Dear Peyman,

Limitations of Finite Element Methods

Finite element methods are extremely versatile and powerful and can enable designers to obtain information about the behavior of complicated structures with almost arbitrary loading.  In spite of the significant advances that have been made in developing finite element packages, the results obtained must be carefully examined before they can be used. This point cannot be overemphasized.

The most significant limitation of finite element methods is that the accuracy of the obtained solution is usually a function of the mesh resolution.  Any regions of highly concentrated stress, such as around loading points and supports, must be carefully analyzed with the use of a sufficiently refined mesh.  In addition, there are some problems which are inherently singular (the stresses are theoretically infinite).  Special efforts must be made to analyze such problems.

An additional concern for any user is that because current packages can solve so many sophisticated problems, there is a strong temptation to "solve" problems without doing the hard work of thinking through them and understanding the underlying mechanics and physical applications.  Modern finite element packages are powerful tools that have become increasingly indispensible to mechanical design and analysis.  However, they also make it easy for users to make big mistakes.

Obtaining solutions with finite element methods often requires substantial amounts of computer and user time.  Nevertheless, finite element packages have become increasingly indispensable to mechanical design and analysis.

For more on this topic, see attached files and following link:

http://www.kkiem.agh.edu.pl/dydakt/fem/fem.htm

Hoping this will be helpful,

Rafik

Hello

Also these links will provide you good information 

Hope help you 

Good Luck 

http://www.iauyazd.ac.ir/iauyazd/UserFiles/File/OmranGroup/files/Zienkiewicz%20O_C_,%20Taylor%20R_L_%20Vol_%201_%20The%20finite%20element%20met.pdf

http://icas.bf.rtu.lv/doc/Book.pdf

http://kntu.ac.ir/DorsaPax/userfiles/file/Mechanical/OstadFile/dr_nakhodchi/DarylL.LoganAFirstCourse.pdf

https://view.officeapps.live.com/op/view.aspx?src=https://engineering.purdue.edu/~ahvarma/CE595/CE595%20Section%205.ppt

http://www.engr.uvic.ca/~mech410/lectures/FEA_Theory.pdhttp://ocw.mit.edu/courses/materials-science-and-engineering/3-11-mechanics-of-materials-fall-1999/modules/fea.pdff

http://ptmts.org.pl/lod-sum-4-06.pdf

I agree the above posters.  The FE method is great but must be used with caution.  This is particularly  the case with the conventional displacement formulation used in most commercial FE systems since if the mesh is not adequately refined the resulting stresses will not be in equilibrium with the applied loads.  The solution is to follow strict simulation governance practices which mesh verifying the finite element software and then verifying the solution you are obtaining.  There is a great danger of the uneducated user perpetrating finite element malpractice and the only way of saving yourself is Sim Gov.  

If I don't misunderstand your question, there is a finite element method called 'the base force element method (BFEM)'. It seems that you have followed a professor (Yijiang Peng, https://www.researchgate.net/profile/Yijiang_Peng) in Researchgate, and professor Peng have published many works in this field. You could try to read professor Peng's papers in BFEM, or email to professor Peng directly, then you may find some help.

https://www.researchgate.net/profile/Yijiang_Peng