The basic finite element formulation used in most commercial FE systems is the conforming displacement method.  The displacement field within in element is assumed to be defined by the shape functions and nodal values of displacement.  Connected elements join at nodes and thus one obtains a fully conforming displacement field over the domain of interest and the compatibility conditions are satisfied a-priori.  Whilst this is a simple approach there are problems with it in that some elements perform badly under certain situations.  For example the four-noded plane stress/strain element is very poor at modelling bending also, for plane strain the material stiffness has a (1-2nu) term in the denominator which goes to zero then nu=0.5 and this clearly causes problems.  As such other formulations are often used to overcome these difficulties.  As long as one follows the general rules one can develop elements in many different ways.  Some of my research, for example, has been based on elements that use an assumed equilibrium stress field.  Assumed strain field elements presumably have 'shape functions' that are assumed strain fields rather than the conventional assumed displacement field.  The incompatible modes method is a very commonly used for the four-noded plane stress/strain element - e.g. plane42 in ANSYS.  Additional bubble type shape functions are added to the formulation that give this element much better bending performance than the standard element.  You can investigate the performance of different elements by choosing a challenging test problem, for which you know the theoretically exact answer, and then examine the convergence of meshes of different elements as you refine the mesh.

Thank you mr Ramsay for your answer.

AS method and incompatible modes method are used to make elements more flexible.

For this purpose Assumed Strain method add incompatible displacement to the basic element's formulation. It seems to be the same as incompatible modes method.

So my question: is these methods are the same. if not, what is the difference between them.

If the elements are based on a displacement formulation then they will be over stiff as you say.  The enhanced elements should be more flexible.  You will need to consult the theory manual of the software or a decent FE text book to answer your questions.

Visit this page.The question is answered.

http://www.eureka.im/3225.html

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