应用数学和力学2011，Vol.32Issue(1)：79-92,14.DOI:10.3879/j.issn.1000-0887.2011.01.009
杂交元零能模式抑制的正交基本变形模式方法
Orthogonal Basic Deformation Mode Method for Zero-Energy Mode Suppression of Hybrid Stress Element
摘要
Abstract
A set of basic deformation modes for hybrid stress finite element were directly derived from the element displacement field.Subsequently by employing the so-called united orthogonal conditions a new orthogonalization method was also proposed.The resulting orthogonal basic deformation modes exhibit simple and clear physical meanings.In addition, they do not involve any material parameters and thus can be efficiently used to examine the element performance and serve as a unified tool to assess different hybrid elements.Therafter a convenient approach for identification of spurious zero-energy modes was presented through using the positive definiteness property of flexibility matrix.Moreover, based upon the orthogonality relationship between the given initial stress modes and the orthogonal basic deformation modes,an alternative method of assumed stress modes to formulate a hybrid element free of spurious modes was discussed.It was also found that the orthogonality of the basic deformation modes was the sufficient and necessary condition for suppression of spurious zero-energy modes.Numerical examples of 2D 4-node quadrilateral element and 3D 8-node hexahedral element were illustrated in details to demonstrate the efficacy of the proposed orthogonal basic deformation mode method.关键词
杂交应力元/基本变形模式/正交化方法/假设应力模式/零能模式抑制分类
数理科学引用本文复制引用
张灿辉,王东东,李同姗..杂交元零能模式抑制的正交基本变形模式方法[J].应用数学和力学,2011,32(1):79-92,14.基金项目
国家自然科学基金资助项目(10972188) （10972188）
中央高校基本科研业务费专项资金资助项目(2010121073) （2010121073）
福建省科技基金资助项目(2007F3096) （2007F3096）
