接触问题的增广拉格朗日块体粘接模型

doi:10.3969/j.issn.1001-2400.2017.04.007

西安电子科技大学学报

接触问题的增广拉格朗日块体粘接模型

孙越;冯象初;李小平;张瑞

(西安电子科技大学数学与统计学院，陕西西安 710071)

收稿日期:2016-06-30 出版日期:2017-08-20 发布日期:2017-09-29
作者简介:孙越(1983-)，男，西安电子科技大学博士研究生, E-mail: yue_sun@163.com
基金资助:
国家自然科学基金资助项目(61271294, 61471338)

Augmented Lagrangian bonding block model for contact problems

SUN Yue;FENG Xiangchu;LI Xiaoping;ZHANG Rui

(School of Mathematics and Statistics, Xidian Univ., Xi'an 710071, China)

Received:2016-06-30 Online:2017-08-20 Published:2017-09-29

摘要/Abstract

摘要：

在弹性接触数值模拟研究中，建立了一种新的块体粘接模型：通过将原模型所求解的问题归结成以粘接弹簧应变能为罚函数项的最小化问题．新模型引入拉格朗日乘子作为粘接弹簧拉力，从而将作为目标函数的系统总势能构造成增广拉格朗日函数．为求解该模型，提出一种新算法，在每个时间步引入一层增广拉格朗日迭代过程取得模型的最优解．数值算例验证了所提出模型和算法的精确性和有效性．

关键词: 弹性接触, 增广拉格朗日方法, 非连续变形分析, 块体粘接模型, 迭代法

Abstract:

A novel bonding block model is proposed for elastic contact simulations. The original model problem is expressed as the minimization problem with the penalty item of gluing spring strain energies, and Lagrangian multipliers are introduced to represent gluing spring forces. In this way, the total potential energy as the objective function becomes an augmented Lagrangian function. To solve this model, a new algorithm is presented by implementing augmented Lagrangian iterations to obtain the optimal solution in every time step. A numerical example is conducted to verify the accuracy and effectiveness of the presented model and algorithm.

Key words: elastic contact, augmented Lagrangian method, discontinuous deformation analysis, bonding block model, iterative method

孙越;冯象初;李小平;张瑞. 接触问题的增广拉格朗日块体粘接模型[J]. 西安电子科技大学学报, 2017, 44(4): 34-39.

SUN Yue;FENG Xiangchu;LI Xiaoping;ZHANG Rui. Augmented Lagrangian bonding block model for contact problems[J]. Journal of Xidian University, 2017, 44(4): 34-39.

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接触问题的增广拉格朗日块体粘接模型

Augmented Lagrangian bonding block model for contact problems

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