Optimal topologies for micropolar solids

Topology optimization of three-dimensional non-centrosymmetric micropolar bodies

“…If the block consists of a micropolar centrosymmetric material, curved beams (exploiting the inherent material flexural stiffness) characterize the optimal configuration (see Figs. 4b,5b), conforming with the findings obtained by other authors for 2D micropolar bodies (Rovati and Veber 2007;Liu and Su 2010). In both cases the optimal configurations match the problem symmetry.…”

“…to Olhoff 1981, Sigmund 2001). As the main scope of the present work is to analyze the influence of the physical and mechanical parameters on the optimal solution for micropolar continua, a complete treatment of the formulation of the problem discretized by finite elements is not reported: for a detailed discussion, refer to Rovati and Veber (2007).…”

“…Some preliminary examples dealing with solids with more complex load conditions were presented in Veber and Taliercio (2010); others are left for a future paper, with a more applicative slant. The coupling between normal force stresses and microcurvatures is likely to lead to optimal configurations much different from those obtained for centrosymmetric solids in bending (see Rovati and Veber 2007) or torsion, as different contributions concur to the structural stiffness. The emphasis here has been mainly put on the extension of the approach to the optimal topology problem based on the SIMP method to non-centrosymmetric materials, rather than on the effects of the boundary conditions on the optimal topology.…”

“…Recently, non conventional solid models (Cosserat or micropolar materials) have been dealt with (Rovati and Veber 2007;Liu and Su 2010). Employing complex continuum models incorporating non-local effects is believed to lead to useful result in important fields such as nano and microtechnologies, biomechanics and tissue engineering.…”

Synthesis of auxetic structures using optimization of compliant mechanisms and a micropolar material model

“…A conventional formulation minimizes the socalled structural compliance to achieve the stiffest layout using a limited amount of material (Bendsøe & Kikuchi 1988). Rovati & Veber (2007), Liu & Su (2010) and Veber & Taliercio (2011) firstly embedded the Cosserat continuum model in this formulation showing that trusslike layouts can be replaced by bending-resistant layouts depending on the value of the characteristic length. This was later confirmed by Bruggi & Taliercio (2012) and Su & Liu (2015), dealing with a min-max problem involving the natural frequencies of micropolar bodies.…”