基于非协调矩形弯曲单元的薄板极限上限分析方法

为了研究板结构的极限承载能力问题,采用ACM非协调矩形弯曲单元对几种不同工况下的正方形板和长方形板进行了极限上限分析。据塑性极限分析的上限定理和Mises屈服条件,建立了基于ACM非协调矩形弯曲单元的刚塑性薄板极限上限分析的数学规划格式,并采用直接迭代算法进行了求解,得到了正方形板和长方形板的极限载荷,相应地绘制出了它们极限状态下的塑性耗散功分布云图。数值计算表明:得到的结果合理,采用非协调矩形弯曲薄板单元ACM进行板的极限上限分析具有格式简单、计算精度较好、计算效率较高、收敛速度较快等优点。

Upper-bound limit analysis method of thin plates based on the nonconforming rectangular bending element

In order to investigate the limit load-carrying capacities of plate structures,this paper implements the upper bound limit analyses of square and rectangular plates under some different loading conditions by using the nonconforming rectangular bending element ACM.According to the upper-bound theorem of plastic limit analysis and the von Mises yield criterion,the ACM-based mathematical programming formulation of perfectly rigid-plastic thin plates is established,and a direct iteration algorithm is used to solve it.The plastic limit loads of square and rectangular plates are obtained,and the relevant plastic dissipation work distributions at the limit states are visually displayed.The numerical results illustrate that the obtained solutions are reasonable.Meanwhile,it is also shown that utilizing nonconforming rectangular bending element ACM to carry out the upper-bound limit analyses has some advantages such as simple formulation,good accuracy,high efficiency and fast convergence.