TopOpt.jl is a topology optimisation package written in pure Julia. Topology optimisation is an exciting field at the intersection of shape representation, physics simulations and mathematical optimisation, and the Julia language is a great fit for this field. To learn more about TopOpt.jl, check the following JuliaCon talk.
The following is a tentative list of projects in topology optimisation that you could be working on in the coming Julia Season of Contributions or Google Summer of Code. If you are interested in exploring any of these topics or if you have other interests related to topology optimisation, please reach out to the main mentor Mohamed Tarek via email.
Project difficulty: Easy to Medium
Work load: 175 or 350 hours
Description: There are numerous ways to use machine learning for design optimisation in topology optimisation. The following are all recent papers with applications of neural networks and machine learning in topology optimisation. There are also exciting research opportunities in this direction.
DNN-based Topology Optimisation: Spatial Invariance and Neural Tangent Kernel
NTopo: Mesh-free Topology Optimization using Implicit Neural Representations
TONR: An exploration for a novel way combining neural network with topology optimization
In this project you will implement one of the algorithms discussed in any of these papers.
Knowledge prerequisites: neural networks, optimisation, Julia programming
Project difficulty: Easy
Work load: 175 hours
Description: There are some topology optimisation formulations that enable the optimisation of the shape of the structure and the material selected simultaneously. In this project, you will implement some multi-material design optimisation formulations, e.g. this paper has a relatively simple approach to integrate in TopOpt.jl. Other methods include using mixed integer nonlinear programming from Nonconvex.jl to select materials in different parts of the design.
Knowledge prerequisites: basic optimisation, Julia programming
Project difficulty: Medium
Work load: 350 hours
Description: Currently in TopOpt.jl, there are only unstructured meshes supported. This is a very flexible type of mesh but it's not as memory efficient as uniform rectilinear grids where all the elements are assumed to have the same shape. This is the most common grid used in topology optimisation in practice. Currently in TopOpt.jl, the uniform rectilinear grid will be stored as an unstructured mesh which is unnecessarily inefficient. In this project, you will optimise the finite element analysis and topology optimisation codes in TopOpt.jl for uniform rectilinear grids.
Knowledge prerequisites: knowledge of mesh types, Julia programming
Project difficulty: Medium
Work load: 350 hours
Description: Topology optimisation problems with more mesh elements take longer to simulate and to optimise. In this project, you will explore the use of adaptive mesh refinement starting from a coarse mesh, optimising and only refining the elements that need further optimisation. This is an effective way to accelerate topology optimisation algorithms.
Knowledge prerequisites: adaptive mesh refinement, Julia programming
Project difficulty: Medium
Work load: 175 or 350 hours
Description: All of the examples in TopOpt.jl and problem types are currently of the linear elasticity, quasi-static class of problems. The goal of this project is to implement more problem types and examples from the field of heat transfer. Both steady-state heat transfer problems and linear elasticity problems make use of elliptic partial differential equations so the code from linear elasticity problems should be largely reusable for heat transfer problems with minimum changes.
Knowledge prerequisites: finite element analysis, heat equation, Julia programming