奇点分析单元法在断裂问题中的应用

将裂纹应力计算问题导向哈密顿体系，利用分离变量法及本征函数向量展开等方法，推导出裂纹尖端的尖力奇性解的计算公式。结合变分原理，提出一种解决应力奇性计算的奇点分析单元。将此分析单元与有限元法相结合，可以进行某些断裂力学或复合材料等应力奇性问题的计算及分析。数值计算结果表明，该方法具有精度同，使用十分方便、灵活等优点，是哈密顿体系优越性的一次具体体现。

APPLICATION OF SINGULAR POINT ANALYTICAL ELEMENT METHOD TO CRACK PROBLEM

The governing equations of stress calculation in singularity point domain are transformed into Hamiltonian form via substitution of variables and the variational principle The method of separation of variables and the method of eigenfunction expansion are applied to derive the equations for calculation of stress singularity at the crack tip A new singularity point analytical element, which is developed for the problem of stress singularity, is installed into the FEM program system Through this element, it is also possible to deal with some fracture mechanics problems and stress singularity problems in composites The proposed method obtained through the corresponding computer program,is supported by the numerical results, which demonstrates the advantage of the theory of Hamiltonian system and the symplectic mathematics