Fuzzy finite element analysis of imprecisely defined structures with fuzzy nodal force

This paper presents the fuzzy finite element analysis for static displacements of fixed free stepped rectangular beam, truss and simplified bridge structure with fuzzy nodal force. The material and geometric properties of the structures 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. A new approach is used here to solve the fuzzy system of linear equations. Numerical results for the three stepped rectangular beam, three-bar truss and simplified bridge with fifteen elements are presented to illustrate the computational aspects of the developed method. The results obtained are depicted in term of plots.

[1]  I. Elishakoff,et al.  Probabilistic Methods in the Theory of Structures , 1984 .

[2]  P. Level,et al.  Fuzzy behavior of mechanical systems with uncertain boundary conditions , 2000 .

[3]  B. Rao,et al.  Efficient explicit formulation for practical fuzzy structural analysis , 2011 .

[4]  Michael Hanss,et al.  Applied Fuzzy Arithmetic: An Introduction with Engineering Applications , 2004 .

[5]  I. Elishakoff,et al.  Convex models of uncertainty in applied mechanics , 1990 .

[6]  Snehashish Chakraverty,et al.  Fuzzy system of linear equations with crisp coefficients , 2013, J. Intell. Fuzzy Syst..

[7]  Mehdi Dehghan,et al.  Solution of the fully fuzzy linear systems using the decomposition procedure , 2006, Appl. Math. Comput..

[8]  Michael Hanss,et al.  The transformation method for the simulation and analysis of systems with uncertain parameters , 2002, Fuzzy Sets Syst..

[9]  M. Hanss,et al.  A fuzzy arithmetical approach to the solution of finite element problems with uncertain parameters , 2000 .

[10]  Wim Desmet,et al.  A response surface based optimisation algorithm for the calculation of fuzzy envelope FRFs of models with uncertain properties , 2008 .

[11]  T. Ross.  Fuzzy Logic with Engineering Applications , 1994 .

[12]  Carlos Alberto Conceição António,et al.  Uncertainty propagation in inverse reliability-based design of composite structures , 2010 .

[13]  A. S. Balu,et al.  Explicit fuzzy analysis of systems with imprecise properties , 2011 .

[14]  Singiresu S. Rao,et al.  Analysis of uncertain structural systems using interval analysis , 1997 .

[15]  Singiresu S Rao,et al.  Fuzzy finite element approach for the analysis of imprecisely defined systems , 1995 .

[16]  A. S. Balu,et al.  High dimensional model representation based formulations for fuzzy finite element analysis of structures , 2012 .

[17]  Snehashish Chakraverty,et al.  Numerical solution of interval and fuzzy system of linear equations , 2011 .

[18]  J. Z. Zhu,et al.  The finite element method , 1977 .

[19]  Ramon E. Moore.  Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.

[20]  Hans-Jürgen Zimmermann,et al.  Fuzzy Set Theory - and Its Applications , 1985 .

[21]  Xiaobin Guo,et al.  58 No . 2 2010 , 157-168 BLOCK GAUSSIAN ELIMINATION METHODS FOR FUZZY MATRIX EQUATIONS , 2010 .

[22]  Abraham Kandel,et al.  Fuzzy linear systems , 1998, Fuzzy Sets Syst..

[23]  Wim Desmet,et al.  A fuzzy finite element analysis technique for structural static analysis based on interval fields , 2010 .

[24]  Tuan D. Pham,et al.  Fuzzy logic applied to numerical modelling of engineering problems , 1995 .

[25]  Unyime O. Akpan,et al.  Practical fuzzy finite element analysis of structures , 2001 .

[26]  Robert L. Mullen,et al.  Formulation of Fuzzy Finite‐Element Methods for Solid Mechanics Problems , 1999 .

[27]  I. Babuska,et al.  Finite Element Analysis , 2021 .

[28]  Unyime O. Akpan,et al.  Fuzzy finite element analysis of smart structures , 2000, Smart Structures.

[29]  Z. Qiu,et al.  Exact bounds for the static response set of structures with uncertain-but-bounded parameters , 2006 .

[30]  W. Graf,et al.  Fuzzy structural analysis using α-level optimization , 2000 .

[31]  Snehashish Chakraverty,et al.  Fuzzy Finite Element based Solution of Uncertain Static Problems of Structural Mechanics , 2013 .

[32]  Singiresu S. Rao,et al.  Nonlinear Membership Functions in Multiobjective Fuzzy Optimization of Mechanical and Structural Systems , 1992 .

[33]  Li Chen,et al.  Fuzzy finite-element approach for the vibration analysis of imprecisely-defined systems , 1997 .

[34]  Snehashish Chakraverty,et al.  A new method for solving real and complex fuzzy systems of linear equations , 2012 .

[35]  Iwona Skalna,et al.  Systems of fuzzy equations in structural mechanics , 2008 .

[36]  C. Pantelides,et al.  Optimum structural design via convex model superposition , 2000 .

[37]  Achintya Haldar,et al.  Reliability Assessment Using Stochastic Finite Element Analysis , 2000 .

[38]  P. Senthilkumar,et al.  New approach to solve symmetric fully fuzzy linear systems , 2011 .

[39]  R. Mullen,et al.  Uncertainty in mechanics problems-interval-based approach , 2001 .