基于等几何分析的复杂结构接触分析Nitsche方法研究

结构接触问题是工程实践中常见的一类问题。与传统有限元相比，等几何分析采用的NURBS基函数可精确描述结构几何边界，接触搜索精度高，天然适用于分析接触问题。然而，当前的等几何接触列式普遍采用的方法实用性不足，相关研究成果难以直接应用于工程实践，基于等几何分析的复杂结构接触分析方法亟待进一步研究。本课题拟基于等几何Nitsche方法发展大变形接触理论，考虑裁剪、拼接和局部加密等模型特征，发展通用的接触边界搜索算法，研究稳定高效的接触列式及相应迭代方法，开发接触求解器。本课题将发展针对复杂CAD模型的接触搜索算法和接触列式，开发针对复杂结构的大变形接触分析求解器，为实际工程应用中的结构接触问题分析提供新方法和新工具。

It is a common situation in engineering practice to simulate contact problems of structures. Compared with traditional finite element analysis, the NURBS basis functions used in isogeometric analysis are able to accurately describe the geometric boundary of structures, the contact detection accuracy is correspondingly improved, thus isogeometric analysis is naturally suitable for analyzing contact problems. However, current methods commonly used in isogeometric contact formulations are far from practical engineering applications, related research results are difficult to be applied directly. Analysis methods for complex structural contact in isogeometric analysis framework urgently needs to be further studied. This project intends to develop large-deformation contact theory based on the isogeometric Nitsche's method, with considering model features such as clipping, splicing and local encryption, to develop a general contact boundary detection algorithm, to study stable and efficient contact formulations as well as corresponding iterative methods, and to develop a contact solver. This research will develop contact search algorithms and contact columns for complex CAD models, develop a large deformation contact analysis solver for complex structures, corresponding research results will provide new methods and new tools for the analysis of structural contact problems in practical engineering applications.