## Details

Originalsprache | Englisch |
---|---|

Seiten (von - bis) | 79-87 |

Seitenumfang | 9 |

Fachzeitschrift | Computers, Materials and Continua |

Jahrgang | 59 |

Ausgabenummer | 1 |

Publikationsstatus | Veröffentlicht - 2019 |

## Abstract

In this study, machine learning representation is introduced to evaluate the flexoelectricity effect in truncated pyramid nanostructure under compression. A NonUniform Rational B-spline (NURBS) based IGA formulation is employed to model the flexoelectricity. We investigate 2D system with an isotropic linear elastic material under plane strain conditions discretized by 45×30 grid of B-spline elements. Six input parameters are selected to construct a deep neural network (DNN) model. They are the Young's modulus, two dielectric permittivity constants, the longitudinal and transversal flexoelectric coefficients and the order of the shape function. The outputs of interest are the strain in the stress direction and the electric potential due flexoelectricity. The dataset are generated from the forward analysis of the flexoelectric model. 80% of the dataset is used for training purpose while the remaining is used for validation by checking the mean squared error. In addition to the input and output layers, the developed DNN model is composed of four hidden layers. The results showed high predictions capabilities of the proposed method with much lower computational time in comparison to the numerical model.

## ASJC Scopus Sachgebiete

- Werkstoffwissenschaften (insg.)
**Biomaterialien**- Mathematik (insg.)
**Modellierung und Simulation**- Ingenieurwesen (insg.)
**Werkstoffmechanik**- Informatik (insg.)
**Angewandte Informatik**- Ingenieurwesen (insg.)
**Elektrotechnik und Elektronik**

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- BibTex
- RIS

**Computational machine learning representation for the flexoelectricity effect in truncated pyramid structures.**/ Hamdia, Khader M.; Ghasemi, Hamid; Zhuang, Xiaoying et al.

in: Computers, Materials and Continua, Jahrgang 59, Nr. 1, 2019, S. 79-87.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

*Computers, Materials and Continua*, Jg. 59, Nr. 1, S. 79-87. https://doi.org/10.32604/cmc.2019.05882

*Computers, Materials and Continua*,

*59*(1), 79-87. https://doi.org/10.32604/cmc.2019.05882

}

TY - JOUR

T1 - Computational machine learning representation for the flexoelectricity effect in truncated pyramid structures

AU - Hamdia, Khader M.

AU - Ghasemi, Hamid

AU - Zhuang, Xiaoying

AU - Alajlan, Naif

AU - Rabczuk, Timon

N1 - Funding Information: The authors extend their appreciation to the Distinguished Scientist Fellowship Program (DSFP) at King Saud University for funding this work.

PY - 2019

Y1 - 2019

N2 - In this study, machine learning representation is introduced to evaluate the flexoelectricity effect in truncated pyramid nanostructure under compression. A NonUniform Rational B-spline (NURBS) based IGA formulation is employed to model the flexoelectricity. We investigate 2D system with an isotropic linear elastic material under plane strain conditions discretized by 45×30 grid of B-spline elements. Six input parameters are selected to construct a deep neural network (DNN) model. They are the Young's modulus, two dielectric permittivity constants, the longitudinal and transversal flexoelectric coefficients and the order of the shape function. The outputs of interest are the strain in the stress direction and the electric potential due flexoelectricity. The dataset are generated from the forward analysis of the flexoelectric model. 80% of the dataset is used for training purpose while the remaining is used for validation by checking the mean squared error. In addition to the input and output layers, the developed DNN model is composed of four hidden layers. The results showed high predictions capabilities of the proposed method with much lower computational time in comparison to the numerical model.

AB - In this study, machine learning representation is introduced to evaluate the flexoelectricity effect in truncated pyramid nanostructure under compression. A NonUniform Rational B-spline (NURBS) based IGA formulation is employed to model the flexoelectricity. We investigate 2D system with an isotropic linear elastic material under plane strain conditions discretized by 45×30 grid of B-spline elements. Six input parameters are selected to construct a deep neural network (DNN) model. They are the Young's modulus, two dielectric permittivity constants, the longitudinal and transversal flexoelectric coefficients and the order of the shape function. The outputs of interest are the strain in the stress direction and the electric potential due flexoelectricity. The dataset are generated from the forward analysis of the flexoelectric model. 80% of the dataset is used for training purpose while the remaining is used for validation by checking the mean squared error. In addition to the input and output layers, the developed DNN model is composed of four hidden layers. The results showed high predictions capabilities of the proposed method with much lower computational time in comparison to the numerical model.

KW - Deep neural networks

KW - Flexoelectricity

KW - Isogeometric analysis

KW - Machine learning prediction

UR - http://www.scopus.com/inward/record.url?scp=85064858465&partnerID=8YFLogxK

U2 - 10.32604/cmc.2019.05882

DO - 10.32604/cmc.2019.05882

M3 - Article

AN - SCOPUS:85064858465

VL - 59

SP - 79

EP - 87

JO - Computers, Materials and Continua

JF - Computers, Materials and Continua

SN - 1546-2218

IS - 1

ER -