状态向量的扩展有限元方法研究

利用哈密顿正则方程的半解析法计算单元位移场和应力场,可以得到精度比较高的解.但此半解析法在计算应力尖峰区域时,该区域要细化网格.当裂纹扩展时,又要重新生成刚度矩阵进行求解,导致求解效率降低.利用扩展有限元处理裂纹的不连续性,当裂纹扩展时可以避免网格的重构.为充分利用状态向量方程和扩展有限元的优势,该文将两者结合起来分析材料的断裂问题:计算应力强度因子和模拟裂纹扩展.最后通过算例分析,验证了该文提出方案的可行性.

THE EXTENDED FINITE ELEMENT METHOD BASED ON THE STATE VECTOR

The displacement field and the stress field are computed by a semi-analytical method based on the Hamilton canonical equation, and the results are found very satisfactory. But when the tip field is considered, the tip field must be more finely meshed. Both the stiffness matrix and the stress field must be calculated anew when the crack propagates, which makes very low resolution efficiency. Based on the extended finite element method, the discontinuity of the crack could be taken care of, to avoid the re-meshing. In order to take a full advantage of the Hamilton system and the extended finite element method, this paper combines them to analyze the fracture problem, such as the calculation of the stress intensity factor and the simulation of the crack propagation. The results from the case analysis demonstrate that the method is feasible.