基于线性规划模型的极限分析上限有限元的实现

极限分析上限有限元法常利用三角形常应变率单元和摩尔-库仑屈服函数线性化的方法，以形成较易求解的线性规划模型。然而为满足计算精度，需引入大量的优化变量，增加了计算和存储的难度。为此，基于线性规划模型，利用MATLAB编制极限分析上限有限元程序，针对线性规划模型等式约束矩阵的高度稀疏性的特点，以稀疏矩阵的方式存储，从而在一定程度上解决了上述问题，使得上限有限元法能处理较大规模的岩土工程稳定性问题。以条形基础地基承载力课题为例进行算例分析，验证该方法的有效性，同时讨论了模型网格单元和塑性乘子数目对计算结果精度的影响。

Implementation of finite element upper bound solution of limit analysis based on linear programming model

Triangular elements with constant strain rate and linearization of Mohr-Coulomb criterion are regularly used for finite element upper bound solution to form a linear programming model.However,a calculating and storage difficulty has been brought out by numerous variables,which are required to be introduced in the linear program,to seek for precision requirement.Calculating program using Matlab for finite element upper bound solution is compiled based on linear programming model.And it takes full advantage o...