A level set-based structural optimization code using FEniCS

TL;DR

This paper introduces an educational FEniCS-based code utilizing the level set method for compliance minimization in structural optimization, emphasizing ease of implementation and adaptability to various PDEs and functionals.

Contribution

It provides a novel, accessible implementation of a level set-based structural optimization code using FEniCS, including extensions for compliant mechanisms.

Findings

Code successfully applied to classical topology optimization benchmarks.

Demonstrates ease of adaptation to different PDEs and functionals.

Facilitates understanding of shape derivatives and their computation.

Abstract

This paper presents an educational code written using FEniCS, based on the level set method, to perform compliance minimization in structural optimization. We use the concept of distributed shape derivative to compute a descent direction for the compliance, which is defined as a shape functional. The use of the distributed shape derivative is facilitated by FEniCS, which allows to handle complicated partial differential equations with a simple implementation. The code is written for compliance minimization in the framework of linearized elasticity, and can be easily adapted to tackle other functionals and partial differential equations. We also provide an extension of the code for compliant mechanisms. We start by explaining how to compute shape derivatives, and discuss the differences between the distributed and boundary expressions of the shape derivative. Then we describe the implementation in details, and show the application of this code to some classical benchmarks of topology optimization. The code is available at http://antoinelaurain.com/compliance.htm, and the main file is also given in the appendix.