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SUMMARYA stabilization procedure is developed for controlling the kinematic modes of the four-node, bilinear quadrilateral element when single-point quadrature is used. These kinematic modes manifest themselves by spatial. oscillations or singularity of the total stiffness. In this stabilization procedure, additional generalized strains are defined which are activated by the kinematic modes; these generalized modes are furthermore not activated by rigid body motions regardless of the shape of the quadrilateral. By using a scaling law developed in an earlier paper, the stabilization parameters are defined so they do not adversely affect the element's performance. Several problems which are subject to kinematic modes are presented to illustrate the performance of this stabilization procedure for linear problems.

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