基于广义Hoek-Brown屈服准则的极限分析下限有限元法

Lower bound finite element limit analysis method based on generalized Hoek-Brown yield criterion

基于复合锥优化技术,提出一种基于广义Hoek-Brown屈服准则的极限分析自适应下限有限元计算方法。广义Hoek-Brown屈服准则在主应力空间中的棱线以及尖点处存在数值奇异性等问题,在极限分析有限元方法中的应用一般都需要对其进行近似化处理。如何准确有效地处理该屈服准则,一直是极限分析有限元方法中的难点问题。针对这一问题,基于复合锥优化技术将广义Hoek-Brown屈服函数转化为由半定规划(SDP)约束和幂锥规划(PCP)约束组成的复合锥优化约束,从而直接将该屈服准则应用到极限分析下限有限元方法中,不需要对其数值奇异性问题做额外近似处理。同时,采用所提方法处理屈服准则可以获得严格的下限解。为了提高所提方法的计算精度,引入一种基于单元节点应力的自适应加密策略,在既有研究的基础上,编制相应的极限分析自适应下限有限元计算程序,并开展经典案例对比分析。结果表明该方法可获取较高精度的下限解。

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.