关键词: 下限理论, 有限元, Hoek-Brown, 复合锥优化

Abstract: Based on the complex cone optimization technique, a lower bound finite element limit analysis method based on the generalized Hoek-Brown yield criterion is proposed in this paper. The generalized Hoek-Brown yield criterion has some problems including the numerical singularity at the edges and sharp points in the principal stress space. The generalized Hoek-Brown yield criterion used in the finite element limit analysis method generally needs to be approximated. How to deal with the yield criterion accurately and effectively is always a difficult problem in the finite element limit analysis method. To solve this problem, using the cone optimization technique, including power cone programming (PCP) and semidefinite programming (SDP), the yield function can be directly transformed into the complex cone optimization model. The application of complex cone optimization can avoid the approximate treatment of yield criterion. In addition, a strict lower bound solution can be obtained by treating the yield criterion with the proposed method. In order to improve the calculation accuracy of the proposed method, an adaptive mesh refinement strategy based on the node stress of the element is introduced. On the basis of the existing research, the corresponding adaptive lower bound limit analysis finite element program is compiled. The results show that the proposed method can yield the lower bound solution with high accuracy, and indirectly reflect the failure mechanism of the structure.

Key words: lower bound theory, finite element, Hoek-Brown, complex cone optimization