ELIMINATION OF SPURIOUS PRESSURE AND KINEMATIC MODES IN BIQUADRATIC 9-NODE PLANE ELEMENT

In two-dimensional penalty finite element analysis of incompressible m aterials, Q9/3P, the 9-node quadrilateral with three assumed quasi-pre ssure modes, is the most popular element not bothered by spurious pres sure. In constructing the penalty matrix of Q9/3P, it is necessary to form a 3 x 18 matrix and a 3 x 3 symmetric matrix, The inverse of the symmetric matrix is then post- and pre-multiplied by the 3 x 18 matrix and its transpose, respectively. By employing a rank subtraction tech nique, a new and more efficient implementation scheme is devised for t he penalty matrix. Same as the conventional Q9 element, when Q9/3P is fully integrated, it becomes expensive and too stiff, On the other han d, there are two spurious kinematic modes should,the element be sub-in tegrated, In the proposed Q9/3P element, the two mechanisms will be an nihilated by judiciously chosen higher-order assumed stress modes in c onjunction with a modified Hellinger-Reissner functional. It will be d emonstrated that the element is of good accuracy and high efficiency.