A neural network-augmented patch adaptive meshless method for 3D solid mechanics

doi:10.1007/s00466-026-02756-z

2026-03-10

PRE

DOI：10.1007/s00466-026-02756-z

原文链接

原文求助

摘要

En 中文

无网格方法在固体力学领域已取得显著成功，通过有效处理大变形并实现无需网格生成的自适应细化。然而，其收敛性和精度可能对单元配置和局部近似敏感，通常需要问题特定的调整。尽管近期先进的基于神经网络的求解器提供了有前景的替代方案，但它们在复杂域中可能仍难以准确捕捉局部特征。本研究提出了一种用于固体力学的神经网络增强无网格方法。具体而言，采用轻量级神经网络在基于能量的训练方案中进行自适应单元形状描述和局部权函数。此外，引入节点增强神经网络基作为局部近似，以准确捕捉局部力学行为。为验证所提出的方法，给出了线性弹性、超弹性和弹塑性中的多种三维数值算例。比较结果表明，所提出的框架在有限的网络参数和求解迭代下实现了更高的精度和更快的收敛速度。

Keyword:

Deep energy method

Meshless method

Solid mechanics

期刊

Computational Mechanics

IF:

3.8

论文数:

3.2K

被引数:

9.0K

机构

College of Mechanical and Vehicle Engineering

学者数:

261

论文数: 88

被引数: 0

beijing institute of technology

学者数:

5.5W

论文数: 4.0W

被引数: 63

引用论文

A posteriori error estimation in large-strain elasticity using equilibrated local Neumann problems

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

IF7.3

1998-08-01

PREAI

Brink, U; Stein, E

Parametrization of Closed Surfaces for 3-D Shape Description

Computer Vision and Image Understanding

IF0

1995-03-01

PREAI

Ch. Brechbühler; G. Gerig; O. Kübler

Point Convolutional Neural Networks by Extension Operators

ACM TRANSACTIONS ON GRAPHICS

IF9.5

2018-07-30

288

OAAI

Atzmon, Matan; Maron, Haggai; Lipman, Yaron

Neural algorithm for solving differential equations

Journal of Computational Physics

IF0

1990-11-01

OAAI

Hyuk Lee; In Seok Kang

Eighty Years of the Finite Element Method: Birth, Evolution, and Future 有限元方法的八十年: 诞生，演变和未来

ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING

IF12.1

2022-06-13

OAAI

Liu, Wing Kam; Li, Shaofan; Park, Harold S.

A deep learning energy-based method for classical elastoplasticity

INTERNATIONAL JOURNAL OF PLASTICITY

IF12.8

2023-03-01

OAAI

He, Junyan; Abueidda, Diab; Abu Al-Rub, Rashid; Koric, Seid; Jasiuk, Iwona

Convolution Hierarchical Deep-learning Neural Networks (C-HiDeNN): finite elements, isogeometric analysis, tensor decomposition, and beyond

COMPUTATIONAL MECHANICS

IF3.8

2023-05-16

PREAI

Lu, Ye; Li, Hengyang; Zhang, Lei; Park, Chanwook; Mojumder, Satyajit; Knapik, Stefan; Sang, Zhongsheng; Tang, Shaoqiang; Apley, Daniel W.; Wagner, Gregory J.; Liu, Wing Kam

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations 物理信息神经网络: 一种用于解决涉及非线性偏微分方程的正反问题的深度学习框架

JOURNAL OF COMPUTATIONAL PHYSICS

IF3.8

2019-02-01

8.2K

OAAI

Raissi, M.; Perdikaris, P.; Karniadakis, G. E.

Compatible-strain mixed finite element methods for 2D compressible nonlinear elasticity

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

IF7.3

2017-01-01

OAAI