一种增广拉格朗日优化方案及其非连续变形分析实现

张洪

doi:10.11779/CJGE201902015

一种增广拉格朗日优化方案及其非连续变形分析实现 English Version

张洪

同济大学土木工程学院,上海 200092

基金项目: 国家自然科学基金项目（51708420）; 上海市浦江人才计划项目（17PJ1409100）; 上海市自然科学基金项目（17ZR1432300）; 中央高校基本科研业务费专项资金项目（2016KJ024）; 上海市高峰高原学科建设计划（I类）项目（土木工程学科）

详细信息

作者简介:
张洪(1986-),男,博士,副研究员,主要从事岩石力学数值计算方面的研究工作。E-mail：hongzhang@tongji.edu.cn。

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出版历程
- 收稿日期: 2017-11-29
- 发布日期: 2019-02-24

An optimized augmented Lagrangian method and its implementation in discontinuous deformation analysis (DDA)

ZHANG Hong

College of Civil Engineering, Tongji University, Shanghai 200092, China

摘要

摘要: 接触力计算精度是关乎非连续变形分析结果有效性的关键因素之一。经典非连续变形分析法（DDA）采用罚法施加块体间的接触约束,实现简单,但合理的罚值选取困难。因此,提出了一种增广拉格朗日优化算法,改进DDA中接触约束的处理。通过结合开闭迭代算法和自适应罚值更新方案等,提出并实现了多面体DDA增广拉格朗日算法及其优化方案。最后,设计了2个经典数值算例,计算结果表明：改进后的三维DDA提高了计算精度且保证了计算效率,可用于复杂多面体块体系统的非连续力学行为分析,如大型节理岩体工程稳定性分析。
- 非连续变形分析 /
- 接触约束 /
- 增广拉格朗日法 /
- 开闭迭代 /
- 自适应罚值更新方案
Abstract: One of the key factors regarding the validity of the results of discontinuous deformation analysis (DDA) is the computational accuracy of the contact force. The classic DDA employs a penalty function to enforce the contact constraints between blocks, which is easy to implement but challenging to choose the penalty value in the actual computation. To overcome the limitation, a three-dimensional (3-D) DDA based on an optimized augmented Lagrangian method (ALM), abbreviated as DDA-3a, is established to modify the treatment of the contact constraints. This study provides necessary knowledge to fully implement and further optimize the ALM in the 3-D DDA by integrating it with the open-close iteration, and an adaptive penalty update scheme. Numerical examples are designed to exhibit the capability of DDA-3a in the computational accuracy, efficiency, and robustness. This study reveals that the DDA-3a can be used to analyze the discontinuous mechanical behavior of polyhedral block systems, such as the stability analysis of jointed rock-masses.
- discontinuous deformation analysis /
- contact constraint /
- augmented Lagrangian method /
- open-close iteration /
- adaptive penalty update scheme

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参考文献(13)

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