含缺陷结构的塑性极限分析

结合极限分析中的数学规划理论和有限元技术，提出了三维含结构极限分析的数学规划方法，并采用罚函数法引入塑性不可压条件，对于考虑多组独立变化载荷作用的情况，提出了加载路径射线辐射求解方案，并基于这种射线射状的加载路径，推导了多组载荷联合作用下结构塑性极限上限分析的数学规划格式，编制了相应的有限元程序，文中的数值了该方法的正确性与有效性。

A MATHEMATICAL PROGRAMMING METHOD FOR LIMIT ANALYSIS OF 3-D STRUCTURES WITH DEFECTS

As one of important methods, limit analysis of 3-D structure with defects has been widely used in procedures of pressure vessel and piping design and structural component integrity assessment. A mathematical programming method for limit analysis of 3-D structures with defects is presented on the basis of finite element technique. For multi-loading system, a solution method of loading path along ray radiation is proposed, the mathematical programming formulation is derived for the upper bound limit analysis of structures with defects and the corresponding finite element program is made. The penalty-function method is used to deal with the plastic-incompressibility condition. All the numerical examples show that the proposed loading path along ray radiation is reasonable and effective. The mathematical programming method without search used here can overcome the numerical difficulties caused by the nonlinearity and nonsmoothness of the objective function.