含缺陷结构上限极限分析的弹性模量缩减法

Elastic Modulus Reduction Method for Upper Bound Limit Analysis of Structure Containing Flaws

为获得含缺陷结构的极限荷载,提出了含缺陷结构上限极限分析的弹性模量缩减法.研究了适用于应力集中条件下的基准承载比算法,建立了含缺陷结构极限分析的弹性模量调整策略,能结合线弹性有限元法构造逼近该类结构极限状态的机动位移场和允许应力场;引入结合虚功原理和基准体概念的上限极限荷载乘子算法,可获得满足上限分析数学规划模型的最优极限荷载解.算例分析表明:该方法可用于含裂纹和凹坑缺陷结构的极限分析;通常可在30个迭代步内得到与解析法及其他数值解相差在5%以内的极限分析结果.

In order to obtain the limit load of a structure containing flaws（SCF）,an elastic modulus reduction method（EMRM） for upper bound limit analysis of SCF was proposed.The determination method for reference element bearing ratio was investigated to a stress concentration problem.An efficient elastic modulus adjustment strategy for SCF was proposed based on the reference element bearing ratio.Using this strategy and the linear elastic finite element method,stress and displacement fields under a limit state can be constructed.By introducing the upper bound limit load multiplier algorithm based on the virtual work principle and the reference volume concept,an efficient optimum solution of the limit load for the upper bound mathematic programming model was obtained.Numerical examples show that the proposed method can be applied to the limit analyses of structures containing cracks or slots and give a solution in 30 iteration steps with a difference within 5% relative to the analytical solution or other numerical solutions.