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

In two-dimensional penalty finite element analysis of incompressible materials, Q9/3P, the 9-node quadrilateral with three assumed quasi-pressure modes, is the most popular element not bothered by spurious pressure. 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 technique, a new and more efficient implementation scheme is devised for the penalty matrix. Same as the conventional Q9 element, when Q9/3P is fully integrated, it becomes expensive and too stiff, On the other hand, there are two spurious kinematic modes should,the element be sub-integrated, In the proposed Q9/3P element, the two mechanisms will be annihilated by judiciously chosen higher-order assumed stress modes in conjunction with a modified Hellinger-Reissner functional. It will be demonstrated that the element is of good accuracy and high efficiency.