An assumed strain quadrilateral element with drilling degrees of freedom
In the framework of the assumed strain method, we specialize the procedure proposed by Simo and Rifai (Int. J. Numer. Methods Eng. 29 (1990) 1595) to the study of a four nodes quadrilateral membrane with drilling degrees of freedom. The proposed numerical model is based on the minimization of the modified HuWashizu functional where the enhanced strain and the enhanced rotation fields are included. By means of a convenient choice of the enhanced displacement gradient in the isoparametric space, the patch test condition is satisfied a priori. The stability and the convergence of the numerical method are discussed and the numerical examples show that the proposed finite element exhibits good behavior for distorted coarse mesh under bending stress states. Then, the proposed finite element is coupled to the DKQ element to provide an effective shell element.
drilling degrees of freedom quadrilateral finite element