克服岩土工程有限病态问题方法的对比与研究.pdf

第25 卷 第 10 期 岩石力学与工程学报 Vol.25 No.10 2006 年 10 月 Chinese Journal of Rock Mechanics and Engineering Oct.，2006 克服岩土工程有限元病态问题方法的对比与研究 党发宁，殷 静，李志宏 (西安理工大学 水利水电学院，陕西 西安 710048) 摘要：位移有限元方法应用于岩土工程数值计算时，常会遇到各种有限元病态问题，诸如材料极不均匀体、极端 各向异性体、不可压缩或几乎不可压缩弹性体、板的“自锁”等有限元病态问题。研究目前岩土工程界提出的多 种克服有限元病态问题的方法及各自的特点(如正则化方法、归一化方法及变刚度方法等) 。通过平面杆件系统的有 限元计算算例，分析和对比正则化方法、归一化方法和变刚度方法在解决有限元病态问题时的优劣性。 关键词：岩土工程；有限元；病态问题；归一化方法；正则化方法；变刚度有限元方法 中图分类号：TU 43 文献标识码：A 文章编号：1000 –6915(2006)10 –1969 –06 COMPARISON AND STUDY ON METHODS FOR SOLVING FINITE ELEMENTS ILL-CONDITIONED PROBLEMS IN GEOTECHNICAL ENGINEERING DANG Faning ，YIN Jing ，LI Zhihong (College of Water Resources and Hydroelectric Engineering ，Xi ′an University of Technology，Xi ′an ，Shaanxi 710048，China) Abstract ：When the displacement finite element model is applied to numerical calculation in geotechnical engineering ，ill-condition problems often occur. This paper comments on these problems such as extreme anisotropy，incompressible or nearly incompressible material as well as shear locking in plate ，etc. and researches the characteristics and applicable situation of many methods to conquer ill-condition problems such as regularization ，standardization and splitting elastic modules finite elements. By the example of calculating plane bar-system problems with finite element method，the advantages and disadvantages of regularization，standardization and splitting elastic modulus finite element method are analyzed and compared. Key words ：geotechnical engineering ；finite elements；ill-conditioned problems ；standardization；regularization ； splitting elastic modulus finite element method