Theory And Application Of Thin Shell Element Based On The Vector Form Intrinsic Finite Element Method

Thin shell structures are widely applied in practical engineering. Under the externnal loading, the behaviors of the thin shell structures usually contain large deformation and large deflection, elastoplastic nonlinear material and complex discontinuous behaviors such as collision-contact, crack-fracture and penetration. For these complex structural behaviors, the traditional finite element analysis need to distinguish the type of the behavior first, then adopt the corresponding special formulas ande process. Thus, for the problems of the structural behavior prediction and the whole process simulation of structural failure, it is difficult to obtain satisfactory results by using the traditional finite element method.The Vector Form Intrinsic Finite Element (VFIFE) is a new analysis method on the basis of vector mechanics theory. This thesis achieves the complex mechanical behaviors for thin metal shell structures by using theoretical analysis, program development and numerical simulation. The study of this thesis along the following two main lines:one is the element development including thin membrane element, thin plate element and thin shell element, and the other is the realization of the complex behaviors including large deformation and large rotation, buckling and post buckling, collision, fracture and penetration.Chapter2introduces the basic concepts, assumptions, principles and deduction ideas of VFIFE. And the related problems such as center differential formula, co-rotational coordinate and reverse movement, nonlinear material, static and dynamic calculation, equivalent mass matrix and inertia matrix, error analysis and internal force balance mechanism are studied. Then the analysis and solving ideas for complex behavior problems such as large deformation and large rotation, buckling and post buckling, collision-contact, crack-fracture and penetration are simply discussed. Finally, the analysis process of VFIFE method is summarized.Chapter3establishes the basic formulas of VFIFE for the triangle CST constant strain membrane element and4-node quadrilateral isoparametric membrane element, describes the principles of motion analysis and the solving method of element node internal forces in deformation coordinate system. Then, some special problems such as the position modes and the numerical integration of the internal force calculation for the4-node quadrilateral isoparametric membrane element are presented, and the corresponding treatment methods are proposed. Computer analysis programs are then developed, and the derived theory and the developed programs are verified through numerical examples finially. In the analysis of complex structural behaviors, for the large deformation and large rotation problems, VFIFE method is used to track the whole process of structural motion and deformation. For the collision-contact problems, the "point-triangle" detection and the penalty contact force method based on the central difference method are adopted separately for the problems of collision detection and collision response, and the whole process of structural collision-contact is tracked. For the crack-fracture problems, the judgment criterion based on the failure stress and the particle splitting method based on VFIFE are adopted to track the whole process of structural crack-fracture.Chapter4establishes the basic theory of VFIFE for the triangle DKT plate element. Then, some special problems such as the mass matrix and inertia matrix of particle, the numerical integration of the stress calculation and interpolation method, and the parameters of time step and damp for the triangle DKT plate element are presented, and the corresponding treatment methods are proposed. All of above are verified by the static and dynamic analysis of plate structural examples finally.Chapter5establishes the basic theory of VFIFE for the triangle shell element based on the combination of the triangle CST constant strain membrane element and the triangle DKT plate element. Then, the processsing methods for the problems are proposed, including the combination and the division of the particle displacements and the internal forces, the combination and the division of the element stresses and strains, and the element node integration scheme. Based on the C-S viscoplastic constitutive model and the dynamic Mises yield criterion, the elastoplastic incremental analysis steps of the C-S constitutive model are deducted, and introduced into the theoretical derivation of the thin shell element of VFIFE. Thus, the plastic hardening effect and the strain rate hardening effect for the nonlinear analysis of the thin metal shell structures are both considered in this material model.Chapter6carries out the research of complex structural behaviors for thin shell structures. For the buckling and post buckling problems, the displacement and the force control methods are used to track the whole process of structural deformation, and the characteristics and applications of the two control methods are then analysed. For the collision-contact problems, the "point-triangle" detection and the penalty contact force method based on the central difference method are still adopted separately for the problems of collision detection and collision response, and the whole process of structural collision-contact is tracked. For the crack-fracture problems, the judgment criterion based on the failure strain and the particle splitting method based on VFIFE are adopted to track the whole process of structural crack-fracture. For the penetration problems, the combination of the collision detection mechanisms, the collision response mechanisms and the fracture criterion based on the failure strain are adopted, and the process of penetration for rigid body-thin shell structure is achieved.Chapter7synthesizes the nonlinear analysical basic theorys for the thin shell structures based on VFIFE, including the theory formulas and the effective algorithms of thin shell element, material constitutive, crack-fracture. And the dynamic response analysis and the whole failure process for the steel tank structures under the explosive loading are achieved. Then, the development of the stresses and the deformationes and the failure modes for flat-roof tank, cone-roof tank and dome-roof tank under the explosive loadings with simplified triangle forms are analysed.The results of this thesis reflect the unique advantages of VFIFE method in dealing with the strong nonlinear and discontinuous mechanics behaviors such as large deformation, large deflection, collision, fracture and penetration. The theory development and the engineering application of VFIFE are pushed, and a new effective method for complex behaviors of thin membrane structures and thin metal shell structures.