Multiscale isogeometric topology optimization for lattice materials

Wang, Yingjun; Xu, Hang; Pasini, Damiano

doi:10.1016/j.cma.2016.08.015

Cited by 203 publications

(88 citation statements)

References 56 publications

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“…The optimization of periodic microstructure for composite materials is an old topic, still very active, see e.g. [5], [6], [7], [16], [21], [30], [31], [33], [34]. Typically, the properties of the microstructures are homogenized (or averaged), then parametrized in order to optimize only a few scalar fields.…”

Section: -D Topology Optimization Of Modulated and Oriented Periodicmentioning

confidence: 99%

3-d topology optimization of modulated and oriented periodic microstructures by the homogenization method

Geoffroy-Donders

Allaire

Pantz³

2020

Journal of Computational Physics

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This paper is motivated by the optimization of so-called lattice materials which are becoming increasingly popular in the context of additive manufacturing. Generalizing our previous work in 2-d we propose a method for topology optimization of structures made of periodically perforated material, where the microscopic periodic cell can be macroscopically modulated and oriented. This method is made of three steps. The first step amounts to compute the homogenized properties of an adequately chosen parametrized microstructure (here, a cubic lattice with varying bar thicknesses). The second step optimizes the homogenized formulation of the problem, which is a classical problem of parametric optimization. The third, and most delicate, step projects the optimal oriented microstructure at a desired length scale. Compared to the 2-d case where rotations are parametrized by a single angle, to which a conformality constraint can be applied, the 3-d case is more involved and requires new ingredients. In particular, the full rotation matrix is regularized (instead of just one angle in 2-d) and the projection map which deforms the square periodic lattice is computed component by component. Several numerical examples are presented for compliance minimization in 3-d.

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Section: -D Topology Optimization Of Modulated and Oriented Periodicmentioning

confidence: 99%

3-d topology optimization of modulated and oriented periodic microstructures by the homogenization method

Geoffroy-Donders

Allaire

Pantz³

2020

Journal of Computational Physics

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“…87 During the last few years, there has been a surge of interest in the application of different variations of (topology) optimization algorithms to AM in general and to the problem of designing optimal lattice structures in particular. 27,28,[88][89][90][91][92][93][94][95][96][97] As a result of this fundamental research, it is expected that optimal solutions and more mature algorithms will emerge in the near future that could be also benefit the topological design of AM porous biomaterials.…”

Section: Topology Optimizationmentioning

confidence: 99%

Additively manufactured porous metallic biomaterials

Zadpoor

2019

J. Mater. Chem. B

166

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“…The problem of unconnected material among lattices is solved. Wang et al presented a periodic lattice materials optimization method in isogeometric analysis. The accuracy and efficiency of this method is studied in detail.…”

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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Multiscale isogeometric topology optimization for lattice materials

Cited by 203 publications

References 56 publications

3-d topology optimization of modulated and oriented periodic microstructures by the homogenization method

3-d topology optimization of modulated and oriented periodic microstructures by the homogenization method

Additively manufactured porous metallic biomaterials

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

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