Topology optimization of three-dimensional non-centrosymmetric micropolar bodies

Abstract

The topology optimization problem for linearly elastic micropolar solids is dealt with. The constituent materials are supposed to lack in general of centro-symmetry, which means that force stresses and microcurvatures are coupled, and so are couple stresses and micropolar strains. The maximum global stiffness is taken as objective function. According to the SIMP model, the constitutive tensors are assumed to be smooth functions of the design variable, that is, the material density. Optimal material distributions are obtained for several significant three-dimensional cases. The differences respect to the optimal configurations obtained with classical Cauchy materials and centrosymmetric materials are pointed out. The influence of the constants defining the non-centrosymmetric behaviour on the optimal configurations is discussed

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

“…This is in agreement with results reported for the minimum compliance formulation, see e.g. Veber & Taliercio (2011). To perform the maximization of the output displacement, regions connecting the 45-degree inclined bars to the remaining part of the design get thinner for increasing values of ℓ.…”

“…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.…”

Topology optimization of periodic beam lattices using Cosserat elasticity

“…Parameter studies have been conducted to investigate the effect of the intrinsic length [27,52,41,5,38], the fundamental eigenfrequencies [13,60,61], the Cosserat shear modulus [17], and even 3D non-centrosymmetricity [64]. A majority of the investigations were based on the use of the SIMP and the level set methods to obtain the results.…”

The effect of non-locality (or size-dependency) on optimum topologies (or material layouts)

“…contain different operators while preserving the primal fields of classical theory. Despite their popularity in describing the overall mechanical response of complex structures, till now only limited number of works have targeted their effect on structural optimization problem [8,9,10,11,12,13,14,15,16,17,18].…”