一种抑制杂交元零能模式的假设应力场方法  

AN ASSUMED STRESS METHOD FOR ZERO-ENERGY MODE SUPPRESSION IN HYBRID FINITE ELEMENTS

作　　者：张灿辉[1] 王东东[1] 

机构地区：[1]厦门大学土木工程系

出　　处：《固体力学学报》2010年第1期40-47,共8页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(10972188;10602049);福建省科技项目(2007F3096);厦门市科技项目(3502Z20073012)资助

摘　　要：基于杂交元位移场直接导出可以表示单元任意变形的简单变形模式,同时指出与所有假设应力模式正交的非零变形为零能机动模式,从而可以用简单变形模式方便地识别和抑制单元零能模式.在此基础上利用初始应力模式与简单变形模式的正交性提出一种假设杂交元应力场的有效方法,结合等函数法应力模式组成初始应力模式,不仅可以根据实际问题需要灵活地假设不同分布规律的应力场,而且所形成杂交元可以完全避免零能机动模式.在数值算例中采用本文方法分别形成了2D-4节点杂交元和3D-8节点杂交元的多种假设应力场,表明本文所提出方法是有效可行的.A set of si hybrid elements are direc mple deformation modes that tly formation mode appears to b derived from the element e kinematic when it is ort can be used to describe the arbitrary deformation for displacement field. It is shown that the nonzero dehogonal to all the assumed stress modes. Thus the spurious kinematic mode of a given element can be easily determined and suppressed by using the proposed simple deformation modes. Based upon the orthogonality relationship between the initial stress modes and the simple deformation modes, an assumed stress method is presented and the related systematic procedure is illustrated in details. Since the stress modes given by the iso-function method are adopted here to derive the initial stress modes, one can find the necessary stress modes to represent the special stress distribution for different problems and the corresponding hybrid element is guaranteed from hour-glass modes. In the numerical examples several assumed stress fields for 2D-4 node and 3D-8 node elements are constructed by the proposed method and the results show that the method is very effective.

关 键 词：杂交应力元 简单变形模式 零能模式 假设应力场 

分 类 号：O302[理学—力学]