Size-dependent optimal microstructure design based on couple-stress theory

Su, Wenzheng; Liu, Shutian

doi:10.1007/s00158-010-0484-z

Cited by 33 publications

(8 citation statements)

References 33 publications

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“…First, optimal microstructures for chiral microstructured materials, such as honeycombs, are obtained in the different regions of the body (see e.g. Su and Liu 2010). Then, homogenization techniques similar to those employed in Dendievel et al (1998), Fatemi et al (2003 can be used to obtain the macroscopic properties of the micropolar material equivalent to the microstructured medium.…”

Section: Applicationsmentioning

confidence: 99%

Topology optimization of three-dimensional non-centrosymmetric micropolar bodies

Veber

Taliercio

2011

Struct Multidisc Optim

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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

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Section: Applicationsmentioning

confidence: 99%

Topology optimization of three-dimensional non-centrosymmetric micropolar bodies

Veber

Taliercio

2011

Struct Multidisc Optim

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“…A usual strategy applied to bridge the two scales is designing an universal material microstructure at the local scale either for a fixed [5,6] or concurrently changed [7] structure at the macroscopic scale. Obviously, such designs have not yet released full potentiality of multiscale analysis.…”

Section: Introductionmentioning

confidence: 99%

Multiscale structural topology optimization with an approximate constitutive model for local material microstructure

Xia

Breitkopf

2015

Computer Methods in Applied Mechanics and Engineering

163

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“…In order to avoid the scale separation in the multiscale framework, Zhang and Sun 34 and Liu and Su 35,36 developed particular methods, such as the design element (DE) concept and couple-stress model, to capture the size effects of microstructures so as to perform scale-related design of materials and structures. Xie et al 37,38 compared the optimal design of material microstructures by a fully explicit meshing at the higher scale and by using the inverse homogenization method to establish a relationship between the two design models.…”

Section: Introductionmentioning

confidence: 99%

Design of heterogeneous mesostructures for nonseparated scales and analysis of size effects

Xia

2020

Int J Numer Methods Eng

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Scale separation is often assumed in most multiscale topology optimization frameworks. In this work, topology optimization of heterogeneous structures consisting of inseparable unit cells is studied. The cell morphology is given first and remains unchanged during the optimization process. A nonlocal numerical homogenization method is used to construct a mesoscopic constitutive relationship between the material and the structural scales. Topology optimization is performed on heterostructures at the higher mesoscale, and only based on a coarse grid for computational savings. Numerical studies show that the structural stiffness has been significantly improved compared to classical multiscale topology optimization using separation assumptions. However, there is still a size dependence of the optimal mesostructure related to the characteristic effect of the unit lattice.

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Size-dependent optimal microstructure design based on couple-stress theory

Cited by 33 publications

References 33 publications

Topology optimization of three-dimensional non-centrosymmetric micropolar bodies

Topology optimization of three-dimensional non-centrosymmetric micropolar bodies

Multiscale structural topology optimization with an approximate constitutive model for local material microstructure

Design of heterogeneous mesostructures for nonseparated scales and analysis of size effects

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