Optimisation of fractal spaceframes under gentle compressive load

The complexity and unpredictability of postbuckling responses in even simple thin shells have raised great challenges to emerging technologies exploiting buckling transitions. Here we comprehensively survey the buckling landscapes to show the full complexity of the stable buckling states and the transition mechanisms between each of them. This is achieved by combining a simple and versatile triangulated lattice model for modelling the shell morphologies with efficient high-di...

Hierarchy seems to pervade complexity in both living and artificial systems. Despite its relevance, no general theory that captures all features of hierarchy and its origins has been proposed yet. Here we present a formal approach resulting from the convergence of theoretical morphology and network theory that allows constructing a 3D morphospace of hierarchies and hence comparing the hierarchical organization of ecological, cellular, technological and social networks. Embedd...

Framework materials and their deformations provide a compelling relation between materials science and algebraic geometry. Physical distance constraints within the material transform into polynomial constraints, making algebraic geometry and associated numerical strategies feasible for finding equilibrium configurations and deformation pathways. In this paper, we build the necessary geometric formulations and numerical strategies to explore the mechanics of two examples of 3-...

The quest for novel designs for lightweight phononic crystals and elastic metamaterials with wide lowfrequency band gaps has proven to be a significant challenge in recent years. In this context, lattice-type materials represent a promising solution, providing both lightweight properties and significant possibilities of tailoring mechanical and dynamic properties. Additionally, lattice structures also enable the generation of hierarchical architectures, in which basic constit...

We present a multi-phase design parameterization to obtain optimized heterogeneous lattice structures. The 3D domain is discretized into a cubical grid wherein each cube has eight distinct unit cell types or phases. When all phases are present, the domain resembles a densely connected ground structure. The cross-section area of beam segments in lattice units, modelled using Timoshenko beam theory, are the design variables. All beam segments in a particular lattice phase have ...

We consider the shape and topology optimization problem to design a structure that minimizes a weighted sum of material consumption and (linearly) elastic compliance under a fixed given boundary load. As is well-known, this problem is in general not well-posed since its solution typically requires the use of infinitesimally fine microstructure. Therefore we examine the effect of singularly perturbing the problem by adding the structure perimeter to the cost. For a uniaxial an...

This paper presents a simple method of calculating the Hausdorff dimension for a class of non-conformal fractals.

A way to add an extra dimension is briefly discussed.

A collection of thin structures buckle, bend, and bump into each-other when confined. This contact can lead to the formation of patterns: hair will self-organize in curls; DNA strands will layer into cell nuclei; paper, when crumpled, will fold in on itself, forming a maze of interleaved sheets. This pattern formation changes how densely the structures can pack, as well as the mechanical properties of the system. How and when these patterns form, as well as the force required...

Fractals are ubiquitous natural emergences that have gained increased attention in engineering applications, thanks to recent technological advancements enabling the fabrication of structures spanning across many spatial scales. We show how the geometries of fractals can be exploited to determine their important mechanical properties, such as the first and second moments, which physically correspond to the center of mass and the moment of inertia, using a family of complex fr...