杂交元零能模式抑制的改进基本变形模式方法  

AN IMPROVED BASIC DEFORMATION MODE METHOD FOR ZERO-ENERGY MODE SUPPRESSION OF HYBRID ELEMENTS

作　　者：张灿辉[1] 王东东[1] 李同姗[1] 

机构地区：[1]厦门大学土木工程系

出　　处：《固体力学学报》2011年第6期630-637,共8页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(10972188);教育部新世纪优秀人才支持计划(NCET-09-0678);福建省科技项目(2007F3096)资助

摘　　要：基本变形模式方法是构造杂交元假设应力场的一种有效方法,但只给出了识别零能模式的必要条件.论文指出基本变形模式方法由于没有考虑耦合影响而存在应用上的局限,在此基础上利用柔度矩阵的正定性给出了判别零能机动模式的充要条件,并且通过内积向量无关性进一步完善了假设杂交元应力场的基本变形模式方法,可以适用于基本变形模式之间耦合的任意形状单元.在数值算例中采用论文方法分别形成了2D-4节点任意形状杂交元的多种假设应力场,结果表明论文所提出方法是有效可行的.Basic deformation mode method is very effective to construct the assumed stress field for hybrid elements. However,this method only provides the necessary condition for a zero-energy mode free element. In this work it is shown that due to the coupled effect among various basic modes, the basic deformation method exists some limitation in application at first. Following, the sufficient and necessary condition for determination of zero energy modes is presented by using the positive definiteness property of flexibility matrix. Finally, the assumed stress method is improved for coupled basic modes by means of the linear independence of special inner product vectors and it is applicable to arbitrary element shapes. Numerical examples of 2D 4-ndoe elements show that the proposed method is effective.

关 键 词：杂交应力元 基本变形模式 零能模式 假设应力场 任意形状 

分 类 号：O241.82[理学—计算数学] O344.1[理学—数学]