基于非线性规划的有限元塑性极限分析下限法研究

Research on lower bound method of plastic limit analysis using finite elements based on nonlinear programming

在分析Sloan建立的有限元塑性极限分析线性规划数学模型存在的局限性基础上,提出了基于非线性规划的有限元塑性极限分析下限法数学模型。采用非线性屈服条件构建了下限法静力容许应力场,建立了求解超载系数、强度储备系数的下限法数学模型,并提出了针对塑性极限分析非线性规划数学模型的求解策略;最后对一个经典算例进行了深入分析,验证了方法的正确性。

Lower bound nonlinear programming model based on limit analysis theory is constructed through the analysis of limitation of linear programming models that are proposed by S.W.Sloan.The statically admissible stress fields for lower bound analysis are constructed by using nonlinear yield conditions;and the nonlinear programming models that can calculate overload coefficient and strength safety coefficient are established;and then the optimization strategy of nonlinear programming problem is put forward.Finally,a classic example of slope stability is given;and the results prove the correctness of the method.