Giga-voxel computational morphogenesis for structural design

Abstract

In the design of industrial products ranging from hearing aids to automobiles and aeroplanes, material is distributed so as to maximize the performance and minimize the cost. Historically, human intuition and insight have driven the evolution of mechanical design, recently assisted by computer-aided design approaches. The computer-aided approach known as topology optimization enables unrestricted design freedom and shows great promise with regard to weight savings, but its applicability has so far been limited to the design of single components or simple structures, owing to the resolution limits of current optimization methods. Here we report a computational morphogenesis tool, implemented on a supercomputer, that produces designs with giga-voxel resolution-more than two orders of magnitude higher than previously reported. Such resolution provides insights into the optimal distribution of material within a structure that were hitherto unachievable owing to the challenges of scaling up existing modelling and optimization frameworks. As an example, we apply the tool to the design of the internal structure of a full-scale aeroplane wing. The optimized full-wing design has unprecedented structural detail at length scales ranging from tens of metres to millimetres and, intriguingly, shows remarkable similarity to naturally occurring bone structures in, for example, bird beaks. We estimate that our optimized design corresponds to a reduction in mass of 2-5 per cent compared to currently used aeroplane wing designs, which translates into a reduction in fuel consumption of about 40-200 tonnes per year per aeroplane. Our morphogenesis process is generally applicable, not only to mechanical design, but also to flow systems, antennas, nano-optics and micro-systems.

Eigenvalue topology optimization via efficient multilevel solution of the frequency response

“…The approach was here tested in a simple MATLAB implementation, limiting the testing to moderately large problems. Future studies will include testing the approach in a parallel PETSc‐based framework to evaluate its potential for solving truly large problems, cf, up to a billion elements . Other future studies will address improvement of the robustness of the method for situations where a large number of eigenvalues are coalescing.…”

Topology optimization of fusiform muscles with a maximum contraction

“…The widely accepted Wolff's law asserts that the internal trabecular bone adapts to external loadings, reorienting with the principal stress trajectories to maximize mechanical efficiency creating a naturally optimum structure. Previous studies have discovered remarkable similarities between the optimized topology of deformation minimized problem and naturally occurring bone structures . Whether or not the remarkable similarities can be discovered between the optimized topology and naturally occurring muscle structures is unknown.…”

A phase field model for stress‐based evolution of load‐bearing structures

“…Numerical methods have become great practical importance in corresponding optimization problems. The material distribution concepts from Bendsøe and Kikuchi have inspired many methods in this branch of mechanics, eg, see other works . Review articles on different approaches are given in other works …”