基于可行弧内点算法的上限有限单元法优化求解

发布时间：2018-04-15 22:06

本文选题：极限分析上限法 + 有限元单元法　；参考：《岩土工程学报》2014年04期

【摘要】：上限有限单元法将寻找机动相容速度场的问题转化为一个数学规划问题,克服了人为构造机动相容速度场的困难,在复杂工程问题中具有广阔的应用前景。基于非线性规划的上限有限单元法,可避免对屈服函数的线性化处理,大大地减少了优化变量数,同时可节约大量存储空间,但由此产生的非线性规划模型十分复杂。为此,在引入一种非线性上限规划模型的基础上,探讨基于可行弧内点算法对其进行优化求解的步骤。首先,采用BFGS公式对屈服函数的Hessian矩阵进行迭代,避免了计算过程中该矩阵病态的问题;其次,通过构造可行弧,克服了当迭代点到达非线性约束边界时搜索步长过短的问题;最后,采用Wolfe非精确搜索技术进行线性搜索,提高了步长搜索效率。通过MATLAB编程进行算例分析表明,基于可行弧内点算法的非线性上限有限单元法,计算效率高、计算误差小、数值稳定性好,可以适应大部分土体稳定性分析计算。
[Abstract]:The upper bound finite element method transforms the problem of finding the compatible velocity field into a mathematical programming problem, which overcomes the difficulty of artificial construction of the maneuvering compatible velocity field and has a broad application prospect in complex engineering problems.The upper bound finite element method based on nonlinear programming can avoid linearization of yield function, reduce the number of optimization variables and save a lot of storage space, but the nonlinear programming model is very complex.Based on the introduction of a nonlinear upper bound programming model, this paper discusses the steps of solving the problem based on the feasible arc interior point algorithm.Firstly, the BFGS formula is used to iterate the Hessian matrix of the yield function to avoid the ill-conditioned problem of the matrix in the calculation process, secondly, the problem of too short search step when the iteration point reaches the nonlinear constraint boundary is overcome by constructing feasible arc.Finally, linear search is carried out by using Wolfe inexact search technology, which improves the efficiency of step-size search.The example analysis by MATLAB programming shows that the nonlinear upper bound finite element method based on feasible arc interior point algorithm has the advantages of high calculation efficiency, small calculation error and good numerical stability. It can be used for most soil stability analysis and calculation.
【作者单位】：湖南大学岩土工程研究所;
【基金】：国家自然科学基金项目(51278187)
【分类号】：TU4;O221

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