一种求解结构塑性极限载荷下限的无搜索迭代算法

根据经典极限分析理论的下限定理，提出了一种求解极限载荷下限因子的数学规划有限元迭代算法。采用罚函数法引入塑性屈服条件，证明了该算法的收敛性。编制了相应的有限元程序，并进行了算例考核，结果表明该算法得到的下限解是合理的和有效的。

An Iteration Algorithm without Search for the Lower Bound of Plastic Limit Load of Structures

The method of plastic limit analysis of structures has been widely used in structural design and safety assessment. In the present paper, a mathematical programming method for the lower bound limit analysis of structures is presented based upon the classical theorem of limit analysis, Von Mises yielding condition and finite element method. In section 1, we derived the mathematical programming formula for the determination of the lower bound of the limit load of structures. The penalty function method is used to deal with the plastic incompressibility condition. Section 2 shows the convergence of the algorithm. A numerical example given in section 3 shows preliminarily that our method is reasonable and effective.