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| Deep energy method for geometrical nonlinear bending analysis of thin plates |
| Received:September 15, 2022 Revised:November 02, 2022 |
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| DOI：10.7511/jslx20220915001 |
| KeyWord:geometric nonlinearity deep energy method incremental neural network Von-Karman nonlinear theory |
| Author | Institution |
| 彭林欣 |
广西大学 土木建筑工程学院, 南宁 ;广西大学 广西防灾减灾与工程安全重点实验室, 工程防灾与结构安全教育部重点实验室, 南宁 |
| 罗伟嫚 |
广西大学 土木建筑工程学院, 南宁 |
| 黄钟民 |
广西大学 土木建筑工程学院, 南宁 |
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| Abstract: |
| An incremental deep energy method is developed to solve geometric nonlinear bending problems of thin plates.According to the minimum potential energy principle and Von-Karman nonlinear theory,an incremental deep neural network model driven by thin plate potential energy is constructed.Firstly,the solution domain of the thin plate is discretized into a grid,and the Hammer integral points are calculated by reading the grid data in Python,which is used as training set to be substituted into the network model to predict the bending displacement of the plate.Then,the load is divided into a series of load increments.In each increment step,the potential energy of the thin plate is calculated as the loss function of the neural network.With the goal of minimizing the potential energy,the parameters of the network model are updated by Adam optimization algorithm,and the calculation of the next load step is continued after the potential energy takes a stationary value.In this paper,the geometric nonlinear bending problem of thin plates with different shapes and different boundary conditions is solved,and the calculated results are compared with the finite element Abaqus solution using Abaqus from the literattere.The research shows that this method is effective and accurate in solving the geometric nonlinear bending problem of thin plates,and the incremental neural network model needs a low computer,and can effectively improve the computational efficiency and the stability of the model. |
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