A method of symplectic singular element and its application for reinforcement of cracked structures

Based on the expansion of symplectic eigensolutions and symplectic relations of adjoint orthonormalization,a model of symplectic singular element is presented in this paper.Combining with finite element software,a numerical method is formed for analysis of cracked structures.Advantages of the method are that stress intensity factors can be obtained directly,and the density localization of finite element mesh and the path of limit do not affect the numerical value of the factor.For reinforcement problem of cracked structures is discussed and analyzed.Some new rules are revealed in numerical results for reinforcement technique.