Design optimization by multiscale lacunarity structures – ITERATE

Saving energy by designing lighter objects while maintaining high mechanical properties is a crucial issue for industry. In this context, we are proposing a new object design solution, subject to a set of mechanical and / or thermal constraints This solution exploits materials whose lacunar structure is multi-scale and resulting from fractal geometry. These structures, present in nature, are often results of natural selection processes leading to optimal solutions. Similar tree structures appear during topological optimization processes, such as for the design of aircraft wing structures, or in the case of constrained problems.
The objective of this project is to develop a topological optimization method using multi-scale lacunar structures. We focus on the mechanical and thermal properties of objects. Our method will be applied to three specific examples of real cases. The validation of the concept will be conducted, on the one hand, by comparing the results of numerical simulation of our method with those of conventional approaches, and on the other hand, by manufacturing optimized structures and by carrying out physical tests.
The expected results are of different natures.
First of all, from a practical point of view, we hope to be able to propose new structures with a material gain ranging from 40% to 70%. We also expect to obtain a "better behavior" of the prototypes in comparison with the classical optimization results, in the face of stresses not initially foreseen, such as: additional mechanical stresses; extreme stresses (destruction); acoustic and thermal insulation. For injection shaping tools, we hope to significantly reduce the warm-up time (saving in production time and energy).
From a methodological point of view, this project will enrich our knowledge on the properties of multi-scale structures. This will allow us to identify operating cases or situations standard in which we can directly propose efficient predefined geometries without having to go through optimization phases. On the other hand, the objective of this project is linked to the exploitation of a set of tools: iterative geometric modeler, homogenization method, optimization algorithm. The experience acquired through the development of these tools and their interoperability will make it possible to develop and propose new approaches to solving design problems. This knowledge can be capitalized in the form of an engineering service or directly in a Computer Aided Engineering (CAE) software suite.
Finally, from a theoretical point of view, we expect several results. We propose to develop a homogenization method for multi-scale lacunar structures exploiting the invariance property by change of scale. These results will allow a significant gain in computation time during the optimization phases. The geometric model, currently used to describe and manipulate multi-scale lacunar shapes, will be extended to deal with: integration and resolution of additive manufacturing constraints; defining and solving differential constraints on structures; the analysis of space subdivisions for the generation of new multi-scale gap structures; the construction of a connection between incompatible multi-scale structures