Stochastic Defect Method For Finite Element Simulation Of Buckling Problems

The occurrence of the buckling problem in engineering structures greatly affects the original design bearing capacity of the structures,so the structural design engineers face a great challenge in judging structural buckling problem.Due to the complexity of buckling problems,the theoretical study of buckling problems is limited to some simple models,but the theory has not been well answered in complex structures.Therefore,in order to predict the occurrence of structural buckling,numerical methods are widely used,especially the finite element method.This paper is about how to calculate buckling problems more accurately by the finite element method.By studying the buckling simulation methods commonly found in literature and forums,it is found that the linear sway methods used in large numbers have defects and limitations,and many other methods based on this have the same problems.In view of this situation,this paper proposes a simulation calculation method with more operability,higher accuracy and better credibility.To discuss this method,this paper first discusses the theoretical feasibility and the operability in projects of the method,followed by a large number of verification simulation calculations,and compared with other simulation methods,indicating the superiority and universality of this method.After the verification of the method,this paper uses the method to calculate the two engineering examples,which reflects the practical application value of the method and opens the way for the calculation of buckling problems.The main research contents of this paper are:(1)Common buckling simulation methods are discussedThe finite element simulation methods for common buckling problems are summarized and the calculation principle behind it is explored.Then the theoretical basis of the random defect method is explained,and different ways of using the random defect method are given,which provides the reader with various ideas.In addition,the influencing factors affecting the calculation accuracy of random defect method are explored.By comparing the large number of simulation results of different examples,the criteria for selecting the calculation parameters when using the random defect method are given.(2)Verification of the effectiveness of random defect methodFrom simple examples to complex examples,verify the validity,advantages and disadvantages of the random defect method.The second chapter of this paper starts from the pressure bar to the buckling problem of the thin plate,and then the buckling problem in the elastic foundation beam,to verify the advantages and disadvantages of the random defect method from many aspects.The consistency of the random defect method and the linear perturbation method is verified by the linear buckling problem,and the random defect method can be used to calculate the highorder buckling mode problem.Subsequently,the limitations of the linear perturbation method and the universality of the stochastic defect method are illustrated by the material nonlinearity and the boundary condition nonlinear problem.(3)Apply the random defect method to engineering examplesAfter preparing for the theory,this paper applies the stochastic defect method to the actual engineering problems,and simulates the problem of rectangular delamination buckling under fiber constraint and the overall instability and local instability of I-beam.When using the random defect method,some conclusions and precautions in Chapter 2 of this paper are referenced,and the results obtained by the simulation are consistent with the theoretical analysis results.