Analysis Of 3D Crack Problems Based On A Symplectic Analytic Singular Element

In comparison with plane fracture problem,the study of three-dimensional(3-D)fracture problem is much difficult.However,the later one is closer to the actual engineering application and hence has a significant research value.In this study,a new symplectic analytical singular element is constructed using the symplectic eigen solutions of 2-D plane and anti-plane crack problems.The finite element formulation of the proposed singular element is derived using the principle of minimum potential energy.By combining the singular element with the 3-D conventional finite element,3-D fracture problems can be numerically analyzed and the stress intensity factors at the crack tip can be obtained directly without any post-processing through the relationship between the coefficient and the fracture parameters.Moreover,the proposed singular element is essentially a displacement mode element,and it has made the element can be assembled into most commercial programs of finite element method,this feature has proven the generality and compatibility.In the last part of this theses,numerical examples are provided to illustrate the method,the penetrated crack and the coin-type cracks are investigated.Numerical results show that the singular element can obtain high precision results with different nodes and mesh densities,which shows the advantages of high precision and good stability of the element.In this paper,the application scope of the symplectic solution system in the fracture problem is expanded,and the symplectic analytical singular element is successfully applied to solve the 3-D fracture problem,the proposed method has a valuable potential in engineering applications.