Abstract: “In Finite Element Analysis, unlike the classical beam theory, when a beam is modeled using Q4 (Bilinear Quadratic) plane element, the bending moment appears to be less than that of the exact one, i.e. the normal stresses are less than their exact values. The difference between the results of the bending moment indicates that the beam is more stiffened. This problem is defined as shear locking. It is related to the linear representation of the displacement field of that plane element. There are several methods to eliminate the shear locking effect either by increasing the mesh size of the elements, using elements with more nodes, or using numerical integration to integrate the stiffness matrix. Each of the mentioned methods are applied on a cantilever beam modeled using MATLAB.”

Keywords: Shear locking; FEM (Finite Element Method); Q4 elements (Bilinear Quadrilateral elements); Q6 elements (Improved Bilinear Quadrilateral elements); Gauss Quadrature