CFP last date
20 January 2025
Call for Paper
February Edition
IJCA solicits high quality original research papers for the upcoming February edition of the journal. The last date of research paper submission is 20 January 2025

Submit your paper
Know more
The week's pick
Responsive image
SFLA-Based Line Balancing and Task Optimization in Master-Slave Controlled Hanger Transportation Systems for Garment Production

Duc Hoang Nguyen
Random Articles
Reseach Article

Fuzzy Finite Element based Solution of Uncertain Static Problems of Structural Mechanics

by Diptiranjan Behera, S. Chakraverty
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 69 - Number 15
Year of Publication: 2013
Authors: Diptiranjan Behera, S. Chakraverty
10.5120/11916-8040

Diptiranjan Behera, S. Chakraverty . Fuzzy Finite Element based Solution of Uncertain Static Problems of Structural Mechanics. International Journal of Computer Applications. 69, 15 ( May 2013), 6-11. DOI=10.5120/11916-8040

@article{ 10.5120/11916-8040,
author = { Diptiranjan Behera, S. Chakraverty },
title = { Fuzzy Finite Element based Solution of Uncertain Static Problems of Structural Mechanics },
journal = { International Journal of Computer Applications },
issue_date = { May 2013 },
volume = { 69 },
number = { 15 },
month = { May },
year = { 2013 },
issn = { 0975-8887 },
pages = { 6-11 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume69/number15/11916-8040/ },
doi = { 10.5120/11916-8040 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:30:19.911485+05:30
%A Diptiranjan Behera
%A S. Chakraverty
%T Fuzzy Finite Element based Solution of Uncertain Static Problems of Structural Mechanics
%J International Journal of Computer Applications
%@ 0975-8887
%V 69
%N 15
%P 6-11
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Fuzzy finite element analysis for static displacements of beam structures with fuzzy forces is considered in this paper. The material properties of the beams are taken as crisp. Fuzzy finite element analysis of static problem for the above structures converts the problem into fuzzy system of linear equations. As such the coefficient matrix and the right hand side vector become crisp and fuzzy respectively. Here, a new method is proposed to solve the fuzzy system of linear equations. Numerical results for the beam structures are presented to illustrate the computational aspects of the developed method. The results obtained by the proposed method are compared with the existing solution method.

References
  1. I. Elishakoff, Probabilistic Methods in the Theory of Structures. Wiley, New York, 1983.
  2. A. Haldar and S. Mahadevan, Reliability Assessment Using Stochastic Finite Element Analysis. John Wiley & Sons, New York, 2000.
  3. C. C. Antonio, and L. N. Hoffbauer, "Uncertainty propagation in inverse reliability-based design of composite structures," Int. J. Mech. Mater. Des. , vol. 6, pp. 89–102, 2010.
  4. R. E. Moore, Methods and Applications of Interval Analysis, SAIM Publication, Philadelphia, 1979.
  5. Y. Ben-Haim and I. Elishakoff, Convex Models of Uncertainty in Applied Mechanics, Elsevier Science, Amsterdam, 1990.
  6. S. Ganzerli, and C. P. Pantelides, "Optimum structural design via convex model superposition," Comput. Struct. , vol. 74, pp. 639–647, 2000.
  7. S. S. Rao, and L. Berke, "Analysis of uncertain structural systems using interval analysis," AIAA J. , vol. 34, pp. 727–735, 1997.
  8. R. L. Muhanna, and R. L. Mullen, "Uncertainty in mechanics problems interval-based approach," ASCE J. Eng. Mech. , vol. 127, pp. 557–566, 2001.
  9. 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.
  10. L. Zadeh, Fuzzy sets", Inf. Control, vol. 8, pp. 338–353, 1965.
  11. S. Valliappan, and T. D. Pham, "Fuzzy logic applied to numerical modeling of engineering problems," Comput. Mech. Adv. , vol. 2, pp. 213–281, 1995.
  12. M. D. Munck, D. Moens, W. Desmet, and D. Vandepitte, "A response surface based optimisation algorithm for the calculation of fuzzy envelope FRFs of models with uncertain properties," Comput. Struct. , vol. 86, pp. 1080–1092, 2008.
  13. B. Moller, W. Graf, and M. Beer, "Fuzzy structural analysis using level optimization," Comput. Mech. , vol. 26, pp. 547–565, 2000.
  14. M. Hanss, "The transformation method for the simulation and analysis of systems with uncertain parameters," Fuzzy Sets Syst. , vol. 130, pp. 277–289, 2002.
  15. M. Hanss, Applied Fuzzy Arithmetic: An Introduction with Engineering Applications, Springer-Verlag, Berlin, 2005.
  16. A. Chekri, G. Plessis, B. Lallemand, T. Tison, and P. Level, "Fuzzy behavior of mechanical systems with uncertain boundary conditions," Comput. Methods Appl. Mech. Eng. , vol. 189, pp. 863-873, 2000.
  17. A. K. Dhingra, S. S. Rao, and V. Kumar, "Nonlinear membership function in multi-objective fuzzy optimization of mechanical and structural systems," AIAA J, vol. 30, pp. 251–260, 1992.
  18. O. C. Zienkiewicz, The Finite Element Method. Tata McGraw Hill Edition, 1979.
  19. 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.
  20. W. Verhaeghe, M. D. Munck, W. Desmet, , D. Vandepitte, and D. Moens, "A fuzzy finite element analysis technique for structural static analysis based on interval fields. ," 4th Int. Workshop Reliable Eng. Comp. , pp. 117-128, 2010.
  21. U. O. Akpan, T. S. Koko, I. R. Orisamolu, and B. K. Gallant, "Practical fuzzy finite element analysis of structures," Finite Elem. Anal. Des. , vol. 38, pp. 93–111, 2001.
  22. 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.
  23. R. L. Muhanna, and R. L. Mullen, "Formulation of fuzzy finite element method for mechanics problems," Comput. -Aided Civil Infrastruct. Eng. , vol. 14, pp. 107-117, 1999.
  24. 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.
  25. A. S. Balu, and B. N. Rao, "Efficient explicit formulation for practical fuzzy structural analysis," Sadhana, vol. 36, pp. 463-488, 2011.
  26. 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.
  27. A. S. Balu, and B. N. Rao, "High dimensional model representation based formulations for fuzzy finite element analysis of structures, "Finite Elem. Anal. Des. ," vol. 50, pp. 217-230, 2012.
  28. M. Friedman, M. Ming, and A. Kandel, "Fuzzy linear systems," Fuzzy Sets Syst. , vol. 96, pp. 201-209, 1998.
  29. X. Guo, and Z. Gong, "Block Gaussian elimination methods for fuzzy matrix equations," Int. J. Pure App. Math. , vol. 58, pp. 157-168, 2010.
  30. P. Senthilkumar, and G. Rajendran, "New approach to solve symmetric fully fuzzy linear systems," Sadhana, vol. 36, pp. 933-940, 2011.
  31. M. Dehghan, and B. Hashemi, "Solution of the fully fuzzy linear system using the decomposition procedure," Appl. Math. Comput. , vol. 182, pp. 1568-1580, 2006.
  32. S. Das, and S. Chakraverty, "Numerical solution of interval and fuzzy system of linear equations," Appl. Appl. Math. : An Int. J. , vol. 7, pp. 334-356, 2012.
  33. I. Skalna, M. V. , Rama Rao, and A. Pownuk, "Systems of fuzzy equations in structural mechanics," J. Comp. Appl. Math. , vol. 218, pp. 149-156, 2008.
  34. D. Behera, D. Datta, and S. Chakraverty, "Development of a finite element solution of a stepped rectangular Bar in presence of fuzziness in material properties," Proc. 5th Int. Conf. Adv. Mech. Eng. , SVNIT, Surat-395 007, India, ICAME-2011, pp. 205-209, 2011.
  35. T. J. Ross, Fuzzy Logic with Engineering Applications. John Wiley & Sons, New York, 2004.
  36. H. J. Zimmermann, Fuzzy Set Theory and its Application. Kluwer academic publishers, London, 2001.
  37. S. S. Bhavikati, Finite Element Analysis. New Age International Publisher, 2005.
  38. S. Chakraverty, and D. Behera, "Fuzzy system of linear equations with crisp coefficients," J. Intell. Fuzzy Syst. , vol. 25, pp. 201-207, 2013.
  39. D. Behera and S. Chakraverty, A new method for solving real and complex fuzzy systems of linear equations, Comp. Math. Model. , Vol. 23, pp. 507-518, 2012.
Index Terms

Computer Science
Information Sciences

Keywords

Triangular fuzzy number Fuzzy system of linear equations Fuzzy finite element method Beam

Powered by PhDFocusTM