Concurrent topology optimization of composite macrostructure and microstructure constructed by constituent phases of distinct Poisson's ratios for maximum frequency

Fig. 1. Our two-scale topology optimization framework allows to optimize continuous material properties mapping to printable microstructures (lee) to fabricate high-resolution functional objects (middle) and minimum compliant structures (right). In this paper we present a novel two-scale framework to optimize the structure and the material distribution of an object given its functional specii-cations. Our approach utilizes multi-material microstructures as low-level building blocks of the object. We start by precomputing the material property gamut-the set of bulk material properties that can be achieved with all material microstructures of a given size. We represent the boundary of this material property gamut using a level set eld. Next, we propose an eecient and general topology optimization algorithm that simultaneously computes an optimal object topology and spatially-varying material properties constrained by the precomputed gamut. Finally, we map the optimal spatially-varying material properties onto the microstructures with the corresponding properties in order to generate a high-resolution print-able structure. We demonstrate the eecacy of our framework by designing, optimizing, and fabricating objects in diierent material property spaces on the level of a trillion voxels, i.e several orders of magnitude higher than what can be achieved with current systems.

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confidence: 99%

Two‐scale topology optimization for composite plates with in‐plane periodicity

Nishi

Terada

Kato

et al. 2017

“…Liu et al proposed a concurrent two‐scale topology optimization algorithm for maximizing natural frequency of structures using the BESO method. Long et al also proposed a concurrent topology optimization methodology for maximizing the frequency of composite macrostructure based on the microstructure with different Poisson's ratios. Zhao et al proposed a combined method of modal superposition with model order reduction (MOR) to optimize the large‐scale structures with proportional damping subjected to harmonic excitations.…”

Section: Introductionmentioning

confidence: 99%

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

Fan

Xiao

et al. 2020

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.

“…Multiscale topology optimization concepts are proposed to accompany with this new manufacturing technology . Different from the traditional topology optimization schemes which aim at seeking the best distributions with fixed solid materials, multiscale topology optimization can achieve the layout updating and the material change simultaneously . In this field, Rodrigues et al proposed a hierarchical computational procedure that integrates the global topology and local material design.…”

Section: Introductionmentioning

confidence: 99%

A novel reliability‐based topology optimization framework for the concurrent design of solid and truss‐like material structures with unknown‐but‐bounded uncertainties

Wang

Liang

et al. 2019

A new nonprobabilistic reliability-based topology optimization method for continuum structures with displacement constraints is proposed in this paper, in which the optimal layout consists of solid material and truss-like microstructure material simultaneously. The unknown-but-bounded uncertainties that exist in material properties, external loads, and safety displacements are considered. By utilizing the representative volume element analysis, rules of macro-micro stiffness performance equivalence can be confirmed. A solid material and truss-like microstructure material structure integrated design interpolation model is firstly constructed, in which design domain elements can be conducted to select solid material or truss-like microstructure material by a combination of the finite element method in the topology optimization process. Moreover, a new nonprobabilistic reliability measuring index, namely, the optimization feature distance is defined by making use of the area-ratio ideas. Furthermore, the adjoint vector method is employed to obtain the sensitivity information between the reliability measure and design variables. By utilizing the method of moving asymptotes, the investigated optimization problem can be iteratively solved. The effectiveness of the developed methodology is eventually demonstrated by two examples. KEYWORDS macro-micro stiffness performance equivalence, nonprobabilistic reliability-based topology optimization (NRBTO), the adjoint vector method, the representative volume element (RVE) analysis, unknown-but-bounded (UBB) uncertainties Int J Numer Methods Eng. 2019;119:239-260.wileyonlinelibrary.com/journal/nme