Volume 53 | Number 4 | Year 2018 | Article Id. IJMTT-V53P539 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P539

In this paper, the finite element analysis for static displacements of some complicated Euler-Bernoulli beam structure is considered in fuzzy environment, where the material and geometric properties are taken as crisp. The numerical examples deals with cantilever beam, a beam clamped at one end and supported by a linear elastic spring. Various loads such as constant distributed,linearly varying, and point loads are considered for the examples. Assembled system of the above structures converts into fuzzy system of linear equations by taking right hand side global force vector as fuzzy keeping coefficient matrix as crisp.The results obtained are represented in terms of plots.

[1]. O.C.Zienkiewicz, The Finite Element Method : Tata McGraw Hill Edition, 1979.

[2]. J.N.Reddy, An Introduction to the Finite Element Method : Tata McGraw Hill Edition, 2005.

[3]. S.S.Bhavikati, Finite Element Analysis : New Age International Publisher, 2005.

[4]. I.Elishakoff, Probabilistic methods in the theory of Structures: New York ,Wiley, 1983.

[5]. A.Haldar and S.Mahadevan, Reliability Assessment Using Stochastic Finite Element Analysis. New York : John Wiley and Sons, 2000.

[6]. L.Zadeh,Fuzzy Sets, Information and control, vol.8, pp. 338-353, 1965.

[7]. D.Dubois and H.Prade, “Operations on fuzzy numbers,” Inter. Journal of Systems Science, vol.9, pp.613-626, 1978.

[8]. R.E.Moore, Methods and Applications of Interval Analysis, Philadelphia : SAIM Publication , 1979.

[9]. S.S.Rao and L.Berke, “Analysis of uncertain structural systems using interval analysis," AIAA Journal., vol. 35, pp. 727-735,1997.

[10]. Z.Qui, X.Wang and J. Chen, “Exact bounds for the static response set of structures with uncertain-but-bounded parameters," Int. J. Sol. Struct., vol. 43, pp.6574-6593, 2006.

[11]. A.Chekri, G. Plessis, B.Lallemand, T.Tison, and P.level, “Fuzzy behavior of mechanical systems with uncertain boundary conditions," Comput. Methods Apll. Mech. Eng., vol.189, pp.863-873, 2000.

[12]. M.Hanss, Applied Fuzzy Arithmetic -An Introduction With Engineering Applications, Berlin : Springer-Verlag, ,2005.

[13]. S.S.Rao and J.P.Sawyer,“Fuzzy finite element approach for the analysis of imprecisely defined systems," AIAA J., vol.33, pp.2364-2370, 1995

[14]. U.O.Akpan, T.S.Koko, I.R.Orisamolu and B.K.Gallant, “Fuzzy finite element analysis of smart structures," Smart Mater. Struct., vol.10, pp.273-284,2001.

[15]. U.O.Akpan, T.S.Koko, I.R.Orisamolu, and B.K.Gallant, “Practical fuzzy finite element analysis of structures," Finite Element Analysis Des., vol.38, pp.93-111, 2001.

[16]. D. Behera and S. Chakraverty, “Fuzzy finite element analysis of imprecisely defined structures with fuzzy nodal force," Eng. Appl. Artificial Intell., vol.26, pp.2458-2466, 2013.

[17]. M.Hanss and K.Willner, “A fuzzy arithmetical approach to the solution of finite element problems with uncertain parameters," Mech.Res.Commun., vol.27, pp.257-272, 2000.

[18]. A.S.Balu and B.N.Rao,“Explicit fuzzy analysis of systems with imprecise properties," Int. J. Mech. Mater. Des., vol.7, pp.283-289,2011.

[19]. A.S.Balu and B.N.Rao,“High dimensional model representation based formulation for fuzzy finite analysis of structures," Finite Elem. Anal. Des.,vol.50, pp.217-230,2012.

[20]. J.J.Buckley and Y.Qu, “Solving system of linear fuzzy equations," Fuzzy Sets and Systems, vol.43, pp.33-43, 1991.

[21]. D. Dubois and H. Prade, Fuzzy Sets and systems: Theory and Applications, New York : Academic Press 1980.

[22]. M.Friedman, M.Ming and A.Kandel,“Fuzzy linear systems," Fuzzy Sets Syst., vol.96, pp.201-209, 1998.

[23]. X.Wang, Z.Zong and M.Ha, “Iteration algorithms for solving a system of fuzzy linear equations," Fuzzy Sets and Systems, vol.119, pp.121-128, 2001.

[24]. A.Kauffman, M.M.Gupta, Introduction to Fuzzy Arithmetic:Theory and Applications, New York : Van Nostrand Reinhold, 1991.

[25]. D. Dubois and H. Prade, “The mean value of a fuzzy number," Fuzzy sets and Systems, vol.24, pp.279-300, 1987.

[26]. O.Kaleva, “Fuzzy differential equations," Fuzzy Sets and Systems, vol.24, pp.301-317, 1987.

[27]. Ming Ma, M.Friedman and A.Kandel, “A new fuzzy arithmetic," Fuzzy Sets and Systems, vol.108, pp.83-90, 1999.

Deb Kumar Ranjit, Tapan Kumar Roy, "Fuzzy Finite Element Method Applied to Euler-Bernoulli Beam Problem," *International Journal of Mathematics Trends and Technology (IJMTT)*, vol. 53, no. 4, pp. 304-320, 2018. *Crossref*, https://doi.org/10.14445/22315373/IJMTT-V53P539