Impact of Integration on Straining Modes and Shear-Locking for Plane Stress Finite Elements

Stiffness matrix of the four-node quadrilateral plane stress element is decomposed into normal and shear components. A computer program is developed to obtain the straining modes using adequate and reduced integration. Then a solution for the problem of mixing straining modes is found. Accuracy of the computer program is validated by a closed-form stiffness matrix, derived for the plane rectangular as well as square element. It is shown that method of integration has no effect on the straining modes, but it influences the eigenvalues of the bending modes. This effect is intensified by increasing the element aspect ratio, confirming the occurrence of shear locking.