Topology optimization of periodic lattice structures taking into account strain gradient

Da, Daicong; Yvonnet, Julien; Xia, Liang; Le, Minh Vuong; Li, Guangyao

doi:10.1016/j.compstruc.2018.09.003

Cited by 45 publications

(18 citation statements)

References 46 publications

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“…Unit cell A is composed of solid materials, except for the central hole, so the volume fraction of solid phase is f v = 60%; unit cell B is an anisotropy structure with four internal rectangles as void to meet the same volume fraction; unit cell C is an optimal microscopic cell for a fixed macrostructure based on the topology optimization scheme presented in the work. 42 (iii) 80 × 80. Therefore, these configurations correspond to the entirely of 80 × 80, 160 × 160, and 320 × 320 elements of the whole mesostructure, respectively.…”

Section: A Heterogeneous Double-clamped Beammentioning

confidence: 99%

“…The beam size is L × H = 2 × 1, as in the referred work. 42 Three different representative unit cells are considered as shown in the second row of Figure 6. Unit cells A and B have circle and rectangular regions as empty phase, respectively, to meet the volume fraction of 60% of solid phase, while unit cell C is obtained by the topological design procedure in Reference 42 for a fixed cantilever beam with the same volume of the solid phase.…”

Section: A Heterogeneous Cantilevermentioning

confidence: 99%

“…More recently, a filter-based nonlocal homogenization method 40,41 is introduced to multiscale topological design of periodic microstructures without scale separation. 42 The method uses a coarse mesh corresponding to a homogenized medium taking into strain gradient through a nonlocal numerical homogenization method.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: A Heterogeneous Double-clamped Beammentioning

confidence: 99%

Section: A Heterogeneous Cantilevermentioning

confidence: 99%

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

Xia

2020

Int J Numer Methods Eng

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“…Due to the scale separation assumption of homogenization method, the result designed by this method is not manufacturable in practices . To break through this barrier between manufacturing and multiscale topology optimization, many related research works have sought the topology method integrated manufacturing from the design of microstructure.…”

Section: Introductionmentioning

confidence: 99%

The substructuring‐based topology optimization for maximizing the first eigenvalue of hierarchical lattice structure

Fan

Xiao

et al. 2020

Numerical Meth Engineering

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Summary This work presents a generalized substructuring‐based topology optimization method for the design hierarchical lattice structures to maximize the first eigenvalue. In this method, the macrostructure is assumed to be composed of substructures with a common artificial lattice geometry pattern. And two different yet connected scales are considered through a lattice geometry feature parameter. The feature parameter, which can control the material distribution of the substructure, determines the relative density of corresponding substructure. Each substructure is condensed into a super‐element to obtain the associated density‐related matrices. A surrogate model using cubic spline interpolation has been particularly built to map the density to stiffness and mass matrices of condensed super‐elements. The derivatives of super‐element matrices to the associated densities can be evaluated efficiently and accurately. Here, an augmented penalized density for this surrogate model is introduced. And the conventional optimality criteria method is selected as updating method of the density design variables. Numerical examples under two lattice patterns of substructures are shown to validate the correctness and superiority of this substructure‐based topology optimization method.

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“…Xia reviewed the recent advances of designing multiscale structural modeling of nonlinear structure. Yvonnet et al proposed a topology optimization for lattice structures in the case of nonseparated scales, where a nonlocal numerical homogenization method is implemented. A compacted and efficient MATLAB code is presented in for the concurrent topology optimization of multiscale composite structures from two‐dimensional to three‐dimensional designs using energy‐based homogenization method.…”

Section: Introductionmentioning

confidence: 99%

Linear and nonlinear topology optimization design with projection‐based ground structure method (P‐GSM)

Deng

2020

Numerical Meth Engineering

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A new topology optimization scheme called the projection-based ground structure method (P-GSM) is proposed for linear and nonlinear topology optimization designs. For linear design, compared to traditional GSM which are limited to designing slender members, the P-GSM can effectively resolve this limitation and generate functionally graded lattice structures. For additive manufacturing-oriented design, the manufacturing abilities are the key factors to constrain the feasible design space, for example, minimum length and geometry complexity. Conventional density-based method, where each element works as a variable, always results in complex geometry with large number of small intricate features, while these small features are often not manufacturable even by 3D printing and lose its geometric accuracy after postprocessing. The proposed P-GSM is an effective method for controlling geometric complexity and minimum length for optimal design, while it is capable of designing self-supporting structures naturally. In optimization progress, some bars may be disconnected from each other (floating in the air). For buckling-induced design, this issue becomes critical due to severe mesh distortion in the void space caused by disconnection between members, while P-GSM has ability to overcome this issue. To demonstrate the effectiveness of proposed method, three different design problems ranging from compliance optimization to buckling-induced mechanism design are presented and discussed in details. K E Y W O R D Sbuckling-induced design, functionally graded lattice, projection-based ground structure method, self-support design, topology optimization

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Topology optimization of periodic lattice structures taking into account strain gradient

Cited by 45 publications

References 46 publications

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

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

The substructuring‐based topology optimization for maximizing the first eigenvalue of hierarchical lattice structure

Linear and nonlinear topology optimization design with projection‐based ground structure method (P‐GSM)

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