Convergence Requirement & Compatibility Requirement

CONVERGENCE REQUIREMENT:

          The finite element provides a numerical solution to a complex problem.It may be therefore expected that solution must converge to the exact solution under certain circumstances.

    Convergence Criteria : It can be shown that the displacement formulation of the method leads to an upper bound to the actual stiffness of the structure.Hence, the mesh is made finer,the solution should converge to exact result and this would be achieved if the following three condition are satisfied by the assumed displacement function. 

1. The displacement function must be continuous within the element.
2. The displacement function must be capable for representing rigid body displacement of the element.
3. The displace function must be capable for representing constant strain state within the element.

COMPATIBILITY REQUIREMENT:

            The compatibility requirement are listed below

1. The displacement must be compatible between adjacent element.
2. The element before there must not be any discontinuity between the element.
3. The element mustn't overlap or separate.
4. In case of beam,plate and cell element,this requirement would also include that there should be no sudden change in slope across the inter element boundary.

The element which satisfy all the three convergence requirement condition and compatibility condition are called as compatible conforming element.