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下限分析有限单元法将下限定理这一数学变分问题转化为一个数学规划问题,克服了人为构造可静应力场的困难,在实际工程中具有广阔的应用前景。通过有限元离散得到的非线性下限规划模型中包含大量的优化变量与约束条件,常规优化算法难以求解。为此,在分析非线性下限规划模型自身特点的基础上,引入可行弧技术和Wolfe非精确搜索技术改进其优化求解效率。算例分析表明,基于可行弧技术和Wolfe非精确搜索技术,下限分析有限单元法优化求解程序的收敛速度和步长搜索效率得到明显的提升,并且其数值稳定性良好、计算精度较高,可以较好地适应实际工程问题的计算。
The finite element method of lower bound analysis transforms the mathematical variational problem of lower bound theorem into a mathematical programming problem, overcomes the difficulty of constructing static stress field and has a broad application prospect in practical engineering. The nonlinear lower bound programming model obtained through finite element discretization contains a large number of optimization variables and constraints, and the conventional optimization algorithm is difficult to solve. Therefore, based on the analysis of the characteristics of nonlinear lower bound programming model, feasible arc technique and Wolfe inaccurate search technique are introduced to improve the efficiency of its optimization solution. The case study shows that based on the feasible arc technique and the Wolfe inexact search technique, the convergence speed and the step search efficiency of the finite element method of finite element method of lower bound analysis are obviously improved, and the numerical stability is good and the calculation accuracy is high. To better adapt to the calculation of actual engineering problems.