Concurrent topology optimization for minimizing frequency responses of two-level hierarchical structures

Vicente, William; Zuo, Zhi Hao; Pavanello, Renato; Calixto, Tainan Khalil Leite; Picelli, Renato; Xie, Yi Min

doi:10.1016/j.cma.2015.12.012

Cited by 115 publications

(39 citation statements)

References 50 publications

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“…This method depends on the method of numerical material testing to determine a single topology within a fixed macrostructural topology. A hierarchical approach is also taken by Vicente et al [14] to determine a macrostructural topology that minimizes the eigenfrequencies of the macrostructure based on the optimization of a single microstructural topology. Additional recent progress in multi-scale topology optimization methods are presented in Yan et al [15], Xia and Breitkopf [16,17], Long et al [18], and Da et al [19].…”

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confidence: 99%

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

Nishi

Terada

Kato

et al. 2017

Numerical Meth Engineering

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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

Numerical Meth Engineering

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“…Moreover, Niu, Yan, and Cheng 2009 also observed that the structure without porosity on micro-scale has higher fundamental frequency than the structure with porosity on micro-scale. A similar viewpoint is expressed in literature Vicente et al 2016 . Taken minimized frequency response as the objective, under the BESO framework, Vicente et al 2016 revealed that the fully solid material structure has a better result compared to the structure consisted of porous microstructure.…”

Section: Introductionmentioning

confidence: 54%

Two-scale topology optimization of macrostructure and porous microstructure composed of multiphase materials with distinct Poisson’s ratios

Jia

Cheng

Long

2018

Lat. Am. j. solids struct.

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Negative Poisson's ratio NPR material attracts a lot of attentions for its unique mechanical properties. However, achieving NPR is at the expense of reducing Young's modulus. It has been observed that the composite stiffness can be enhanced when blending positive Poisson's ratio PPR material into NPR material. Based on the respective interpolation of Young's modulus and Poisson's ratio, two concurrent topology optimization problems with different types of constraints, called Problem A and B, are respectively discussed to explore the Poisson's ratio effect in porous microstructure. In Problem A, the volume constraints are respectively imposed on macro and micro structures; in Problem B, besides setting an upper bound on the total available base materials, the micro thermal insulation capability is considered as well. Besides considering the influence of micro thermal insulation capability on the optimized results in Problem B, the similar and dissimilar influences of Poisson's ratios, volume fractions in Problem A and B are also investigated through several 2D and 3D numerical examples. It is observed that the concurrent structural stiffness resulting from the mixture of PPR and NPR base materials can exceed the concurrent structural stiffness composed of any individual base material.

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“…[20][21][22][23][24]. These studies show that CTO can evidently extend the design space than those using the single-scale based approaches, and further improve the structural performances, such as compliance [12], dynamic compliance [25], natural frequency [8,26] and frequency responses [27].…”

Section: Introductionmentioning

confidence: 97%

Robust concurrent topology optimization of structure and its composite material considering uncertainty with imprecise probability

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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This paper studied a robust concurrent topology optimization (RCTO) approach to design the structure and its composite materials simultaneously. For the first time, the material uncertainty with imprecise probability is integrated into the multi-scale concurrent topology optimization (CTO) framework. To describe the imprecise probabilistic uncertainty efficiently, the type I hybrid interval random model is adopted. An improved hybrid perturbation analysis (IHPA) method is formulated to estimate the expectation and stand variance of the objective function in the worst case. Combined with the bi-directional evolutionary structural optimization (BESO) framework, the robust designs of the structure and its composite material are carried out. Several 2D and 3D numerical examples are presented to illustrate the effectiveness of the proposed method. The results show that the proposed method has high efficiency and low precision loss. In addition, the proposed RCTO approach remains efficient in both of linear static and dynamic structures, which shows its extensive adaptability.where J Y and J Y denote the lower and upper bounds of interval vector J Y . The symbol m J Y is the mean value of J Y , which can be calculated by averaging the lower and upper bounds value as shown in Eq. (16b). I J Y denotes the variation interval of J Y , which depends on the difference of the lower and upper bound values as shown in Eq. (16c). The deviation J Y  of the symmetrical interval can be acquired by averaging the upper and lower bounds of J Y as shown in Eq. (16d). In the combined form, the J-th hybrid interval random parameter( ) JJ X Y can be formulated as RCTO Volume fraction of solid: 95.6% Volume fraction of Phase 1: 70.3% DCTO Volume fraction of solid: 95.1% Volume fraction of phase 1: 70.7% 33 (b) Macrostructure Micro base-cell Composite material Phase 1 only RCTO Volume fraction of solid: 93.0% Volume fraction of phase 1: 72.4% DCTO Volume fraction of solid: 92.7% Volume fraction of phase 1: 72.7% (c) Macrostructure Micro base-cell Composite material Phase 1 only RCTO Volume fraction of solid: 90.4% Volume fraction of phase 1: 74.9% DCTO Volume fraction of solid: 88.9% Volume fraction of phase 1: 76.3%JJ J ee JJ J J J J e J J e J J JJ J e e J J J J J J J J e J J e 2 2 J J J J JK J e e J J J J J J J J J J J J J e J J JJ JJ e J J J J JJ J J e J J J J e JJ e J J J J 3m d I e J J J J x X X e J J e J J e J J e J J e J J e J J e e e e J J J J e J J J J e J J J J H T A a J J J J H a J J J J pT A J J J J A e J J J J A e J J J J J J J J a i A Y J J J J p a i A Y J J J J a i J J J J a i A Y J J J J p a i A Y J J J J Ne ia A i J J J J a i J J J J Ne ia A i J J J J

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Concurrent topology optimization for minimizing frequency responses of two-level hierarchical structures

Cited by 115 publications

References 50 publications

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

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

Two-scale topology optimization of macrostructure and porous microstructure composed of multiphase materials with distinct Poisson’s ratios

Robust concurrent topology optimization of structure and its composite material considering uncertainty with imprecise probability

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