The present work aims at handling uncertain materials in shape and topology optimisation applied to additive manufacturing. More specifically, we minimise an objective function combining the mean values of standard cost functions and assume that the uncertainties are small and generated by two random variables. These two variables representing the amplitude of the Young's modulus correspond to the zone of porosity inclusion and surface roughness defects. A deterministic approach that relies on a secondorder Taylor expansion of the cost function has been proposed by Allaire & Dapogny [2]. The present work proposes a general framework to handle uncertainties of the Young's modulus in which its amplitude is divided into N zones and then applied onto two zones corresponding to the porosity inclusion and surface roughness defects. We demonstrate the effectiveness of the approach in the context of the level-set-based topology optimisation for the robust compliance minimisation of three-dimensional cantilever test cases.
Abstract
The present work aims at handling uncertain materials in shape and topology optimisation applied to additive manufacturing. More specifically, we minimise an objective function combining the mean values of standard cost functions and assume that the uncertainties are small and [...]
Brick masonry is a multicomponent composite material, characterized by a marked inhomogeneity, a highly anisotropic behavior arising from the complex interactions between joints and bricks, and a considerable spatial variability of material properties, particularly relevant in the case of historical masonries. The focus of this paper is on the interdependence between the spatial variability of mechanical properties of joints and the overall homogenized response of a given volume element of masonry. It is assumed that mechanical properties of bed joints may vary according to a fixed probability distribution and correlation function and the mechanical response of the volume element is investigated in terms of the overall elastic stiffness. As confirmed by preliminary results, the spatial variability of the mechanical properties may affect the overall response of a masonry wall.
Abstract
Brick masonry is a multicomponent composite material, characterized by a marked inhomogeneity, a highly anisotropic behavior arising from the complex interactions between joints and bricks, and a considerable spatial variability of material properties, particularly [...]