杂交元零能模式抑制的改进基本变形模式方法

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.

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

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 between various basic modes, the basic deformation method has a severe limitation for zero-energy mode free element construction. Subsequently by using the positive definiteness property of flexibility matrix the sufficient and necessary condition for determination of zero energy modes is presented. Moreover 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 very effective.