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

通过杂交元位移场直接推导了单元基本变形模式,并且采用联合正交条件提出一种新的正交化方法,所得到的正交基本变形模式不仅具有简单的变形特征而且和材料参数无关,可以方便有效地考察单元性能,为评价不同杂交元提供了一个统一的参考标准.在此基础上利用柔度矩阵正定性给出一种简单有效的零能模式识别方法,并进一步利用基本变形模式和初始应力模式之间耦合关系,提出一种抑制杂交元零能模式的假设应力场方法,同时指出基本变形模式正交性是抑制单元零能模式的充分必要条件.2D-4节点和3D-8节点单元的数值算例说明了该文基本变形模式方法的有效性.

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.