摘要
基于Taylor级数,将三角形单元内的应力场在三角形单元中心点处展开,从而可以借助于中心点应力及应力场梯度来表达整个单元应力场,再利用平衡方程中应力场梯度之间的线性关系,使单元中未知量的个数从9个减少到7个。由于已经满足了平衡方程,因此得到下限问题的数学规划模型不仅减少了变量的个数,而且也减少了等式约束的个数,从而降低了模型的规模。该方法丰富了下限原理有限元法的理论,为进一步提高求解效率打下了基础。计算结果表明与经典Sloan方法得到的结果完全一致。
Based on Taylor series theory, the stress field of a triangle element can be expanded through center point stress and its stress gradients. Along with the equilibrium equations, which is a linearized relationship of stress gradients, the numbers of variables in a triangle element can be reduced from 9 to 7. Because of pre-satisfied equilibrium, the obtained lower bound mathematical programming model not only decreases the variables, but also reduces the equations, so this programming model has lower models compared with Sloan method. The method enriches the lower bound finite element theory and lays foundation to increase the solving efficiency. The results of examDles show this method can get the same results as Sloan method gets.
出处
《工程力学》
EI
CSCD
北大核心
2015年第10期38-43,59,共7页
Engineering Mechanics
基金
国家重点基础研究发展计划(973)项目(2011CB013505)
关键词
下限分析
有限元法
TAYLOR级数
稳定性
极限荷载
lower bound limit analysis
finite element method
Taylor series
stability
limit load
