Shear Locking Error

Shear locking error

As it is said earlier, reduced integration elements are suffering hourglass effect due to their low bending stiffness. On the other hand higher bending stiffness of full integration elements might cause another numerical issue, called shear locking effect.

Fully integrated first order elements, such as solid elements, Timoshenko beam elements, may exhibit shear locking effect.  As a result, FEA codes might give false results when this type of element is used.

In reality when a block of material is subjected to pure bending, it experiences a curved shape, but when we simulated it with full integration elements things might be a bit differenet from the real behavior of material.

Unfortunately the edges of the fully integrated first order element are, however, not able to bend to curves. As a result the final deformation of the elements is similar to this figure.

In this condition, which is called shear locking effect, the upper surface experiences tensile stress, and the lower surface experiences compressive stress.as it is shown in the figure, dotted lines remain straight and angle A changes, which requires an artificial shear stress to be introduced. This shear stress makes the element overly stiff.Consequently, wrong displacements, inaccurate stresses are common consequences of shear locking effect of fully integration elements.

How to coup with shear locking effect

As it is mentioned earlier, shear locking happens only for full integration elements which are subjected to bending moments. But these elements are highly efficient for other loading such as shear or axial loading. It is recommended to use second order full integration elements to ease this problem.

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