Research On The Improvement Of Finite Element Stress Solution Based On Machine Learning Methods

Finite element method is one of the most widely used numerical methods in the field of science and technology.In the field of mechanics,large general-purpose finite element software is mostly developed by the finite element method of displacement element.The stress precision of the finite element finite element of the displacement element is lower than that the displacement,and the stress is generally discontinuous on the boundary of the unit(including the common nodes).But in the strength analysis,the stress of the nodes is the most important concern,therefore,giving high precision and continuous node stress is one of the goals that is pursued by the researchers engaged in the finite element research.The finite element software is now widely used to improve the stress solution of the nodes by using the classical holistic,piecewise and other smoothing methods,however,thisarticle explores the improvement based on machine learning methods.This paper use three kinds of machine learning methods,BP,SVM and GPR to improve the stress solution of the nodes.The examination question is a cantilever deep beam which is simplified to the isotropic and uniformly distributed load of the plane stress problem.To study in depth,two finite element models of the cantilever beam are setted up.The model of the quadrilateral element(large sample)of the 4 nodes and the quadrilateral element(small sample)of the 8 nodes.Stress investigation is measured by Equivalent Stress of Mises Stress.The Gauss integral points are the sample points,and the angle nodes of the unit are the improvement points.Between the machine learning methods and the classical method and the machine learning methods,the improvement effect is compared as follows:1)Compared with the classical method,the machine learning method can be improved directly by the peer effect force.2)For the overall error of all angular nodes(after weighted conversion),4 node model: Classical overall stress improvement is22.18%,BP is 10.45%,SVM is 8.02%,GPR is 6.34%;8 node model: Classical overall stress improvement is25.96%,BP is 12.05%,SVM is 5.59%,GPR is 5.98%.From here we see that,for the two models of 4 nodes and 8 nodes,the effect of stress improvement of the three kinds of machine learning methods,the improvement of the classical whole stress of the finite element is obvious,the effect of SVM and GPR is better.The improvement effect of the 8 nodes model,BP is slightly inferior than the 4 node,but,SVM and GPR are better than that of the 4 nodes.3)The total error of the sample points of the 4 node model is 11.17%,the overall error of all corner nodes of the four improvement methods is like the above 2).From here we see that,the classic whole is much larger than the sample points,but,the three machine learning methods are smaller than the sample points,and SVM and GPR are much more smaller,the total error of the sample points of the 4 node model is 6.54%,the overall error of all corner nodes of the four improvement methods is like the above 2).From here we see that,the classic whole is much larger than the sample points,the BP is also larger than the sample points,while the SVM and GPR are slightly smaller than the sample points.4)The overall error for the boundary angle nodes,4 node model: Classical overall stress improvement is24.37%,BP is 11.02%,SVM is 8.45%,GPR is 6.24%;8 node model: Classical overall stress improvement is27.95%,BP is 12.48%,SVM is 5.81%,GPR is 6.39%.The overall error for the internal angle nodes,4 node model: Classical overall stress improvement is9.91%,BP is 7.43%,SVM is 5.83%,GPR is 6.76%;8 node model: Classical overall stress improvement is 5.08%,BP is 8.20%,SVM is 4.07%,GPR is 2.35%.From here we see that,for the two models of 4 nodes and 8 nodes,the improvement effect of the boundary angle nodes is more significant than that of the internal nodes.5)View all the corner nodes relative error,It is found that the error of GPR is less than that of SVM,in addition,the improved stress of the angle nodes,GPR can also give 95% confidence intervals,that is,the output has a probability meaning.6)4 node model: The 5 boundary node(fixed end end point)and the 10 nodes and 15 nodes near the fixed end of the upper end.The relative error of the stress improvement in the solution is-13.02%,3.72% and-13.18%,and the GPR method is-6.08%,-2.14% and-0.52%.8 node model: The 5 boundary node(fixed end end point)and the 10 nodes and 15 nodes near the fixed end of the upper end.The relative error of the stress improvement in the solution is-4.62%,2.14% and 1.02%,and the GPR method is-0.46%,-0.08% and-0.20%.From here we see that,for the 4 and 8 node models,the stress solution of the boundary node is improved.The GPR method is more effective than the classical method of improving the slice stress.7)In order to guarantee the effect of good modification,the classical piecing method is generally only improved for several nodes in the film.However,In order to obtain the improved values of multiple nodes,a number of pieces are required to be calculated piecewise.The GPR method can flexibly draw a large and small subdomain containing all the nodes to be improved,and the improvement of these nodes is completed at a time,and as far as the improvement effect of the internal node is concerned,it is equivalent to the classical slice.8)The stress improvement effect of two kinds of machine learning methods under different input conditions is also explored in this paper.The improvement effect of double transmission(coordinate and displacement)compared with single input(coordinate): The BP network is better;the SVM is not good;the distinction of GPR is not obvious.The above results show that: It is feasible to improve the finite element stress solution based on machine learning method.And compared to the classical method,the reciprocity effect can be improved directly,and the effect is better.