Research On Finite Element Method Of Flexural Shell Model

Flexural shell theory is an important research direction in elastic shell theory,and its application fields are very wide,especially in the fields of aerospace engineering,biomedical,civil engineering and nuclear industry.Based on the Koiter elastic thin shell theory,in the 1996s,Ciarlet team first proposed the concept of a flexural shell,and gave proof that the two-dimensional model approximates the three-dimensional equation when the shell thickness approaches zero.In the numerical calculation of the shell model,the most discussed is the finite element method.Therefore,in this paper,we give a conforming finite element method for the flexural shell model.When solving the complex models,the solution error becomes very large due to the singularity of the local area.However,when the adaptive grid method is used to for calculation,the grid will is automatically refined in the area where the solution changes drastically,and the grid is relatively coarse in the area where the solution is flat.Therefore,in this paper,we also give adaptive grid calculation method for the flexural shell model.In this paper,the main work is as follows:(1)The finite element method coupled penalty method is used to numerically calculate and analyze the flexural shell model.First,the proof of the existence and uniqueness theorems of the solution of the flexural shell model is proved.Secondly,since there is a constraint condition ???((?))=0 on the integration region ? in the function space (?)F(?),it is difficult to construct the discrete subspace,so first use the penalty method to deal with the variational problem,and then use the conforming finite element method is used to discretize the displacement variables,and give proof of the existence,uniqueness and convergence of the solution to the discrete problem.Finally,the numerical simulation and analysis are carried out on conical shells and cylindrical shells,the stability and effectiveness of the numerical method are verified.(2)Based on the flexural shell model processed by the penalty method,it is numerically calculated and analyzed by the adaptive grid method.Based on the residual posterior error estimation indicator and the Dorfler criterion and the newest vertex bisection grid refinement principle,an adaptive grid algorithm given.Based on this algorithm,the numerical simulation and analysis are carried out on conical shells.The experimental results show that,compared with the uniformly refined grid,the adaptive grid method can automatically refine the grid in the areas where the solution changes drastically,and obtain a high-accuracy solution with a small amount of calculation,the experimental results verify the stability and effectiveness of the adaptive grid method for the flexural shell model.