposes. Another goal is efficiency, for which extensive use of vectorization is made. This paper details the formulation of the geometry projection, discusses implementation aspects of the code, and demonstrates some of its capabilities by presenting several 2D and 3D compliance minimization examples. Keywords Topology optimization . Geometry projection
1 Introduction The prevalent techniques to perform topology optimization of continua are the density-based and the level-set methods (Sigmund and Maute 2013). These techniques produce organic designs that are highly efficient. In some cases, a design that closely follows the optimal topology can be manufactured using, for example, additive manufacturing or casting techniques. However, when the most economical fabrication process consists of joining stock material such as bars or plates, it can be very difficult to translate the optimal topology into a design that conforms to that process. This difficulty has motivated the development of topology optimization techniques that produce designs exclusively made of geometric primitives. One of the topology optimization techniques that render designs made of geometric components is the geometry This work was supported by the U.S. Office of Naval Research, Grant Number N00014-17-1-2505. Responsible Editor: Xu Guo * Julián A. Norato [email protected] 1
The University of Connecticut, 191 Auditorium Road, U-3139, Storrs, CT 06269, USA
projection method (GPM) (Bell et al. 2012; Norato et al. 2004, 2015). There exist other techniques to perform topology optimization using geometric components, such as the moving morphable components method (Guo et al. 2014; Zhang et al. 2016b); a review of these techniques is outside of the scope of this paper; and we refer the reader to the recent review by Wein et al. (2019). The purpose of this work is to introduce a MATLAB code to illustrate the GPM for the topology optimization of 2D and 3D structures made of bars. The GPM is described in detail in Section 2. In particular, we aim to demonstrate how the geometry mapping can be performed in an efficient manner using vectorized operations. Unlike other educational codes published in this journal, we do not attempt to fit the code into a relatively low number of lines and include it in the
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