The Research On Element Differential Method For Static And Dynamic Fracture Analysis

Hypersonic vehicles and other modern aircraft often work in high temperature,high pressure,thermal shock and other complex working environment.Fracture accident analyses show that fracture is closely related to defects or cracks existing in the structure,and fracture failure of mechanical structure caused by cracks and other defects is the main failure mode in engineering.Therefore,the analysis of fracture mechanical behavior of cracked structures facing extreme environment can effectively prevent the occurrence of structural fracture,reduce the failure probability of structures and increase the service life of them.In this paper,a new method for numerical analysis of important parameters such as stress intensity factor in structural fracture mechanical behavior has been developed.The main research works are shown as follows:Firstly,a strong-weak coupling element differential method for static fracture behavior analysis is proposed.The characteristic of element differential method is that geometric variables and physical variables are expressed by the first and second derivatives of shape function with respect to global coordinates.On the basis of the equilibrium equation,the system equation of solving the problem is established directly without any integral form.In addition,a new point configuration scheme is proposed,in which the governing equation and the traction balance equation are used to construct the equations for the points inside elements and other nodes respectively.Furthermore,a mixed element differential method with strong and weak configurations is proposed to deal with the mechanical responses in the complex computational domains such as crack tip,structural edges and corners.The governing equations of the internal nodes in the element are established by using the weak-form of the weighted residual method.Based on the simulation of homogeneous materials,the developed element differential method is further extended and applied to the simulation of fracture mechanical behavior of functionally graded materials.The accuracy and stability of the element differential method and the element differential method with mixed configuration in the calculation of fracture problems are verified by the classical examples of two-dimensional and three-dimensional fracture problems.Secondly,the element differential method is proposed to analyze the dynamic mechanical behavior of structural fracture under dynamic load.In this method,the point technique used in the element differential method for static fracture problems is extended to solve the problem of structural dynamic response.The equations of the system for solving the dynamic problem are directly established through the dynamic equation of the structure at the internal point of the element and the surface force equilibrium condition at other boundary nodes.In this method,compared with the traditional finite element method,It can be seen that the element differential method does not need variational principle and virtual work principle to establish the solution scheme of boundary value problems.On the other hand,the mass matrix obtained naturally satisfies the lumped-mass matrix scheme,which has advantages in solving complex dynamic response problems such as dynamic fracture problems.Then,the J-integral scheme is introduced into the element differential method to solve the fracture parameters of dynamic fracture problems.The J-integral of the dynamic problem is decomposed into the static term and the inertia term based on the Lagrange isoparametric element.By solving the equivalent integral region of the static term and superposing the inertia term,the dynamic J-integral scheme of elements around the crack is formed,and the fracture parameters of the dynamic fracture problem will be solved.Furthermore,the fracture problem of structures with a center crack and a side crack under dynamic load is analyzed to verify the accuracy of the proposed method.