摘要
本文研究理想刚塑性介质极限载荷因子的计算方法。根据极限分权理论的上限定理,建立了计算极限载荷因子的一般数学规划有限元格式。针对这种格式的特点,提出了一个求解极限载荷因子的无搜索迭代算法。这个算法中采用逐步识别刚性、塑性分区,不断修正目标函数的方案,克服了目标函数非光滑所导致的困难。本文提出的算法建立于位移模式有限元基础上,有较广的适用范围,且具有计算效率高,稳定性好,格式简单易于程序实现等优点。
It is well known from plasticity theory that there are two fundamental theore-ms, static and kinematic theorem, which can be used to determine lower and upper bounds of the collapse multipliers of proportionally loaded structures. According to these theorems the lower and upper bounds can be got by the maximization and minimization procedures, respectively. Both of the procedures can be formulated in mathematical programming forms, and related algorithm are constructed on these forms.In this paper attention is focused on the mathematical programming formulation for upper bound. Discretizing velocity field by finite element technique, we propose an iteration algorithm for solving this mathematical programming formulation: In the algorithm there are no searching processes that usually occur in mathematical programming procedures. Only displacement variables are used in the algorithm. In every iteration step the rigid and plasaic zones are recognized and the goal function of the mathematical programming formulation is modified relevantly. The difficulties caused by undetermined rigid zones and undifferentiable goal function are overcome. The computational processes in every step is much similar to that of elastic analyses of the same problem. The initial value for the velocity field is chosen naturally The feasibility and convergence of the algorrhm are studied. It is proved that the multiplier and associated velocity field produced by the iteration processes are convergent.The numerical implementation of the algorithm is fairly easy. The storage used in practical computation is the same as in the elastic analysis, so that the algorithm can be used to carry our limit analyses as long as elastic analyses are provided. Because only displacement variables occur in the algorithm, it is easily realized by means of current existing displacement based finite element codes.This algorithm have been successfully applied to the limit analyses of the plane stress, plate and shell problems. Some sample problems were presented. From the results we can see that the algorithm possesses high efficiency.It is well known from plasticity theory that there are two fundamental theore-ms, static and kinematic theorem, which can be used to determine lower and upper bounds of the collapse multipliers of proportionally loaded structures. According to these theorems the lower and upper bounds can be got by the maximization and minimization procedures, respectively. Both of the procedures can be formulated in mathematical programming forms, and related algorithm are constructed on these forms.In this paper attention is focused on the mathematical programming formulation for upper bound. Discretizing velocity field by finite element technique, we propose an iteration algorithm for solving this mathematical programming formulation: In the algorithm there are no searching processes that usually occur in mathematical programming procedures. Only displacement variables are used in the algorithm. In every iteration step the rigid and plasaic zones are recognized and the goal function of the mathematical programming formulation is modified relevantly. The difficulties caused by undetermined rigid zones and undifferentiable goal function are overcome. The computational processes in every step is much similar to that of elastic analyses of the same problem. The initial value for the velocity field is chosen naturally The feasibility and convergence of the algorrhm are studied. It is proved that the multiplier and associated velocity field produced by the iteration processes are convergent.The numerical implementation of the algorithm is fairly easy. The storage used in practical computation is the same as in the elastic analysis, so that the algorithm can be used to carry our limit analyses as long as elastic analyses are provided. Because only displacement variables occur in the algorithm, it is easily realized by means of current existing displacement based finite element codes.This algorithm have been successfully applied to the limit analyses of the plane
出处
《力学学报》
EI
CSCD
北大核心
1991年第4期433-442,共10页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金
关键词
极限分析
数学规划
有限元法
Limit Analysis, Mathematical Programming, Finite Element Method
