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Abstract A set of simple deformation modes that can be used to describe the arbitrary deformation for hybrid elements are directly derived from the element displacement field. It is shown that the nonzero deformation mode appears to be kinematic when it is orthogonal 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 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.
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Received: 16 September 2008
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2010, Vol. 31 
