The Uncertainty Analysis Based On Edge-based Smoothed Finite Element And Its Research In Electromagnetic Forming

Electromagnetic forming is a dynamic forming process with high speed and high efficiency,which has the characteristics of short forming and no pollution.Among the existing numerical simulation methods of electromagnetic forming,the traditional finite element method has some problems,such as complex calculation process,rigid system and inability to resist mesh distortion.The smooth finite element method can effectively improve the stiffness of the system and has the advantages of high accuracy and strong stability when dealing with complex problems such as dynamic large deformation analysis.In practical engineering,due to the influence of environment,manufacturing and measurement error,the uncertain factors in electromagnetic forming are inevitable.In order to ensure the accuracy and reliability of electromagnetic forming,it is necessary to effectively predict the response of uncertain electromagnetic forming.Although the uncertain electromagnetic problem has received extensive attention in recent years,the research on the uncertain electromagnetic forming field is very rare and needs to be researched and developed.Therefore,this paper combined the edge smooth finite element method and the uncertainty analysis method,aiming at the common interval and random uncertainty problems in electromagnetic,structural and magneto-mechanical coupling analysis,made further analysis and research.The main research work as follows:(1)A stochastic analysis method based on edge smoothing finite element method and moment analysis is proposed to solve the stochastic response of uncertain eddy current problems.By studying and determining the response mean of the structural parameters,it is verified that the edge smoothing finite element method can effectively improve the defect of the traditional finite element method,and ensure the calculation accuracy and accuracy.The gradient of the response with respect to the uncertain parameters was obtained by sensitivity analysis.Based on the second order Taylor expansion,the first four moment formulas of the structural random response are derived,and the probability distribution function and probability density function of the response are solved by combining Lagrange multiplier and maximum entropy theory.Compared with the value of MCS,the proposed method requires fewer calls to the structure control function to obtain the corresponding probability density function.In addition,the effects of different random variables on the structural response is handled by the fourth moment of response.(2)The problems of electromagnetic field eddy current analysis and dynamic large deformation of structure field involved in the electromagnetic forming process are studied,and the methods of mesh updating and magneto-mechanical coupling are introduced.Based on edge smooth moment analysis of finite element method is used for pipe fittings,plate stamping random response analysis of the uncertainty was deduced electromagnetic forming problem solving related formula,at the same time considering the uncertainty of electromagnetic field and mechanical field parameters on the influence of electromagnetic forming,predict the displacement deformation of structural response and the first four moments of the probability density function.By comparing with Monte Carlo method,the feasibility and high efficiency of the stochastic analysis method in practical uncertain electromagnetic forming analysis are verified.In addition,the anti-mesh distortion ability and stability of edge smoothing finite element method were verified by comparing the air mesh at different deformation moments,and the influence of random parameters with different variation coefficients on the structural response was analyzed.(3)An interval analysis method based on edge smoothing finite element method and perturbation method is developed,and an interval displacement and potential derivative analysis model based on first order interval perturbation method is established to predict the boundary of eddy current and fiber-reinforced composite plates.Compared with the traditional interval perturbation finite element method and MCS,the algorithm is much more accurate and efficient,and because the edge smoothing finite element method has the characteristics of anti-mesh distortion,this method can be applied to complex engineering problems.