Abstract：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.
2011, Vol. 32 
