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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。
Limit Analysis Upper Limit Finite element methods often use the method of triangular constant strain rate element and the linearization of the molar-Coulomb yield function to form a linear programming model that is easier to solve. However, in order to meet the calculation accuracy, a large number of optimization variables need to be introduced, which increases the difficulty of calculation and storage. Therefore, based on the linear programming model, the limit analysis upper bound finite element program is developed by using MATLAB. According to the sparse matrix of the linear programming model, the sparse matrix is used to solve the above problems. Making the upper limit finite element method to deal with large-scale geotechnical stability problems. Taking the bearing capacity of strip foundation as an example, an example is given to verify the effectiveness of the method. The influence of the number of model grid elements and plastic multipliers on the accuracy of the calculation results is also discussed.