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On-line Access: 2021-06-21

Received: 2020-07-18

Revision Accepted: 2020-08-04

Crosschecked: 2021-05-17

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Citations:  Bibtex RefMan EndNote GB/T7714


Timon Rabczuk


Arvin Mojahedin


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Journal of Zhejiang University SCIENCE A 2021 Vol.22 No.6 P.492-498


A deep energy method for functionally graded porous beams

Author(s):  Arvin Mojahedin, Mohammad Salavati, Timon Rabczuk

Affiliation(s):  Institute of Structural Mechanics, Bauhaus-Universitt Weimar, Weimar 99423, Germany; more

Corresponding email(s):   timon.rabczuk@tdtu.edu.vn

Key Words:  Energy-based method, Multilayer perceptron methodology, Functionally graded porous materials, Euler-Bernoulli beam theory

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Arvin Mojahedin, Mohammad Salavati, Timon Rabczuk. A deep energy method for functionally graded porous beams[J]. Journal of Zhejiang University Science A, 2021, 22(6): 492-498.

@article{title="A deep energy method for functionally graded porous beams",
author="Arvin Mojahedin, Mohammad Salavati, Timon Rabczuk",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T A deep energy method for functionally graded porous beams
%A Arvin Mojahedin
%A Mohammad Salavati
%A Timon Rabczuk
%J Journal of Zhejiang University SCIENCE A
%V 22
%N 6
%P 492-498
%@ 1673-565X
%D 2021
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A2000317

T1 - A deep energy method for functionally graded porous beams
A1 - Arvin Mojahedin
A1 - Mohammad Salavati
A1 - Timon Rabczuk
J0 - Journal of Zhejiang University Science A
VL - 22
IS - 6
SP - 492
EP - 498
%@ 1673-565X
Y1 - 2021
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A2000317

We present a deep energy method (DEM) to solve functionally graded porous beams. We use the Euler-Bernoulli assumptions with varying mechanical properties across the thickness. DEM is subsequently developed, and its performance is demonstrated by comparing the analytical solution, which was adopted from our previous work. The proposed method completely eliminates the need of a discretization technique, such as the finite element method, and optimizes the potential energy of the beam to train the neural network. Once the neural network has been trained, the solution is obtained in a very short amount of time.


概要:本文提出了一种深度能量方法(DEM)来求解功能梯度多孔梁.采用欧拉-伯努利假设,且功能梯度多孔梁在整个厚度范围内具有不同的力学性能.随后开发了DEM,并通过与作者在以前的工作中采用的解析解进行对比证明了其性能.本文所提出的方法完全不需要离散化技术(例如有限元方法),而是通过优化梁的势能来训练神经网络. 一旦神经网络训练好,其求解可在很短的时间内完成.

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