基于现代数学方法的变结构多体系统动力学若干问题研究

项目名称： 基于现代数学方法的变结构多体系统动力学若干问题研究

项目编号： No.11272167

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 姚文莉

作者单位： 青岛理工大学

项目金额： 72万元

中文摘要： 含碰撞、摩擦、弹塑性等突变因素的变结构多体系统动力学有很强的工程应用背景，一直是国际上该领域研究的热点，因其力学及数学上的复杂性及特殊性，在经典的常规力学方法的框架下，尚有理论难点问题难以得到满意的解答。本课题将以现代数学理论作为工具，围绕变结构多体系统动力学的科学问题开展研究，拟主要研究以下问题：（1）借助于变分不等式、互补性及不可微优化理论之间的关系建立完善变结构多体系统动力学优化形式的数学模型及研究相应的数值算法。该模型与用常规方法建立的模型在数学上等价，但数值特性不同，发展日益成熟的数学规划方法将为动力学理论难点问题的解决及数值运算方法提供更好的数学基础；（2）借助现代数学中的突变理论，研究多刚（柔）体系统碰撞(动力接触)问题中速度突变的奇异性及解决方案；（3）借助于精密的实验及精细化处理碰撞问题的柔性多体系统动力学，研究多点碰撞及协调接触条件下碰撞恢复系数的表达形式。

中文关键词： 变结构；多体系统；动力学；优化；高斯最小拘束原理

英文摘要： Dynamics of multibody system with variable structure including mutation factors, such as friction,contact or collision, has stronge engineering background and is the hot issue in the dynamical field. Due to the complexity and speciality in the models of mechanics and mathematics, under the frame of traditional and regular methods, some difficulties still exsit in theoretical and numerical problems. In this project, we will carry out the research work around the scientific problems in dynamics of multibody system with variable structure. The following problems will be studied. First, the mathematical models in the optimized forms and the corresponding numerical methods will be established by virtue of the relationship among variational inequality, complementary problems and non-smooth optimization. This kind of model is equivalent with the regular dynamical models, but the numerical characteristics are different and the newly developed mathematical programming methods can provide better mathematical base for dealing with the theoretical difficulties and numerical operation of high efficiency. Second, using the mutation theory in modern mathematics, the singularity resulting from velocity mutation for the problems of dynamic contact of the multibody systems will be investigated. Third, the analytical expressions

英文关键词： variable constructure；system of multibody system；dynamics；optimization；Gauss principle of least constraint