中文摘要：

为采用梁单元高效准确求解平面圆管结构极限承载力,提出了相应的极限上限分析的弹性模量缩减法。首先利用齐次广义屈服函数定义结构的单元承载比,然后结合弹性模量缩减过程获得逼近结构塑性极限状态的失效模式,同时,基于平截面假设推导了平面圆管截面的弹性应变能与塑性耗散功的计算公式,进而在结构失效模式上构造出平面圆管结构极限上限荷载的迭代计算方法。算例分析表明,平面圆管结构极限上限分析的弹性模量缩减法具有良好的计算精度和效率,其与EPIA误差在7%以内,迭代次数较EPIA减少一半以上,解决了由于梁单元截面各处的等效应变和应力不相同而导致的上限荷载乘子不能直接运用的问题。研究结果可为平面圆管结构的极限分析和安全评估提供参考。

英文摘要：

The elastic modulus reduction method（ EMRM） for upper bound limit analysis is presented to determine the ultimate load bearing capacity of planar structures with thin-walled circular section. The element bearing ratio（ EBR） of a structure with thin-walled circular section is defined in term of the homogeneous generalized yield function（ HGYF）,and the reference EBR（ REBR） is given as a threshold which identifies the highly loaded areas dynamically. Then,the strategy for elastic modulus adjustment based on the strain energy equivalence principle is established,which is used in linear elastic iterative technique to simulate failure evolution until theplastic limit state is identified. Meanwhile,the formula of the elastic strain energy and plastic dissipation for the plane circular section are derived based on the plane section assumption. Then,the linear elastic iterative technique for the upper bound limit analysis of planar structures with thinwalled circular section is constructed on the basis of structural failure mode. Numerical examples show that the linear elastic iterative technique possesses the advantages of good accuracy and high efficiency. The limit load of a planar structure with thin-walled circular section determined by the elastic modulus reduction method for upper bound limit analysis deviates by about 7% from the limit load determined by the elastic plastic incremental analysis（ EPIA）. And the EMRM requires only a half or less of iterative steps that the EPIA requires. The proposed method can provide reference for the limit analysis and safety evaluation of planar structures with thin-walled circular section.