Finite Element Computation Of Hyperelastic Structure And Its Application In Aircraft Tire

For the structure of aircratf tires,the volume of rubber accounts for 70%of the entire structure.Due to the complexity of the mechanical properties for the rubber,it is necessary to analyze its mechanical behavior by adopting an appropriate constitutive model.This thesis focuses on the finite element solution problem of approximate incompressible hyperelastic rubber structure,derives different hyperelastic constitutive models,and finally achieves the finite element computation of hyperelasticity,applies it to the inflation analysis of aircraft tire.This thesis summerized as follows.In Chapter 2,the basis of continuum mechanics was introduced,which obtained the theory of finite deformation,and the relationship between strain energy density and stress.Then the thesis described stress tensor and strain tensor,and obtained the general formula of hyperelastic constitutive for the rubber materials.This chapter provided a theoretical basis for the construction of hyperelastic constitutive model.In Chapter 3,the hyperelastic constitutive model expressions were obtained which included Neo-Hookean,Mooney-Rivlin,Yeoh and Ogden.The corresponding constitutive matrixes were derived by the strain energy density of each constitutive model.Then the linear least squares method and Levenberg-Maquardt optimization iterative algorithm were used to fit the experimental data to obtain the material parameters of each hyperelastic constitutive model.This chapter simulated the different mechanical behaviors of hyperelastic materials,which provided the method for finite element analysis of hyperelastic rubber.In Chapter 4,the finite element analysis methods were introduced for hyperelastic structures.The three-field mixed variational equation was derived,where involved displacement fields,hydrostatic pressure fields and volume change rate fields.Then,the threefield mixed variational equation was discretized by using pentahedral and hexahedral elements.For the pressure adjoint problem,the variational of external load to displacement was obtained,and the modified stiffness matrix and external load vector was reducted.Lastly,this chapter provided the solution procedure of the nonlinear finite element equation,and completed the finite element solution of the hyperelastic structure.In Chapter 5,the finite element solution of hyperelastic materials was introduced,and various hyperelastic constitutive model solvers were developed.According to advanced programming technology and modern development environment,various technologies such as Pardiso solver and VTK graphics rendering were used to achieve efficient and accurate hyperelastic material solution and graphics display.Different hyperelastic constitutive models had been used for finite element analysis of simple specimens.Then suitable constitutive models were selected for finite element solution of the aircraft tire,and the aircraft tire were inflated and the solution results were compared.Finally,the thesis was summarized and prospected.