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Abstract
Stress analysis and deformation prediction have always been the focuses of the field of mechanics. The accurate force prediction in plate deformation plays important role in the production, processing and performance analysis of materials. In this paper, we propose an ARIMA-FEM method, which can be used to solve some mechanical problems of 2D porous elastic plate. We have given a detailed theory and solving steps of ARIMA-FEM. In addition, three numerical examples are given to predict the stress–strain of thin porous elastic metal plates. This article uses CST, LST and Q4 elements to discrete the rectangular plates, square plates and circle plates with holes. As for variable force prediction, this paper compared with linear regression, nonlinear regression and neural network prediction, and the results show that the ARIMA method has a higher prediction accuracy. Furthermore, we calculate the numerical solution at four mesh scales, and the numerical convergence is consistent with the theoretical convergence, which also shows the effectiveness of our method. The image smoothing algorithm is applied to keep edge information with high resolution, which can more concisely describe the plate internal changes. Finally, the application scope of ARIMA-FEM, model expansion, superconvergence analysis and other issues have been given enlightening views in the discussion section. In fact, this algorithm combined statistics and mechanics. It also reflects the knowledge integration of interdisciplinary and uses it better to serve practical applications.
Highlights
IntroductionThe problem of material deformation and stress analysis has always been the focus of research in the field of material application and computational mechanics
Figure 9b: We can see that the blue points are concentrated around the red line, the QQ chart can show that the selected set of data obeys a normal distribution, and these points in the chart are on the diagonal line, indicating that the analysis model is reasonable and the observed value of p value should be consistent with the expected value
The application range of autoregressive integrated moving average (ARIMA)-finite element method (FEM) model proposed in this paper is suitable for the load problem of thin plate with variable loading, which is different from other mechanical models
Summary
The problem of material deformation and stress analysis has always been the focus of research in the field of material application and computational mechanics. There are still many defects in the mechanical application of thin plates, which need to be improved urgently. The accuracy and convergence of predicting the mechanical changes of thin plates are still in a state to be studied. The main purpose of this paper is to predict the stress problem of thin plate, improve the prediction accuracy, provide the numerical convergence analysis and output the cloud map of stress, strain and displacement. The significance of our research is that researchers quickly compare the stress changes of thin plates at a certain time in the future to improve the accuracy of numerical solutions
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