Skip to main content
Log in

Efficient explicit formulation for practical fuzzy structural analysis

  • Published:
Sadhana Aims and scope Submit manuscript

Abstract

This paper presents a practical approach based on High Dimensional Model Representation (HDMR) for analysing the response of structures with fuzzy parameters. The proposed methodology involves integrated finite element modelling, HDMR based response surface generation, and explicit fuzzy analysis procedures. The uncertainties in the material, geometric, loading and structural parameters are represented using fuzzy sets. To facilitate efficient computation, a HDMR based response surface generation is employed for the approximation of the fuzzy finite element response quantity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Adduri PR, Penmetsa RC 2008 ‘Confidence bounds on component reliability in the presence of mixed uncertain variables,’ Int. J. Mech. Sci. 50(3): 481–489

    Article  Google Scholar 

  • Akpan UO, Koko TS, Orisamolu IR, Gallant BK 2001a ‘Practical fuzzy finite element analysis of structures,’ Finite Elem. Anal. Des. 38: 93–111

    Article  MATH  Google Scholar 

  • Akpan UO, Koko TS, Orisamolu IR, Gallant BK 2001b ‘Fuzzy finite element analysis of smart structures,’ Smart Mater. Struct. 10: 273–284

    Article  Google Scholar 

  • Alefeld G, Herzberger J 1983 Introduction to interval computations, (New York, USA: Academic Press)

    MATH  Google Scholar 

  • Anderson TL 1995 Fracture mechanics: Fundamentals and applications, Boca Raton, Florida: CRC Press Inc.

    MATH  Google Scholar 

  • Chen C 1996 Fuzzy logic and neural network handbook, Computer engineering series, New York: McGraw-Hill

    Google Scholar 

  • Chen L, Rao SS 1997 ‘Fuzzy finite element approach for the vibration analysis of imprecisely defined systems,’ Finite Elem. Anal. Des. 27: 69–83

    Article  MATH  Google Scholar 

  • Chowdhury R, Rao BN, Prasad AM 2008 ‘High dimensional model representation for piece wise continuous function approximation,’ Commun. Numer. Methods Eng. 24(12): 1587–1609

    Article  MathSciNet  MATH  Google Scholar 

  • Dessombz O, Thouverez F, Laîné JP, Jézéquel L 2001 ‘Analysis of mechanical systems using interval computations applied to finite element methods,’ J. Sound Vib. 239(5): 949–968

    Article  Google Scholar 

  • Dhingra AK, Rao SS, Kumar V 1992 ‘Nonlinear membership function in multi-objective fuzzy optimization of mechanical and structural systems,’ AIAA J. 30: 251–260

    Article  MATH  Google Scholar 

  • Donders S, Vandepitte D, Van de Peer J, Desmet W 2005 ‘Assessment of uncertainty on structural dynamic responses with the short transformation method,’ J. Sound Vib. 288(3): 523–549

    Article  Google Scholar 

  • Dong WM, Shah HC 1987 ‘Vertex method for computing functions of fuzzy variables,’ Fuzzy Sets Syst. 24(1): 65–78

    Article  MathSciNet  MATH  Google Scholar 

  • Dong WM, Wong FS 1987 ‘Fuzzy weighted averages and implementation of the extension principle,’ Fuzzy Sets Syst. 21(2): 183–199

    Article  MathSciNet  MATH  Google Scholar 

  • Drucker H, Burges CJC, Kaufman L, Smola A, Vapnik V 1997 ‘Support vector regression machines,’ Adv. Neural Inf. Process. Syst. 9: 155

    Google Scholar 

  • Elishakoff I 1995 ‘Essay on uncertainties in elastic and viscoelastic structures: from A.M. Freudenthal’s criticism to modern convex modelling,’ Comput. Struct. 56(2): 871–895

    Article  MATH  Google Scholar 

  • Farkas L, Moens D, Vandepitte D, Desmet W 2008 ‘Application of fuzzy numerical techniques for product performance analysis in the conceptual and preliminary design stage,’ Comput. Struct. 86(10): 1061–1079

    Article  Google Scholar 

  • Gersem HD, Moens D, Desmet W, Vandepitte D 2007 ‘Interval and fuzzy dynamic analysis of finite element models with superelements,’ Comput. Struct. 85(5–6): 304–319

    Article  Google Scholar 

  • Haldar A, Mahadevan S 2000 Reliability assessment using stochastic finite element analysis, 1st Edition, (New York: John Wiley & Sons, Inc.)

    Google Scholar 

  • Hansen E 1992 Global optimization using interval analysis, New York, USA: Marcel Dekker, Inc.

    MATH  Google Scholar 

  • Hanss M 2002 ‘The transformation method for the simulation and analysis of systems with uncertain parameters,’ Fuzzy Sets Syst. 130(3): 277–289

    Article  MathSciNet  MATH  Google Scholar 

  • Harvey RL 1994 Neural network principles, NJ, USA: Prentice-Hall Inc.

    MATH  Google Scholar 

  • Jones DR, Schonlau M, Welch WJ 1998 ‘Efficient global optimization of expensive black-box functions,’ J. Glob. Optim. 13(4): 455–492

    Article  MathSciNet  MATH  Google Scholar 

  • Lernout EC, Pellissetti M, Pradlwarter H, Schueller GI, Soize C 2006 ‘Data and model uncertainties in complex aerospace engineering systems,’ J Sound Vib. 295(3–5): 923–938

    Google Scholar 

  • Li G, Rosenthal C, Rabitz H 2001a ‘High dimensional model representations,’ J. Phys. Chem. A 105: 7765–7777

    Article  Google Scholar 

  • Li G, Wang SW, Rabitz H 2001b ‘High dimensional model representations generated from low dimensional data samples-I. mp-Cut-HDMR,’ J. Math. Chem. 30(1): 1–30

    Article  MathSciNet  Google Scholar 

  • Moens D, Vandepitte D 2004 ‘Non-probabilistic approaches for non-deterministic dynamic FE analysis of imprecisely defined structures,’ Proceedings of the International Conference on Noise and Vibration Engineering, ISMA, Leuven, 3095–3119

  • Möller B, Graf W, Beer M 2000 ‘Fuzzy structural analysis using α-level optimization,’ Comput. Mech. 26(60): 547–565

    MATH  Google Scholar 

  • Moore RE 1979 Methods and applications of interval analysis, Philadelphia, USA: SAIM Publication

    Book  MATH  Google Scholar 

  • Muhanna RL, Mullen RL 2001 ‘Uncertainty in mechanics problems interval-based approach, J. Eng. Mech., ASCE, 127(6): 557–566

    Article  Google Scholar 

  • Munck MD, Moens D, Desmet W, Vandepitte D 2008 ‘A response surface based optimisation algorithm for the calculation of fuzzy envelope FRFs of models with uncertain properties,’ Comput. Struct. 86(10): 1080–1092

    Article  Google Scholar 

  • Pellissetti MF, Schueller GI 2007 ‘The effects of uncertainties in structural analysis,’ J. Struct. Eng. Mech. 25(3): 311–330

    Google Scholar 

  • Qiu Z, Elishakoff I 1998 ‘Antioptimization of structures with large uncertain-but-non-random parameters via interval analysis,’ Comput. Methods Appl. Mech. Eng. 152(3–4): 361–372

    Article  MATH  Google Scholar 

  • Rao BN, Chowdhury R 2008 ‘Probabilistic analysis using high dimensional model representation and fast Fourier transform,’ Int. J. Comput. Methods Eng. Sci. Mech. 9(6): 342–357

    Article  MATH  Google Scholar 

  • Rao SS and Berke L 1997 ‘Analysis of uncertain structural systems using interval analysis,’ AIAA J. 34(4): 727–735

    Article  Google Scholar 

  • Ross TJ 2004 Fuzzy Logic with Engineering Applications, Second Edition, Chichester: John Wiley & Sons Ltd.

    Google Scholar 

  • Schueller GI, Pradlwarter HJ, Koutsourelakis P 2004 ‘A critical appraisal of reliability estimation procedures for high dimensions,’ Probab. Eng. Mech. 19(4): 463–474

    Article  Google Scholar 

  • Sobol IM 1993 ‘Sensitivity estimates for nonlinear mathematical models,’ Math. Model. Comput. Exper. 1: 407–414

    MathSciNet  MATH  Google Scholar 

  • Sobol IM 2003 ‘Theorems and examples on high dimensional model representations,’ Chem. Reliab. Eng. Syst. Saf. 79(2): 187–193

    Article  MathSciNet  Google Scholar 

  • Soize C 2009 ‘Nonparametric probabilistic approach of uncertainties for elliptic boundary value problem,’ Int. J. Numer. Methods Eng. 80(6–7): 673–688

    Article  MathSciNet  MATH  Google Scholar 

  • Valliappan S, Pham TD 1995 ‘Fuzzy logic applied to numerical modeling of engineering problems,’ Comput. Mech. Adv. 2: 213–281

    MathSciNet  MATH  Google Scholar 

  • Yau JF, Wang SS, Corten HT 1980 ‘A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity,’ J. Appl. Mech. 47: 335–341

    Article  MATH  Google Scholar 

  • Zadeh L 1965 ‘Fuzzy sets,’ Inf. Control 8(3): 338–353

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to B N RAO.

Rights and permissions

Reprints and permissions

About this article

Cite this article

BALU, A.S., RAO, B.N. Efficient explicit formulation for practical fuzzy structural analysis. Sadhana 36, 463–488 (2011). https://doi.org/10.1007/s12046-011-0035-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12046-011-0035-3

Keywords

Navigation