Topology optimization of piezoelectric nanostructures

Nanthakumar, S.S.; Lahmer, Tom; Zhuang, Xiaoying; Park, Harold S.; Rabczuk, Timon

doi:10.1016/j.jmps.2016.03.027

Cited by 84 publications

(33 citation statements)

References 43 publications

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“…Topology optimization is a widely used computational method for generating optimal structural designs by systematically distributing material throughout a two-or three-dimensional working domain. The method was first proposed by Bendsøe and Kikuchi [1] in 1988 and has been used to solve a wide variety of problems, from the design of piezoelectric nanostructures [2] to synthesis of bistable viscoelastic systems [3]. The method relies upon finite element analysis to discretize the working domain and model the mechanical response of the structure.…”

Section: Introductionmentioning

confidence: 99%

An Artificial Neural Network Approach for Generating High-Resolution Designs From Low-Resolution Input in Topology Optimization

Napier

Sriraman

Tran

et al. 2019

Journal of Mechanical Design

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We address a central issue that arises within element-based topology optimization. To achieve a sufficiently well-defined material interface, one requires a highly refined finite element mesh; however, this leads to an increased computational cost due to the solution of the finite element analysis problem. By generating an optimal structure on a coarse mesh and using an artificial neural network to map this coarse solution to a refined mesh, we can greatly reduce computational time. This approach resulted in time savings of up to 85% for test cases considered. This significant advantage in computational time also preserves the structural integrity when compared with a fine-mesh optimization with limited error. Along with the savings in computational time, the boundary edges become more refined during the process, allowing for a sharp transition from solid to void. This improved boundary edge can be leveraged to improve the manufacturability of the optimized designs.

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Section: Introductionmentioning

confidence: 99%

An Artificial Neural Network Approach for Generating High-Resolution Designs From Low-Resolution Input in Topology Optimization

Napier

Sriraman

Tran

et al. 2019

Journal of Mechanical Design

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“…Recently, an innovative type of topology optimization method coined “discontinuity layout optimization (DLO)” was presented in Smith and Gilbert, which determines the critical layout of discontinuities and associated upper‐bound limit load for the plane (2D) and 3‐dimensional (3D) plasticity problems. By introducing a great amount of potential discontinuities, the layout of activated discontinuity will be automatically obtained by solving the corresponding linear programming (LP) and second‐order cone programming problems.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of shotcrete supported crown of NATM tunnels with discontinuity layout optimization

Zhang

Zhuang

Lackner

2018

Num Anal Meth Geomechanics

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Summary For tunnel constructed by New Austrian Tunnelling Method, the crown is the upper part of tunnel section, constructed during excavation process and supported by shotcrete. The stability of the crown has great influence on the safety of tunnel itself and the buildings above, which correlates, among others, with geometrical setup of tunnel and material properties of shotcrete and soil/rock. In this paper, aiming at analyzing the stability of shotcrete supported crown, a recently presented numerical method discontinuity layout optimization is adopted, which introduces a great amount of potential discontinuities cross over one another and provides a wide search space for efficient upper limit analysis. In the analysis, a well‐established hydration model of cementitious material is implemented for accounting the hydration of shotcrete. Then assumptions based on convergence‐confinement method are used for accounting the 3‐dimensional effect in 2‐dimensional analysis, finally providing time‐space–dependent assessments of stability of shotcrete supported crown.

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“…Recent efforts incorporating geometrical non-linearity and manufacturability constraint in the design optimization can be found in the works of Wang et al [33] and Clausen et al [34], with the resulting structures having high geometrical simplicity, design flexibility, and manufacturability. Other design techniques for molecular structures and multi-scale problems can be found in [35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Isogeometric shape optimization of smoothed petal auxetic structures via computational periodic homogenization

Wang

Poh

Dirrenberger

et al. 2017

Computer Methods in Applied Mechanics and Engineering

117

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International audienceAn important feature that drives the auxetic behaviour of the star-shaped auxetic structures is the hinge-functional connection at the vertex connections. This feature poses a great challenge for manufacturing and may lead to significant stress concentrations. To overcome these problems, we introduced smoothed petal-shaped auxetic structures, where the hinges are replaced by smoothed connections. To accommodate the curved features of the petal-shaped auxetics, a parametrisation modelling scheme using multiple NURBS patches is proposed. Next, an integrated shape design frame work using isogeometric analysis is adopted to improve the structural performance. To ensure a minimum thickness for each member, a geometry sizing constraint is imposed via piece-wise bounding polynomials. This geometry sizing constraint, in the context of isogeometric shape optimization, is particularly interesting due to the non-interpolatory nature of NURBS basis. The effective Poisson ratio is used directly as the objective function, and an adjoint sensitivity analysis is carried out. The optimized designs – smoothed petal auxetic structures – are shown to achieve low negative Poisson’s ratios, while the difficulties of manufacturing the hinges are avoided. For the case with six petals, an in-plane isotropy is achieved

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Topology optimization of piezoelectric nanostructures

Cited by 84 publications

References 43 publications

An Artificial Neural Network Approach for Generating High-Resolution Designs From Low-Resolution Input in Topology Optimization

An Artificial Neural Network Approach for Generating High-Resolution Designs From Low-Resolution Input in Topology Optimization

Stability analysis of shotcrete supported crown of NATM tunnels with discontinuity layout optimization

Isogeometric shape optimization of smoothed petal auxetic structures via computational periodic homogenization

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